Tifa's CP Library

:heavy_check_mark: src/test_cpverifier/library-checker/vertex_set_path_composite.d63.test.cpp

Depends on

Code

#define AUTO_GENERATED
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite/"

#include "../../code/ds/hld.hpp"
#include "../../code/tree/lca_hld.hpp"

constexpr u32 MOD = 998244353;

#include "../../code/math/mint_d63.hpp"

using mint = tifa_libs::math::mint_d63<-1>;
using Ty = mint;
using T = std::pair<Ty, Ty>;
using F = T;

auto op(T a, T b) {  // b(a(x))
  swap(a, b);
  return T{a.first * b.first, a.first * b.second + a.second};
}
auto op1(T a, T b) {  // a(b(x))
  return T{a.first * b.first, a.first * b.second + a.second};
}
auto e() { return T{1, 0}; }
auto id() { return e(); }
auto mapping(F f, T a) { return op(f, a); }
auto composition(F, F) { return F(1, 0); }

int main() {
  mint::set_mod(MOD);
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u32 n, q;
  std::cin >> n >> q;
  vec<T> a(n);
  for (auto &x : a) std::cin >> x.first >> x.second;
  tifa_libs::graph::tree tr(n);
  for (u32 i = 1, u, v; i < n; ++i) std::cin >> u >> v, tr.add_arc(u, v), tr.add_arc(v, u);
  tifa_libs::graph::lca_hld lca(tr);
  tifa_libs::ds::hld<T, op, e, F, mapping, composition, id> hld(tr, a);
  tifa_libs::ds::hld<T, op1, e, F, mapping, composition, id> hld1(tr, a);
  for (u32 i = 0, opt; i < q; ++i) {
    std::cin >> opt;
    if (opt == 0) {
      u32 x;
      Ty y, z;
      std::cin >> x >> y >> z;
      hld.node_set(x, T(y, z)), hld1.node_set(x, T(y, z));
    } else {
      u32 x, y;
      Ty z;
      std::cin >> x >> y >> z;
      auto [retu, retv] = lca.getchain(x, y);
      T ret1 = e(), ret2 = e();
      for (auto x : retu) ret1 = op(ret1, hld1.chain_query(x.first, x.second));
      for (auto x : retv) ret2 = op(ret2, hld.chain_query(x.first, x.second));
      ret1 = op(ret1, ret2);
      std::cout << ret1.first * z + ret1.second << '\n';
    }
  }
  return 0;
}
#line 1 "src/test_cpverifier/library-checker/vertex_set_path_composite.d63.test.cpp"
#define AUTO_GENERATED
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite/"

#line 1 "src/code/ds/hld.hpp"



#line 1 "src/code/tree/tree.hpp"



#line 1 "src/code/graph/alist.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/stdc++.h>

template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;

using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;

using f32 = float;
using f64 = double;
using f128 = long double;

template <class T>
using ptt = std::pair<T, T>;
template <class T>
using pt3 = std::tuple<T, T, T>;
template <class T>
using pt4 = std::tuple<T, T, T, T>;

template <class T, usz N>
using arr = std::array<T, N>;
template <class T>
using vec = std::vector<T>;
template <class T>
using vvec = vec<vec<T>>;
template <class T>
using v3ec = vec<vvec<T>>;
template <class U, class T>
using vecp = vec<std::pair<U, T>>;
template <class U, class T>
using vvecp = vvec<std::pair<U, T>>;
template <class T>
using vecpt = vec<ptt<T>>;
template <class T>
using vvecpt = vvec<ptt<T>>;

template <class T, class C = std::less<T>>
using pq = std::priority_queue<T, vec<T>, C>;
template <class T>
using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;

using strn = std::string;
using strnv = std::string_view;

using vecu = vec<u32>;
using vvecu = vvec<u32>;
using v3ecu = v3ec<u32>;
using vecu64 = vec<u64>;
using vecb = vec<bool>;
using vvecb = vvec<bool>;

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using namespace std::literals;

constexpr i8 operator""_i8(unsigned long long x) { return (i8)x; }
constexpr i16 operator""_i16(unsigned long long x) { return (i16)x; }
constexpr i32 operator""_i32(unsigned long long x) { return (i32)x; }
constexpr i64 operator""_i64(unsigned long long x) { return (i64)x; }
constexpr isz operator""_iz(unsigned long long x) { return (isz)x; }

constexpr u8 operator""_u8(unsigned long long x) { return (u8)x; }
constexpr u16 operator""_u16(unsigned long long x) { return (u16)x; }
constexpr u32 operator""_u32(unsigned long long x) { return (u32)x; }
constexpr u64 operator""_u64(unsigned long long x) { return (u64)x; }
constexpr usz operator""_uz(unsigned long long x) { return (usz)x; }

inline const auto fn_0 = [](auto&&...) {};
inline const auto fn_is0 = [](auto x) { return x == 0; };


#line 5 "src/code/graph/alist.hpp"

namespace tifa_libs::graph {

template <bool with_deg = false>
struct alist {
  using weight_type = u32;
  using value_type = vvecu;
  value_type g;
  u32 cnt_arc;
  vecu deg_in;

  //! vertex ID: [0, n)
  explicit constexpr alist(u32 n = 0) : g(n), cnt_arc(0), deg_in(0) {
    if constexpr (with_deg) deg_in.resize(n);
  }

  constexpr void add_arc(u32 u, u32 v) {
    g[u].push_back(v), ++cnt_arc;
    if constexpr (with_deg) ++deg_in[v];
  }
};
template <class G>
concept is_alist = (std::is_base_of_v<alist<true>, G> || std::is_base_of_v<alist<false>, G>);

}  // namespace tifa_libs::graph


#line 5 "src/code/tree/tree.hpp"

namespace tifa_libs::graph {

struct tree : alist<false> {
  u32 root;

  explicit constexpr tree(u32 n, u32 root = 0) : alist(n), root(root) {}
};

}  // namespace tifa_libs::graph


#line 1 "src/code/tree/tree_top.hpp"



#line 1 "src/code/tree/dfs_info.hpp"



#line 1 "src/code/graph/dfs.hpp"



#line 5 "src/code/graph/dfs.hpp"

namespace tifa_libs::graph {
namespace dfs_impl_ {
template <class G, class Fb, class Fp, class Fs, class Fr>
constexpr void dfs_(G const& fg, u32 u, u32 fa, Fb&& init, Fp&& pre_dfs, Fs&& post_dfs, Fr&& before_return) {
  init(u, fa);
  for (auto v : fg.g[u])
    if constexpr (is_alist<G>) {
      if (v != fa) {
        pre_dfs(v, u);
        dfs_(fg, v, u, std::forward<Fb>(init), std::forward<Fp>(pre_dfs), std::forward<Fs>(post_dfs), std::forward<Fr>(before_return));
        post_dfs(v, u);
      }
    } else {
      if (v.first != fa) {
        pre_dfs(v.first, u, v.second);
        dfs_(fg, v.first, u, std::forward<Fb>(init), std::forward<Fp>(pre_dfs), std::forward<Fs>(post_dfs), std::forward<Fr>(before_return));
        post_dfs(v.first, u, v.second);
      }
    }
  before_return(u, fa);
}
}  // namespace dfs_impl_

template <class G, class Fb, class Fp, class Fs, class Fr>
constexpr void dfs(G const& fg, u32 start, Fb&& init, Fp&& pre_dfs, Fs&& post_dfs, Fr&& before_return) { dfs_impl_::dfs_(fg, start, -1_u32, std::forward<Fb>(init), std::forward<Fp>(pre_dfs), std::forward<Fs>(post_dfs), std::forward<Fr>(before_return)); }

}  // namespace tifa_libs::graph


#line 5 "src/code/tree/dfs_info.hpp"

namespace tifa_libs::graph {

enum tree_dfs_info_mask {
  td_dfn = 1,
  td_sz = 2,
  td_fa = 4,
  td_dep = 8,
  td_maxson = 16,
  td_maxdfn = 32,
  td_euler = 64,
  td_go = 128,
  td_dis = 256
};

template <class G>
struct tree_dfs_info {
  using weight_type = typename G::weight_type;

  vecu dfn, sz, fa, dep, maxson, maxdfn, euler;
  vvecu go;
  vec<weight_type> dis;

  template <int state>
  constexpr tree_dfs_info& reset_dfs_info(G const& tree) {
    u32 n = (u32)tree.g.size();
    if constexpr (state & td_dfn) dfn = vecu(n);
    if constexpr (state & (td_sz | td_maxson)) sz = vecu(n);
    if constexpr (state & td_fa) fa = vecu(n);
    if constexpr (state & td_dep) dep = vecu(n);
    if constexpr (state & td_maxson) maxson = vecu(n, n);
    if constexpr (state & td_maxdfn) maxdfn = vecu(n);
    if constexpr (state & td_euler) euler = vecu(n);
    if constexpr (state & td_go) go = vvecu(n, vecu(21u, n));
    if constexpr (state & td_dis) dis = vec<weight_type>(n);

    u32 cnt = 0;
    dfs(
        tree, tree.root,
        [&](u32 u, u32 f) {
          if constexpr (state & td_dfn) dfn[u] = cnt;
          if constexpr (state & td_euler) euler[cnt] = u;
          if constexpr (state & (td_dfn | td_maxdfn | td_euler)) ++cnt;
          if constexpr (state & (td_sz | td_maxson)) sz[u] = 1;
          if constexpr (state & td_fa) fa[u] = f;
          if constexpr (state & td_go) {
            go[u][0] = f;
            for (u32 i = 1; i <= 20u && go[u][i - 1] < n; i++) go[u][i] = go[go[u][i - 1]][i - 1];
          }
        },
        [&](u32 to, u32 u, weight_type const& w = 1) {
          if constexpr (state & td_dep) dep[to] = dep[u] + 1;
          if constexpr (state & td_dis) dis[to] = dis[u] + w;
        },
        [&](u32 to, u32 u, weight_type const& = 1) {
          if constexpr (state & (td_sz | td_maxson)) sz[u] += sz[to];
          if constexpr (state & td_maxson)
            if (maxson[u] == n || sz[to] > sz[maxson[u]]) maxson[u] = to;
        },
        [&](u32 u, u32) {
          if constexpr (state & td_maxdfn) maxdfn[u] = cnt - 1;
        });
    return *this;
  }
};

}  // namespace tifa_libs::graph


#line 5 "src/code/tree/tree_top.hpp"

namespace tifa_libs::graph {

template <class G, bool need_dfn = false>
constexpr vecu tree_top(G const &tr, tree_dfs_info<G> &info) {
  u32 n = (u32)tr.g.size();
  if (info.maxson.empty()) info.template reset_dfs_info<td_maxson>(tr);
  if constexpr (need_dfn) info.dfn = vecu(n);

  vecu top(n, n);
  u32 cnt = 0;
  auto dfs = [&](auto &&dfs, u32 u, u32 top_) -> void {
    if constexpr (need_dfn) info.dfn[u] = cnt++;
    top[u] = top_;
    if (info.maxson[u] == tr.g.size()) return;
    dfs(dfs, info.maxson[u], top_);
    for (auto v : tr.g[u])
      if constexpr (is_alist<G>) {
        if (top[v] == tr.g.size()) dfs(dfs, v, v);
      } else {
        if (top[v.first] == tr.g.size()) dfs(dfs, v.first, v.first);
      }
  };

  dfs(dfs, tr.root, tr.root);
  return top;
}

}  // namespace tifa_libs::graph


#line 1 "src/code/ds/segtree.hpp"



#line 5 "src/code/ds/segtree.hpp"

namespace tifa_libs::ds {
namespace segtree_impl_ {
template <bool use_tag, class T, auto op, auto e, class F, auto mapping, auto composition, auto id>
requires requires(T val, T val_l, T val_r, F tag) {
  { e() } -> std::same_as<T>;
  { op(val_l, val_r) } -> std::same_as<T>;
  { id() } -> std::same_as<F>;
  { mapping(tag, val) } -> std::same_as<T>;
}
class segtree {
  vec<T> t;
  vec<F> sign;
  vecb set_sign;
  u32 n;

 public:
  explicit constexpr segtree(vec<T> const &a) : t(a.size() * 4), sign(), set_sign(), n((u32)a.size()) {
    if constexpr (use_tag) sign.resize(t.size()), set_sign.resize(t.size());
    build(a, 1, 0, n - 1);
  }
  explicit constexpr segtree(u32 N = 0) : t(N * 4), sign(), set_sign(), n(N) {
    if constexpr (use_tag) sign.resize(t.size()), set_sign.resize(t.size());
    if (n) build(vec<T>(n, e()), 1, 0, n - 1);
  }

  constexpr void update(u32 L, u32 R, F f) { update(1, 0, n - 1, L, R, f); }
  constexpr void update(u32 pos, F f) { update(1, 0, n - 1, pos, pos, f); }
  constexpr void set(u32 L, u32 R, T f) { set(1, 0, n - 1, L, R, f); }
  constexpr void set(u32 pos, T f) { set(1, 0, n - 1, pos, pos, f); }
  constexpr T query(u32 L, u32 R) { return query(1, 0, n - 1, L, R); }
  constexpr T query(u32 pos) { return query(1, 0, n - 1, pos, pos); }

 private:
  constexpr void pushup(u32 x) { t[x] = op(t[x * 2], t[x * 2 + 1]); }
  constexpr void all_update(u32 x, F f) {
    t[x] = mapping(f, t[x]);
    if constexpr (use_tag) sign[x] = composition(f, sign[x]);
  }
  constexpr void all_set(u32 x, T f) {
    t[x] = f;
    if constexpr (use_tag) sign[x] = id(), set_sign[x] = 1;
  }
  constexpr void pushdown(u32 x) {
    if constexpr (use_tag) {
      if (set_sign[x]) all_set(x * 2, t[x]), all_set(x * 2 + 1, t[x]), set_sign[x] = 0;
      else all_update(x * 2, sign[x]), all_update(x * 2 + 1, sign[x]), sign[x] = id();
    }
  }
  constexpr void build(vec<T> const &a, u32 x, u32 l, u32 r) {
    if constexpr (use_tag) sign[x] = id();
    if (l == r) return void(t[x] = a[l]);
    u32 mid = l + (r - l) / 2;
    build(a, x * 2, l, mid), build(a, x * 2 + 1, mid + 1, r);
    pushup(x);
  }
  constexpr void update(u32 x, u32 l, u32 r, u32 L, u32 R, F f) {
    assert(R >= l && L <= r);
    if (L <= l && R >= r) return void(all_update(x, f));
    pushdown(x);
    u32 mid = l + (r - l) / 2;
    if (L <= mid) update(x * 2, l, mid, L, R, f);
    if (R > mid) update(x * 2 + 1, mid + 1, r, L, R, f);
    pushup(x);
  }
  constexpr void set(u32 x, u32 l, u32 r, u32 L, u32 R, T f) {
    assert(R >= l && L <= r);
    if (L <= l && R >= r) return void(all_set(x, f));
    pushdown(x);
    u32 mid = l + (r - l) / 2;
    if (L <= mid) set(x * 2, l, mid, L, R, f);
    if (R > mid) set(x * 2 + 1, mid + 1, r, L, R, f);
    pushup(x);
  }
  constexpr T query(u32 x, u32 l, u32 r, u32 L, u32 R) {
    assert(R >= l && L <= r);
    if (L <= l && R >= r) return t[x];
    pushdown(x);
    u32 mid = l + (r - l) / 2;
    T ret = e();
    if (L <= mid) ret = op(ret, query(x * 2, l, mid, L, R));
    if (R > mid) ret = op(ret, query(x * 2 + 1, mid + 1, r, L, R));
    return ret;
  }
};
}  // namespace segtree_impl_

template <class T, auto op, auto e, class F, auto mapping, auto composition, auto id>
requires requires(F tag_l, F tag_r) {
  { composition(tag_l, tag_r) } -> std::same_as<F>;
}
using segtree = segtree_impl_::segtree<true, T, op, e, F, mapping, composition, id>;
template <class T, auto op, auto e>
using segtree_notag = segtree_impl_::segtree<false, T, op, e, T, op, op, e>;

}  // namespace tifa_libs::ds


#line 7 "src/code/ds/hld.hpp"

namespace tifa_libs::ds {

template <class T, auto op, auto e, class F = T, auto mapping = op, auto composition = e, auto id = e>
requires requires(T val, T val_l, T val_r, F tag, F tag_l, F tag_r) {
  { e() } -> std::same_as<T>;
  { id() } -> std::same_as<F>;
  { op(val_l, val_r) } -> std::same_as<T>;
  { mapping(tag, val) } -> std::same_as<T>;
  { composition(tag_l, tag_r) } -> std::same_as<F>;
}
class hld {
  segtree<T, op, e, F, mapping, composition, id> t;

 public:
  graph::tree& tr;
  graph::tree_dfs_info<graph::tree> info;
  vecu top;

  explicit constexpr hld(graph::tree& tr) : t(), tr(tr), info() {
    info.template reset_dfs_info<graph::td_dep | graph::td_fa>(tr);
    top = graph::tree_top<graph::tree, true>(tr, info);
  }
  explicit constexpr hld(graph::tree& tr, vec<T> const& a) : hld(tr) {
    vec<T> b(a.size());
    for (u32 i = 0; i < a.size(); ++i) b[info.dfn[i]] = a[i];
    build(b);
  }

  constexpr void build(vec<T> const& a) { t = segtree<T, op, e, F, mapping, composition, id>(a); }
  constexpr void chain_update(u32 u, u32 v, F f) {
    while (top[u] != top[v]) {
      if (info.dep[top[u]] < info.dep[top[v]]) std::swap(u, v);
      t.update(info.dfn[top[u]], info.dfn[u], f), u = info.fa[top[u]];
    }
    if (info.dfn[u] < info.dfn[v]) std::swap(u, v);
    t.update(info.dfn[v], info.dfn[u], f);
  }
  constexpr void subtree_update(u32 u, F f) { t.update(info.dfn[u], info.dfn[u] + info.sz[u] - 1, f); }
  constexpr void node_update(u32 u, F f) { t.update(info.dfn[u], f); }
  constexpr void chain_set(u32 u, u32 v, T f) {
    while (top[u] != top[v]) {
      if (info.dep[top[u]] < info.dep[top[v]]) std::swap(u, v);
      t.set(info.dfn[top[u]], info.dfn[u], f), u = info.fa[top[u]];
    }
    if (info.dfn[u] < info.dfn[v]) std::swap(u, v);
    t.set(info.dfn[v], info.dfn[u], f);
  }
  constexpr void subtree_set(u32 u, T f) { t.set(info.dfn[u], info.dfn[u] + info.sz[u] - 1, f); }
  constexpr void node_set(u32 u, T f) { t.set(info.dfn[u], f); }
  constexpr T chain_query(u32 u, u32 v) {
    T ret = e();
    while (top[u] != top[v]) {
      if (info.dep[top[u]] < info.dep[top[v]]) std::swap(u, v);
      ret = op(ret, t.query(info.dfn[top[u]], info.dfn[u])), u = info.fa[top[u]];
    }
    if (info.dfn[u] < info.dfn[v]) std::swap(u, v);
    return op(ret, t.query(info.dfn[v], info.dfn[u]));
  }
  constexpr T subtree_query(u32 u) { return t.query(info.dfn[u], info.dfn[u] + info.sz[u] - 1); }
  constexpr T node_query(u32 u) { return t.query(info.dfn[u]); }
};

}  // namespace tifa_libs::ds


#line 1 "src/code/tree/lca_hld.hpp"



#line 7 "src/code/tree/lca_hld.hpp"

namespace tifa_libs::graph {

struct lca_hld {
  tree_dfs_info<tree> info;
  vecu top;

  constexpr lca_hld(tree& tr) {
    info.template reset_dfs_info<td_dep | td_fa>(tr);
    top = tree_top(tr, info);
  }

  constexpr u32 operator()(u32 u, u32 v) const {
    while (top[u] != top[v]) info.dep[top[u]] < info.dep[top[v]] ? v = info.fa[top[v]] : u = info.fa[top[u]];
    return info.dep[u] > info.dep[v] ? v : u;
  }
  constexpr ptt<vecpt<u32>> getchain(u32 u, u32 v) {
    u32 lca = (*this)(u, v);
    vecpt<u32> retu, retv;
    while (top[u] != top[lca]) {
      retu.emplace_back(u, top[u]), u = info.fa[top[u]];
    }
    retu.emplace_back(u, lca);
    while (top[v] != top[lca]) {
      retv.emplace_back(top[v], v), v = info.fa[top[v]];
    }
    if (v != lca) retv.emplace_back(info.maxson[lca], v);
    std::ranges::reverse(retv);
    return {retu, retv};
  }
};

}  // namespace tifa_libs::graph


#line 6 "src/test_cpverifier/library-checker/vertex_set_path_composite.d63.test.cpp"

constexpr u32 MOD = 998244353;

#line 1 "src/code/math/mint_d63.hpp"



#line 1 "src/code/math/mint.hpp"



#line 1 "src/code/nt/inverse.hpp"



#line 1 "src/code/nt/inv_gcd.hpp"



#line 1 "src/code/math/safe_mod.hpp"



#line 1 "src/code/util/traits.hpp"



#line 5 "src/code/util/traits.hpp"

namespace tifa_libs {

template <class T>
concept iterable_c = requires(T v) {
  { v.begin() } -> std::same_as<typename T::iterator>;
  { v.end() } -> std::same_as<typename T::iterator>;
};

template <class T>
concept container_c = iterable_c<T> && !std::derived_from<T, std::basic_string<typename T::value_type>>;

template <class T>
constexpr bool is_char_v = std::is_same_v<T, char> || std::is_same_v<T, signed char> || std::is_same_v<T, unsigned char>;
template <class T>
concept char_c = is_char_v<T>;

template <class T>
constexpr bool is_s128_v = std::is_same_v<T, __int128_t> || std::is_same_v<T, __int128>;
template <class T>
concept s128_c = is_s128_v<T>;

template <class T>
constexpr bool is_u128_v = std::is_same_v<T, __uint128_t> || std::is_same_v<T, unsigned __int128>;
template <class T>
concept u128_c = is_u128_v<T>;

template <class T>
constexpr bool is_i128_v = is_s128_v<T> || is_u128_v<T>;
template <class T>
concept i128_c = is_u128_v<T>;

template <class T>
constexpr bool is_int_v = std::is_integral_v<T> || is_i128_v<T>;
template <class T>
concept int_c = is_int_v<T>;

template <class T>
constexpr bool is_sint_v = is_s128_v<T> || (is_int_v<T> && std::is_signed_v<T>);
template <class T>
concept sint_c = is_sint_v<T>;

template <class T>
constexpr bool is_uint_v = is_u128_v<T> || (is_int_v<T> && std::is_unsigned_v<T>);
template <class T>
concept uint_c = is_uint_v<T>;

template <class T>
concept mint_c = requires(T x) {
  { x.mod() } -> uint_c;
  { x.val() } -> uint_c;
};

template <class T>
constexpr bool is_arithm_v = std::is_arithmetic_v<T> || is_int_v<T>;
template <class T>
concept arithm_c = is_arithm_v<T>;

template <class T>
struct to_sint : std::make_signed<T> {};
template <>
struct to_sint<u128> {
  using type = u128;
};
template <>
struct to_sint<i128> {
  using type = u128;
};
template <class T>
using to_sint_t = typename to_sint<T>::type;

template <class T>
struct to_uint : std::make_unsigned<T> {};
template <>
struct to_uint<u128> {
  using type = u128;
};
template <>
struct to_uint<i128> {
  using type = u128;
};
template <class T>
using to_uint_t = typename to_uint<T>::type;

}  // namespace tifa_libs


#line 5 "src/code/math/safe_mod.hpp"

namespace tifa_libs::math {

template <sint_c T>
constexpr T safe_mod(T x, to_uint_t<T> mod) { return ((x %= (T)mod) < 0 ? x + (T)mod : x); }

}  // namespace tifa_libs::math


#line 1 "src/code/nt/exgcd.hpp"



#line 5 "src/code/nt/exgcd.hpp"

namespace tifa_libs::math {

// Binary exgcd
template <uint_c U, bool only_x = false>
constexpr auto exgcd_b(U a, U b) {
  using T = to_sint_t<U>;
  if constexpr (only_x) {
    if (!a) return std::make_tuple(b, (T)0);
    if (!b) return std::make_tuple(a, (T)1);
  } else {
    if (!a) return std::make_tuple(b, (T)0, (T) !!b);
    if (!b) return std::make_tuple(a, (T)1, (T)0);
  }
  auto r = std::__countr_zero(a | b);
  a >>= r, b >>= r;
  T x = (T)a, y = (T)b;
  T s = 1, t = 0, u = 0, v = 1;
  while (x) {
    while (!(x & 1)) {
      x /= 2;
      if (!((s | t) & 1)) s /= 2, t /= 2;
      else s = (s + (T)b) / 2, t = (t - (T)a) / 2;
    }
    while (!(y & 1)) {
      y /= 2;
      if (!((u | v) & 1)) u /= 2, v /= 2;
      else u = (u + (T)b) / 2, v = (v - (T)a) / 2;
    }
    if (x >= y) x -= y, s -= u, t -= v;
    else y -= x, u -= s, v -= t;
  }
  if (y > 1) a /= (U)y, b /= (U)y;
  if (a && (U)abs(v) >= a) {
    T _ = v / (T)a;
    v -= _ * (T)a, u += _ * (T)b;
  }
  if (b && (U)abs(u) >= b) {
    T _ = u / (T)b;
    u -= _ * (T)b, v += _ * (T)a;
  }
  if (T u_ = u + (T)b, v_ = v - (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
  if (T u_ = u - (T)b, v_ = v + (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
  if constexpr (only_x) return std::make_tuple(U(y << r), u);
  else return std::make_tuple(U(y << r), u, v);
}
// @return then return tuple(g, x[, y]) s.t. g = gcd(a, b), xa + yb = g, |x| + |y| is the minimal (primary) and x <= y (secondarily)
template <sint_c T, bool only_x = false>
constexpr auto exgcd(T a, T b) {
  using U = to_uint_t<T>;
  if (auto [x, y] = std::minmax(a, b); x >= 0 && y <= T(U(-1) >> sizeof(U))) return exgcd_b<U, only_x>((U)a, (U)b);
  if constexpr (only_x) {
    T s = 1, u = 0;
    while (b) {
      T c = a / b;
      std::tie(s, u, a, b) = std::make_tuple(u, s - u * c, b, a - b * c);
    }
    return std::make_tuple((U)a, s);
  } else {
    T s = 1, t = 0, u = 0, v = 1;
    while (b) {
      T c = a / b;
      std::tie(s, t, u, v, a, b) = std::make_tuple(u, v, s - u * c, t - v * c, b, a - b * c);
    }
    return std::make_tuple((U)a, s, t);
  }
}

}  // namespace tifa_libs::math


#line 6 "src/code/nt/inv_gcd.hpp"

namespace tifa_libs::math {

template <uint_c T>
constexpr ptt<T> inv_gcd(T n, T mod) {
  using U = to_sint_t<T>;
  auto [g, x] = exgcd<U, true>(U(n % mod), (U)mod);
  return {g, safe_mod(x, mod)};
}

}  // namespace tifa_libs::math


#line 5 "src/code/nt/inverse.hpp"

namespace tifa_libs::math {

template <uint_c T, uint_c U>
constexpr U inverse(T n, U mod) {
  auto [g, x] = inv_gcd(U(n % mod), mod);
  assert(g == 1);
  return x;
}

}  // namespace tifa_libs::math


#line 6 "src/code/math/mint.hpp"

namespace tifa_libs::math {

template <class D, uint_c Rt>
class mint {
  constexpr D const &d() const { return static_cast<D const &>(*this); }
  constexpr D &d() { return static_cast<D &>(*this); }

 protected:
  Rt v_{};

 public:
  constexpr mint() {}
  template <int_c T>
  constexpr mint(T v) : v_(D::mod_(v)) {}
  constexpr operator D() { return d(); }

  using raw_type = Rt;
  using sraw_type = to_sint_t<Rt>;
  static constexpr raw_type mod() { return D::mod_(); }
  static constexpr sraw_type smod() { return (sraw_type)D::mod_(); }
  constexpr raw_type val() const { return d().val_(); }
  constexpr sraw_type sval() const { return (sraw_type)d().val_(); }
  constexpr raw_type &data() { return d().data_(); }

  template <int_c T>
  explicit constexpr operator T() const { return (T)val(); }
  constexpr mint &operator+=(mint const &r) { return d().adde_(r.d()); }
  constexpr mint &operator-=(mint const &r) { return d().sube_(r.d()); }
  constexpr mint &operator*=(mint const &r) { return d().mule_(r.d()); }
  constexpr mint &operator/=(mint const &r) { return *this = *this * r.inv(); }
  constexpr mint const &operator+() const { return *this; }
  constexpr mint operator-() const { return d().neg_(); }
  constexpr mint inv() const { return inverse(val(), mod()); }
  friend constexpr mint operator+(mint l, mint const &r) { return l += r; }
  friend constexpr mint operator-(mint l, mint const &r) { return l -= r; }
  friend constexpr mint operator*(mint l, mint const &r) { return l *= r; }
  friend constexpr mint operator/(mint l, mint const &r) { return l /= r; }
  friend constexpr bool operator==(mint const &l, mint const &r) { return l.val() == r.val(); }
  friend constexpr auto operator<=>(mint const &l, mint const &r) { return l.sval() - r.sval(); }
  friend std::istream &operator>>(std::istream &is, mint &x) {
    i64 _;
    is >> _;
    x = mint(_);
    return is;
  }
  friend std::ostream &operator<<(std::ostream &os, mint const &x) { return os << x.val(); }
  friend constexpr mint abs(mint const &x) { return x.val(); }
};

}  // namespace tifa_libs::math


#line 5 "src/code/math/mint_d63.hpp"

namespace tifa_libs::math {

template <int ID>
class mint_d63 : public mint<mint_d63<ID>, u64> {
  using base = mint<mint_d63<ID>, u64>;
  friend base;

  static inline u64 MOD, R, R2;

  static constexpr u64 mul_h(u64 x, u64 y) {
    u64 a = x >> 32, b = (u32)x, c = y >> 32, d = (u32)y, ad = a * d, bc = b * c;
    return a * c + (ad >> 32) + (bc >> 32) + (((ad & 0xFFFFFFFF) + (bc & 0xFFFFFFFF) + (b * d >> 32)) >> 32);
  }
  static constexpr u64 redc_mul(u64 x, u64 y) {
    u64 res = mul_h(x, y) - mul_h(x * y * R, MOD);
    return res + (MOD & -(res >> 63));
  }
  static constexpr u64 norm(i64 x) { return u64(x + i64(MOD & u64(-(x < 0)))); }

 public:
  static constexpr bool FIXED_MOD = false;
  static constexpr void set_mod(u64 m) {
    assert(!((m & 1) == 0 || m == 1 || m >> 63));
    MOD = m;
    u64 t = 2, iv = MOD * (t - MOD * MOD);
    iv *= t - MOD * iv, iv *= t - MOD * iv, iv *= t - MOD * iv;
    R = iv * (t - MOD * iv);
    R2 = -MOD % MOD;
    for (u32 i = 0; i != 64; ++i)
      if ((R2 *= 2) >= MOD) R2 -= MOD;
  }

  constexpr mint_d63() {}
  template <int_c T>
  constexpr mint_d63(T v) { this->v_ = mod_(v); }

 private:
  using raw_t = typename base::raw_type;
  using sraw_t = typename base::sraw_type;
  template <int_c T>
  static constexpr raw_t mod_(T v) { return redc_mul(norm(i64(v % (std::conditional_t<sint_c<T>, i64, u64>)mod_())), R2); }
  static constexpr raw_t mod_() { return MOD; }
  constexpr raw_t val_() const {
    raw_t res = -mul_h(this->v_ * R, MOD);
    return res + (MOD & -(res >> 63));
  }
  constexpr raw_t &data_() { return this->v_; }

  constexpr mint_d63 neg_() const {
    mint_d63 res;
    res.v_ = (MOD & -(this->v_ != 0)) - this->v_;
    return res;
  }
  constexpr mint_d63 &adde_(mint_d63 const &r) {
    this->v_ += r.v_ - MOD, this->v_ += MOD & -(this->v_ >> 63);
    return *this;
  }
  constexpr mint_d63 &sube_(mint_d63 const &r) {
    this->v_ -= r.v_, this->v_ += MOD & -(this->v_ >> 63);
    return *this;
  }
  constexpr mint_d63 &mule_(mint_d63 const &r) {
    this->v_ = redc_mul(this->v_, r.v_);
    return *this;
  }
};

}  // namespace tifa_libs::math


#line 10 "src/test_cpverifier/library-checker/vertex_set_path_composite.d63.test.cpp"

using mint = tifa_libs::math::mint_d63<-1>;
using Ty = mint;
using T = std::pair<Ty, Ty>;
using F = T;

auto op(T a, T b) {  // b(a(x))
  swap(a, b);
  return T{a.first * b.first, a.first * b.second + a.second};
}
auto op1(T a, T b) {  // a(b(x))
  return T{a.first * b.first, a.first * b.second + a.second};
}
auto e() { return T{1, 0}; }
auto id() { return e(); }
auto mapping(F f, T a) { return op(f, a); }
auto composition(F, F) { return F(1, 0); }

int main() {
  mint::set_mod(MOD);
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u32 n, q;
  std::cin >> n >> q;
  vec<T> a(n);
  for (auto &x : a) std::cin >> x.first >> x.second;
  tifa_libs::graph::tree tr(n);
  for (u32 i = 1, u, v; i < n; ++i) std::cin >> u >> v, tr.add_arc(u, v), tr.add_arc(v, u);
  tifa_libs::graph::lca_hld lca(tr);
  tifa_libs::ds::hld<T, op, e, F, mapping, composition, id> hld(tr, a);
  tifa_libs::ds::hld<T, op1, e, F, mapping, composition, id> hld1(tr, a);
  for (u32 i = 0, opt; i < q; ++i) {
    std::cin >> opt;
    if (opt == 0) {
      u32 x;
      Ty y, z;
      std::cin >> x >> y >> z;
      hld.node_set(x, T(y, z)), hld1.node_set(x, T(y, z));
    } else {
      u32 x, y;
      Ty z;
      std::cin >> x >> y >> z;
      auto [retu, retv] = lca.getchain(x, y);
      T ret1 = e(), ret2 = e();
      for (auto x : retu) ret1 = op(ret1, hld1.chain_query(x.first, x.second));
      for (auto x : retv) ret2 = op(ret2, hld.chain_query(x.first, x.second));
      ret1 = op(ret1, ret2);
      std::cout << ret1.first * z + ret1.second << '\n';
    }
  }
  return 0;
}

Test cases

Env Name Status Elapsed Memory
g++-12 almost_line_00 :heavy_check_mark: AC 1106 ms 86 MB
g++-12 almost_line_01 :heavy_check_mark: AC 1083 ms 87 MB
g++-12 example_00 :heavy_check_mark: AC 7 ms 4 MB
g++-12 example_01 :heavy_check_mark: AC 7 ms 4 MB
g++-12 line_00 :heavy_check_mark: AC 903 ms 88 MB
g++-12 line_01 :heavy_check_mark: AC 869 ms 89 MB
g++-12 long-path-decomposition_killer_00 :heavy_check_mark: AC 997 ms 84 MB
g++-12 max_random_00 :heavy_check_mark: AC 1760 ms 84 MB
g++-12 max_random_01 :heavy_check_mark: AC 1855 ms 84 MB
g++-12 max_random_02 :heavy_check_mark: AC 1876 ms 84 MB
g++-12 random_00 :heavy_check_mark: AC 1198 ms 55 MB
g++-12 random_01 :heavy_check_mark: AC 1301 ms 64 MB
g++-12 random_02 :heavy_check_mark: AC 789 ms 25 MB
g++-12 small_00 :heavy_check_mark: AC 12 ms 4 MB
g++-12 small_01 :heavy_check_mark: AC 10 ms 4 MB
g++-12 small_02 :heavy_check_mark: AC 9 ms 4 MB
g++-12 small_03 :heavy_check_mark: AC 11 ms 4 MB
g++-12 small_04 :heavy_check_mark: AC 9 ms 4 MB
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