// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/min_of_mod_of_linear
#include "../../../src/math/min_mod_linear/lib.hpp"
using namespace tifa_libs;
int main() {
std::cin.tie(nullptr)->std::ios::sync_with_stdio(false);
u32 t;
std::cin >> t;
while (t--) {
u32 n, m, a, b;
std::cin >> n >> m >> a >> b;
std::cout << min_mod_linear(n, m, a, b) << '\n';
}
return 0;
}
#line 1 "test/cpv/library-checker-number_theory/min_of_mod_of_linear.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/min_of_mod_of_linear
#line 2 "src/math/min_mod_linear/lib.hpp"
#line 2 "src/util/alias/num/lib.hpp"
#line 2 "src/util/util/lib.hpp"
// https://github.com/Tiphereth-A/CP-lib
#include <bits/extc++.h>
// clang-format off
namespace tifa_libs {
#define CEXP constexpr
#define CEXPE constexpr explicit
#define CR const&
#define CP const*
#define PC *const
#define CPC const*const
#define TPN typename
#define NE noexcept
#define CNE const noexcept
#define ND [[nodiscard]]
#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t) * 2, __VA_ARGS__, __VA_ARGS__ CR>
// NOLINTNEXTLINE(misc-const-correctness)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)
#define retif_(cond, if_true, ...) if cond return if_true __VA_OPT__(; else return __VA_ARGS__)
#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif
using namespace std::ranges;
using namespace std::literals;
template <class T>
CEXP T abs(T x) NE { retif_((x < 0), -x, x); }
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/num/lib.hpp"
// clang-format off
namespace tifa_libs {
#define mk0_(w, t) using w = t; using c##w = const t
#define mk_(w, t) mk0_(w, t); CEXP w operator""_##w(unsigned long long x) NE { return (w)x; }
mk_(i8, int8_t) mk_(u8, uint8_t) mk_(i16, int16_t) mk_(u16, uint16_t) mk_(i32, int32_t) mk_(u32, uint32_t) mk_(i64, int64_t) mk_(u64, uint64_t) mk_(isz, ssize_t) mk_(usz, size_t) mk_(chr, char) mk_(schr, signed char) mk_(uchr, unsigned char) mk_(sint, signed) mk_(uint, unsigned);
mk0_(i128, __int128_t); mk0_(u128, __uint128_t); mk0_(f32, float); mk0_(f64, double); mk0_(f128, long double);
#undef mk0_
#undef mk_
} // namespace tifa_libs
// clang-format on
#line 4 "src/math/min_mod_linear/lib.hpp"
namespace tifa_libs {
CEXP u32 min_mod_linear(u32 n, u32 m, u32 a, u32 b, u32 cnt = 1, u32 p = 1, u32 q = 1) NE {
if (!a) return b;
if (cnt & 1) {
if (b >= a) {
cu32 t = (m - b + a - 1) / a, c = (t - 1) * p + q;
if (n <= c) return b;
n -= c, b += a * t - m;
}
b = a - 1 - b;
} else {
if (b < m - a) {
cu32 t = (m - b - 1) / a, c = t * p;
if (n <= c) return a * ((n - 1) / p) + b;
n -= c, b += a * t;
}
b = m - 1 - b;
}
cu32 d = m / a, c = min_mod_linear(n, a, m % a, b, ++cnt, (d - 1) * p + q, d * p + q);
retif_((cnt & 1), m - 1 - c, a - 1 - c);
}
} // namespace tifa_libs
#line 3 "test/cpv/library-checker-number_theory/min_of_mod_of_linear.cpp"
using namespace tifa_libs;
int main() {
std::cin.tie(nullptr)->std::ios::sync_with_stdio(false);
u32 t;
std::cin >> t;
while (t--) {
u32 n, m, a, b;
std::cin >> n >> m >> a >> b;
std::cout << min_mod_linear(n, m, a, b) << '\n';
}
return 0;
}
test/cpv/library-checker-number_theory/min_of_mod_of_linear.cpp