#include using i64 = long long; i64 ceilDiv(i64 a, i64 b) { if (a >= 0) { return (a + b - 1) / b; } else { return a / b; } } i64 floorDiv(i64 a, i64 b) { if (a >= 0) { return a / b; } else { return (a - b + 1) / b; } } i64 exgcd(i64 a, i64 b, i64 &x, i64 &y) { if (!b) { x = 1; y = 0; return a; } i64 g = exgcd(b, a % b, y, x); y -= a / b * x; return g; } void solve() { i64 M, A, B, K; std::cin >> M >> A >> B >> K; if (K > A) { std::cout << "0\n"; return; } if (K == A) { i64 ans = M / A - 1; ans -= M / B; ans += M / std::lcm(A, B); ans += M - M % B > M - M % A; std::cout << ans << "\n"; return; } i64 x, y; i64 g = exgcd(A, B, x, y); if (K % g != 0) { std::cout << 0 << "\n"; return; } A /= g, B /= g; K /= g; M /= g; x = 1LL * x * K % B; y = (K - A * x) / B; i64 L = A * B; i64 ans = 0; i64 l = std::max(ceilDiv(1 - A * x, L), ceilDiv(1 + B * y, L)); i64 r = std::min(floorDiv(M - A * x, L), floorDiv(M + B * y, L)); ans += std::max(0LL, r - l + 1); l = std::max(ceilDiv(1 + A * x, L), ceilDiv(1 - B * y, L)); r = std::min(floorDiv(M + A * x, L), floorDiv(M - B * y, L)); ans += std::max(0LL, r - l + 1); std::cout << ans << "\n"; } int main() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); int T; std::cin >> T; while (T--) { solve(); } return 0; }