// ===== template.hpp ===== #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define OVERRIDE(a, b, c, d, ...) d #define REP2(i, n) for (i32 i = 0; i < (i32) (n); ++i) #define REP3(i, m, n) for (i32 i = (i32) (m); i < (i32) (n); ++i) #define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__) #define PER(i, n) for (i32 i = (i32) (n) - 1; i >= 0; --i) #define ALL(x) begin(x), end(x) using namespace std; using u32 = unsigned int; using u64 = unsigned long long; using u128 = __uint128_t; using i32 = signed int; using i64 = signed long long; using i128 = __int128_t; template using Vec = vector; template bool chmin(T &x, const T &y) { if (x > y) { x = y; return true; } return false; } template bool chmax(T &x, const T &y) { if (x < y) { x = y; return true; } return false; } [[maybe_unused]] constexpr i32 INF = 1000000100; [[maybe_unused]] constexpr i64 INF64 = 3000000000000000100; struct FastIO { FastIO() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(10); } } fast_io; // ===== template.hpp ===== #ifdef DEBUGF #include "new_library/other/debug.hpp" #else #define DBG(x) (void) 0 #endif // ===== mod_int.hpp ===== #ifndef MOD_INT_HPP #define MOD_INT_HPP #include #include #include // ===== utils.hpp ===== #ifndef UTILS_HPP #define UTILS_HPP #include constexpr bool is_prime(unsigned n) { if (n == 0 || n == 1) return false; for (unsigned i = 2; i * i <= n; ++i) { if (n % i == 0) return false; } return true; } constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) { unsigned ret = 1, self = x; while (y != 0) { if (y & 1) ret = (unsigned long long)ret * self % mod; self = (unsigned long long)self * self % mod; y >>= 1; } return ret; } template constexpr unsigned primitive_root() { static_assert(is_prime(mod), "`mod` must be a prime number."); if (mod == 2) return 1; unsigned primes[32] = {}; std::size_t it = 0; { unsigned m = mod - 1; for (unsigned i = 2; i * i <= m; ++i) { if (m % i == 0) { primes[it++] = i; while (m % i == 0) m /= i; } } if (m != 1) primes[it++] = m; } for (unsigned i = 2; i < mod; ++i) { bool ok = true; for (std::size_t j = 0; j < it; ++j) { if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) { ok = false; break; } } if (ok) return i; } return 0; } #endif // ===== utils.hpp ===== template > * = nullptr> constexpr unsigned safe_mod(T x, unsigned mod) { if (x < 0) { return (unsigned)(x % (T)mod + mod); } else { return (unsigned)(x % (T)mod); } } template > * = nullptr> constexpr unsigned safe_mod(T x, unsigned mod) { return (unsigned)(x % mod); } template class ModInt { static_assert(mod != 0, "`mod` must not be equal to 0."); static_assert( mod < (1u << 31), "`mod` must be less than (1u << 31) = 2147483648."); unsigned val; public: constexpr ModInt() : val(0) {} template constexpr ModInt(T x) : val(safe_mod(x, mod)) {} static constexpr ModInt raw(unsigned x) { ModInt ret; ret.val = x; return ret; } constexpr unsigned get_val() const { return val; } constexpr ModInt operator+() const { return *this; } constexpr ModInt operator-() const { return ModInt(0u) - *this; } constexpr ModInt &operator+=(const ModInt &rhs) { val += rhs.val; if (val >= mod) val -= mod; return *this; } constexpr ModInt &operator-=(const ModInt &rhs) { if (val < rhs.val) val += mod; val -= rhs.val; return *this; } constexpr ModInt &operator*=(const ModInt &rhs) { val = (unsigned long long)val * rhs.val % mod; return *this; } constexpr ModInt &operator/=(const ModInt &rhs) { val = (unsigned long long)val * rhs.inv().val % mod; return *this; } friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) += rhs; } friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) -= rhs; } friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) *= rhs; } friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) /= rhs; } constexpr ModInt pow(unsigned long long x) const { ModInt ret = ModInt::raw(1); ModInt self = *this; while (x != 0) { if (x & 1) ret *= self; self *= self; x >>= 1; } return ret; } constexpr ModInt inv() const { static_assert(is_prime(mod), "`mod` must be a prime number."); assert(val != 0); return this->pow(mod - 2); } friend std::istream &operator>>(std::istream &is, ModInt &x) { is >> x.val; // x.val %= mod; return is; } friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val; return os; } friend bool operator==(const ModInt &lhs, const ModInt &rhs) { return lhs.val == rhs.val; } friend bool operator!=(const ModInt &lhs, const ModInt &rhs) { return lhs.val != rhs.val; } }; [[maybe_unused]] constexpr unsigned mod998244353 = 998244353; [[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007; #endif // ===== mod_int.hpp ===== using Mint = ModInt; // ===== linear_function.hpp ===== #ifndef LINEAR_FUNCTION_HPP #define LINEAR_FUNCTION_HPP template struct LinearFunction { T slope; T intercept; LinearFunction() : slope(), intercept() {} LinearFunction(const T &s, const T &i) : slope(s), intercept(i) {} T operator()(const T &x) const { return intercept + slope * x; } // (this)(other(x)) LinearFunction composite(const LinearFunction &other) const { return LinearFunction( slope * other.slope, slope * other.intercept + intercept); } }; #endif // ===== linear_function.hpp ===== using F = LinearFunction; i32 floor_log2(i32 n) { return 31 - __builtin_clz(n); } int main() { i32 n, q; cin >> n >> q; Vec f(n); REP(i, n) { cin >> f[i].slope >> f[i].intercept; } i32 m = floor_log2(n); i32 bl = m / 2; Vec> precalc(1 << (m - bl), Vec(1 << bl)); REP(i, 1 << (m - bl)) { i32 l = i << bl, r = (i + 1) << bl; REP(j, 1 << bl) { F g(Mint(1), Mint(0)); REP(k, l, r) { g = f[j ^ k].composite(g); } precalc[i][j] = g; } } REP(qi, q) { i32 l, r, p; Mint x; cin >> l >> r >> p >> x; if ((l >> bl) == (r >> bl)) { F g(Mint(1), Mint(0)); REP(i, l, r) { g = f[i ^ p].composite(g); } cout << g(x) << '\n'; continue; } i32 lower = p & ((1 << bl) - 1); i32 upper = p >> bl; i32 lb = (l >> bl) + 1, rb = r >> bl; F g(Mint(1), Mint(0)); REP(i, l, lb << bl) { g = f[i ^ p].composite(g); } REP(i, lb, rb) { i32 idx = i ^ upper; g = precalc[idx][lower].composite(g); } REP(i, rb << bl, r) { g = f[i ^ p].composite(g); } cout << g(x) << '\n'; } }