#include using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() using ll = long long; constexpr int INF = 0x3f3f3f3f; constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL; constexpr double EPS = 1e-8; constexpr int MOD = 998244353; // constexpr int MOD = 1000000007; constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1}; constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1}; constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1}; template inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; } template inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; } struct IOSetup { IOSetup() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << fixed << setprecision(20); } } iosetup; template struct MInt { unsigned int v; MInt() : v(0) {} MInt(const long long x) : v(x >= 0 ? x % mod() : x % mod() + mod()) {} static int get_mod() { return mod(); } static void set_mod(const int divisor) { mod() = divisor; } static void init(const int x) { inv(x); fact(x); fact_inv(x); } template static MInt inv(const int n) { // assert(0 <= n && n < mod() && std::gcd(x, mod()) == 1); static std::vector inverse{0, 1}; const int prev = inverse.size(); if (n < prev) return inverse[n]; if constexpr (MEMOIZES) { // "n!" and "M" must be disjoint. inverse.resize(n + 1); for (int i = prev; i <= n; ++i) { inverse[i] = -inverse[mod() % i] * (mod() / i); } return inverse[n]; } int u = 1, v = 0; for (unsigned int a = n, b = mod(); b;) { const unsigned int q = a / b; std::swap(a -= q * b, b); std::swap(u -= q * v, v); } return u; } static MInt fact(const int n) { static std::vector factorial{1}; const int prev = factorial.size(); if (n >= prev) { factorial.resize(n + 1); for (int i = prev; i <= n; ++i) { factorial[i] = factorial[i - 1] * i; } } return factorial[n]; } static MInt fact_inv(const int n) { static std::vector f_inv{1}; const int prev = f_inv.size(); if (n >= prev) { f_inv.resize(n + 1); f_inv[n] = inv(fact(n).v); for (int i = n; i > prev; --i) { f_inv[i - 1] = f_inv[i] * i; } } return f_inv[n]; } static MInt nCk(const int n, const int k) { if (n < 0 || n < k || k < 0) return 0; return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) : fact_inv(n - k) * fact_inv(k)); } static MInt nPk(const int n, const int k) { return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k); } static MInt nHk(const int n, const int k) { return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k)); } static MInt large_nCk(long long n, const int k) { if (n < 0 || n < k || k < 0) return 0; inv(k); MInt res = 1; for (int i = 1; i <= k; ++i) { res *= inv(i) * n--; } return res; } MInt pow(long long exponent) const { MInt res = 1, tmp = *this; for (; exponent > 0; exponent >>= 1) { if (exponent & 1) res *= tmp; tmp *= tmp; } return res; } MInt& operator+=(const MInt& x) { if (std::cmp_greater_equal(v += x.v, mod())) v -= mod(); return *this; } MInt& operator-=(const MInt& x) { if (std::cmp_greater_equal(v += mod() - x.v, mod())) v -= mod(); return *this; } MInt& operator*=(const MInt& x) { v = static_cast(v) * x.v % mod(); return *this; } MInt& operator/=(const MInt& x) { return *this *= inv(x.v); } auto operator<=>(const MInt& x) const = default; MInt& operator++() { if (std::cmp_equal(++v, mod())) v = 0; return *this; } MInt operator++(int) { const MInt res = *this; ++*this; return res; } MInt& operator--() { v = (v == 0 ? mod() - 1 : v - 1); return *this; } MInt operator--(int) { const MInt res = *this; --*this; return res; } MInt operator+() const { return *this; } MInt operator-() const { return MInt(v ? mod() - v : 0); } MInt operator+(const MInt& x) const { return MInt(*this) += x; } MInt operator-(const MInt& x) const { return MInt(*this) -= x; } MInt operator*(const MInt& x) const { return MInt(*this) *= x; } MInt operator/(const MInt& x) const { return MInt(*this) /= x; } friend std::ostream& operator<<(std::ostream& os, const MInt& x) { return os << x.v; } friend std::istream& operator>>(std::istream& is, MInt& x) { long long v; is >> v; x = MInt(v); return is; } private: static int& mod() { static int divisor = 0; return divisor; } }; template struct SegmentTree { using Monoid = typename T::Monoid; explicit SegmentTree(const int n) : SegmentTree(std::vector(n, T::id())) {} explicit SegmentTree(const std::vector& a) : n(a.size()), p2(std::bit_ceil(a.size())) { dat.assign(p2 << 1, T::id()); std::copy(a.begin(), a.end(), dat.begin() + p2); for (int i = p2 - 1; i > 0; --i) { dat[i] = T::merge(dat[i << 1], dat[(i << 1) + 1]); } } void set(int idx, const Monoid val) { idx += p2; dat[idx] = val; while (idx >>= 1) dat[idx] = T::merge(dat[idx << 1], dat[(idx << 1) + 1]); } Monoid get(int left, int right) const { Monoid res_l = T::id(), res_r = T::id(); for (left += p2, right += p2; left < right; left >>= 1, right >>= 1) { if (left & 1) res_l = T::merge(res_l, dat[left++]); if (right & 1) res_r = T::merge(dat[--right], res_r); } return T::merge(res_l, res_r); } Monoid operator[](const int idx) const { return dat[idx + p2]; } template int find_right(int left, const G g) { if (left >= n) [[unlikely]] return n; Monoid val = T::id(); left += p2; do { while (!(left & 1)) left >>= 1; Monoid nxt = T::merge(val, dat[left]); if (!g(nxt)) { while (left < p2) { left <<= 1; nxt = T::merge(val, dat[left]); if (g(nxt)) { val = nxt; ++left; } } return left - p2; } val = nxt; ++left; } while (!std::has_single_bit(static_cast(left))); return n; } template int find_left(int right, const G g) { if (right <= 0) [[unlikely]] return -1; Monoid val = T::id(); right += p2; do { --right; while (right > 1 && (right & 1)) right >>= 1; Monoid nxt = T::merge(dat[right], val); if (!g(nxt)) { while (right < p2) { right = (right << 1) + 1; nxt = T::merge(dat[right], val); if (g(nxt)) { val = nxt; --right; } } return right - p2; } val = nxt; } while (!std::has_single_bit(static_cast(right))); return -1; } private: const int n, p2; std::vector dat; }; namespace monoid { template struct RangeMinimumQuery { using Monoid = T; static constexpr Monoid id() { return std::numeric_limits::max(); } static Monoid merge(const Monoid& a, const Monoid& b) { return std::min(a, b); } }; template struct RangeMaximumQuery { using Monoid = T; static constexpr Monoid id() { return std::numeric_limits::lowest(); } static Monoid merge(const Monoid& a, const Monoid& b) { return std::max(a, b); } }; template struct RangeSumQuery { using Monoid = T; static constexpr Monoid id() { return 0; } static Monoid merge(const Monoid& a, const Monoid& b) { return a + b; } }; } // namespace monoid template struct FenwickTree { explicit FenwickTree(const int n, const Abelian ID = 0) : n(n), ID(ID), data(n, ID) {} void add(int idx, const Abelian val) { for (; idx < n; idx |= idx + 1) { data[idx] += val; } } Abelian sum(int idx) const { Abelian res = ID; for (--idx; idx >= 0; idx = (idx & (idx + 1)) - 1) { res += data[idx]; } return res; } Abelian sum(const int left, const int right) const { return left < right ? sum(right) - sum(left) : ID; } Abelian operator[](const int idx) const { return sum(idx, idx + 1); } int lower_bound(Abelian val) const { if (val <= ID) [[unlikely]] return 0; int res = 0; for (int mask = std::bit_ceil(static_cast(n + 1)) >> 1; mask > 0; mask >>= 1) { const int idx = res + mask - 1; if (idx < n && data[idx] < val) { val -= data[idx]; res += mask; } } return res; } private: const int n; const Abelian ID; std::vector data; }; template std::vector> prime_factorization(T n) { std::vector> res; for (T i = 2; i * i <= n; ++i) { if (n % i == 0) [[unlikely]] { int exponent = 0; for (; n % i == 0; n /= i) { ++exponent; } res.emplace_back(i, exponent); } } if (n > 1) res.emplace_back(n, 1); return res; } int main() { using ModInt = MInt<0>; struct M { using Monoid = ModInt; static Monoid id() { return 1; } static Monoid merge(const Monoid& a, const Monoid& b) { return a * b; } }; int n, b, q; cin >> n >> b >> q; ModInt::set_mod(b); if (b == 1) { while (q--) cout << 0 << '\n'; return 0; } const auto pf_b = prime_factorization(b); const int s = pf_b.size(); vector fac(n, vector(s, 0)); SegmentTree seg(n), other(n); FenwickTree num_b(n); const auto mul = [&](const int i, ll m) { if (m == 0) { ranges::fill(fac[i], 0); seg.set(i, 0); num_b.add(i, -num_b[i]); return; } if (m == b && num_b[i] > 0) { num_b.add(i, -1); return; } int ex = INF; ModInt tmp = 1; REP(x, s) { for (; m % pf_b[x].first == 0; m /= pf_b[x].first) { ++fac[i][x]; } chmin(ex, fac[i][x] / pf_b[x].second); tmp *= ModInt(pf_b[x].first).pow(fac[i][x] % pf_b[x].second); } seg.set(i, seg[i] * m); other.set(i, tmp); if (ex > 0) { REP(x, s) fac[i][x] -= pf_b[x].second * ex; num_b.add(i, ex); } }; REP(i, n) { ll a; cin >> a; mul(i, a); } while (q--) { int j, l, r; ll m; cin >> j >> m >> l >> r; mul(j, m); cout << (num_b.sum(l, r + 1) == 0 ? seg.get(l, r + 1) * other.get(l, r + 1) : 0) << '\n'; } return 0; }