#line 1 "main.cpp" //#pragma GCC target("avx") //#pragma GCC optimize("O3") //#pragma GCC optimize("unroll-loops") #include #ifdef LOCAL #include #define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else #define debug(...) (static_cast(0)) #endif using namespace std; using ll = long long; using ld = long double; using pll = pair; using pii = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vpii = vector; using vpll = vector; using vs = vector; template using pq = priority_queue, greater>; #define overload4(_1, _2, _3, _4, name, ...) name #define overload3(a,b,c,name,...) name #define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER) #define rep2(i, n) for (ll i = 0; i < (n); ++i) #define rep3(i, a, b) for (ll i = (a); i < (b); ++i) #define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c)) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep1(n) for(ll i = (n) - 1;i >= 0;i--) #define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--) #define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--) #define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c) #define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__) #define all1(i) begin(i) , end(i) #define all2(i,a) begin(i) , begin(i) + a #define all3(i,a,b) begin(i) + a , begin(i) + b #define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__) #define sum(...) accumulate(all(__VA_ARGS__),0LL) template bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; } template bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; } template auto min(const T& a){ return *min_element(all(a)); } template auto max(const T& a){ return *max_element(all(a)); } template void in(Ts&... t); #define INT(...) int __VA_ARGS__; in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__; in(__VA_ARGS__) #define STR(...) string __VA_ARGS__; in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__; in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__; in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__; in(__VA_ARGS__) #define VEC(type, name, size) vector name(size); in(name) #define VV(type, name, h, w) vector> name(h, vector(w)); in(name) ll intpow(ll a, ll b){ ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;} ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;if(a < 0) a += p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; } ll GCD(ll a,ll b) { if(a == 0 || b == 0) return 0; if(a % b == 0) return b; else return GCD(b,a%b);} ll LCM(ll a,ll b) { if(a == 0) return b; if(b == 0) return a;return a / GCD(a,b) * b;} namespace IO{ #define VOID(a) decltype(void(a)) struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(30);}} setting; template struct P : P{}; template<> struct P<0>{}; template void i(T& t){ i(t, P<3>{}); } void i(vector::reference t, P<3>){ int a; i(a); t = a; } template auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; } template auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); } template void ituple(T& t, index_sequence){ in(get(t)...);} template auto i(T& t, P<0>) -> VOID(tuple_size{}){ ituple(t, make_index_sequence::value>{});} #undef VOID } #define unpack(a) (void)initializer_list{(a, 0)...} template void in(Ts&... t){ unpack(IO :: i(t)); } #undef unpack static const double PI = 3.1415926535897932; template struct REC { F f; REC(F &&f_) : f(forward(f_)) {} template auto operator()(Args &&...args) const { return f(*this, forward(args)...); }}; //constexpr int mod = 1000000007; constexpr int mod = 998244353; #line 2 "library/modint/barrett-reduction.hpp" struct Barrett { using u32 = unsigned int; using i64 = long long; using u64 = unsigned long long; u32 m; u64 im; Barrett() : m(), im() {} Barrett(int n) : m(n), im(u64(-1) / m + 1) {} constexpr inline i64 quo(u64 n) { u64 x = u64((__uint128_t(n) * im) >> 64); u32 r = n - x * m; return m <= r ? x - 1 : x; } constexpr inline i64 rem(u64 n) { u64 x = u64((__uint128_t(n) * im) >> 64); u32 r = n - x * m; return m <= r ? r + m : r; } constexpr inline pair quorem(u64 n) { u64 x = u64((__uint128_t(n) * im) >> 64); u32 r = n - x * m; if (m <= r) return {x - 1, r + m}; return {x, r}; } constexpr inline i64 pow(u64 n, i64 p) { u32 a = rem(n), r = m == 1 ? 0 : 1; while (p) { if (p & 1) r = rem(u64(r) * a); a = rem(u64(a) * a); p >>= 1; } return r; } }; #line 3 "library/modint/ArbitaryModint.hpp" struct ArbitraryModint { int x; ArbitraryModint():x(0) {} ArbitraryModint(int64_t y) { int z = y % get_mod(); if(z < 0) z += get_mod(); x = z; } ArbitraryModint &operator+=(const ArbitraryModint &p) { if((x += p.x) >= get_mod()) x -= get_mod(); return *this; } ArbitraryModint &operator-=(const ArbitraryModint &p) { if((x += get_mod() - p.x) >= get_mod()) x -= get_mod(); return *this; } ArbitraryModint &operator*=(const ArbitraryModint &p) { x = rem((unsigned long long)x * p.x); return *this; } ArbitraryModint &operator/=(const ArbitraryModint &p) { *this *= p.inverse(); return *this; } ArbitraryModint operator-() const {return ArbitraryModint(-x);}; ArbitraryModint operator+(const ArbitraryModint &p) const{ return ArbitraryModint(*this) += p; } ArbitraryModint operator-(const ArbitraryModint &p) const{ return ArbitraryModint(*this) -= p; } ArbitraryModint operator*(const ArbitraryModint &p) const{ return ArbitraryModint(*this) *= p; } ArbitraryModint operator/(const ArbitraryModint &p) const { return ArbitraryModint(*this) /= p; } bool operator==(const ArbitraryModint &p) {return x == p.x;} bool operator!=(const ArbitraryModint &p) {return x != p.x;} ArbitraryModint inverse() const { int a = x,b = get_mod(),u = 1,v = 0,t; while(b > 0) { t = a / b; swap(a -= t * b,b); swap(u -= t * v,v); } return ArbitraryModint(u); } ArbitraryModint pow(int64_t n) const { ArbitraryModint ret(1),mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os,const ArbitraryModint &p) { return os << p.x; } friend istream &operator>>(istream &is,ArbitraryModint &a) { int64_t t; is >> t; a = ArbitraryModint(t); return (is); } int get() const {return x;} inline unsigned int rem(unsigned long long p) {return barrett().rem(p);}; static inline Barrett &barrett() { static Barrett b; return b; } static inline int &get_mod() { static int mod = 0; return mod; } static void set_mod(int md) { assert(0 < md && md <= (1LL << 30) - 1); get_mod() = md; barrett() = Barrett(md); } }; #line 87 "main.cpp" using mint = ArbitraryModint; using vm = vector; using vvm = vector; using vvvm = vector; #line 2 "library/math/factorize.hpp" vector> prime_factorization(long long n) { vector> ret; int c = 0; while(n % 2 == 0) { c++; n >>= 1; } if(c) ret.emplace_back(2,c); for(long long i = 3; i * i <= n; i += 2) { c = 0; while(n % i == 0) { n /= i; c++; } if(c) ret.emplace_back(i,c); } if (n != 1) ret.emplace_back(n,1); return ret; } vector divisor(long long n) { vector ret; for(long long i = 1; i * i <= n; i++) { if (n % i == 0) { ret.push_back(i); if(i * i != n) {ret.push_back(n / i);} } } sort(ret.begin(),ret.end()); return ret; } #line 2 "library/segtree/segtree.hpp" template struct segtree { int N; int size; vector seg; const F f; const T I; segtree(F _f, const T &I_) : N(0), size(0), f(_f), I(I_) {} segtree(int _N, F _f, const T &I_) : f(_f), I(I_) { init(_N); } segtree(const vector &v, F _f, T I_) : f(_f), I(I_) { init(v.size()); for (int i = 0; i < (int)v.size(); i++) { seg[i + size] = v[i]; } build(); } void init(int _N) { N = _N; size = 1; while (size < N) size <<= 1; seg.assign(2 * size, I); } void build() { for (int k = size - 1; k > 0; k--) { seg[k] = f(seg[2 * k], seg[2 * k + 1]); } } void set(int k, T x) { assert(0 <= k && k < N); k += size; seg[k] = x; while (k >>= 1) { seg[k] = f(seg[2 * k], seg[2 * k + 1]); } } void add(int k, T x) { assert(0 <= k && k < N); k += size; seg[k] += x; while (k >>= 1) { seg[k] = f(seg[2 * k], seg[2 * k + 1]); } } T get(int k) const { assert(0 <= k && k < N); return seg[k + size]; } // query to [l, r) T prod(int l, int r) { assert(0 <= l && l <= r && r <= N); T L = I, R = I; for (l += size, r += size; l < r; l >>= 1, r >>= 1) { if (l & 1) L = f(L, seg[l++]); if (r & 1) R = f(seg[--r], R); } return f(L, R); } // check(a[l] * ... * a[r-1]) が true となる最大の r // (右端まですべて true なら N を返す) template int max_right(int l, C check) { assert(0 <= l && l <= N); assert(check(I) == true); if (l == N) return N; l += size; T sm = I; do { while (l % 2 == 0) l >>= 1; if (!check(f(sm, seg[l]))) { while (l < size) { l = (2 * l); if (check(f(sm, seg[l]))) { sm = f(sm, seg[l]); l++; } } return l - size; } sm = f(sm, seg[l]); l++; } while ((l & -l) != l); return N; } // check(a[l] * ... * a[r-1]) が true となる最小の l // (左端まで true なら 0 を返す) template int min_left(int r, C check) { assert(0 <= r && r <= N); assert(check(I) == true); if (r == 0) return 0; r += size; T sm = I; do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!check(f(seg[r], sm))) { while (r < size) { r = (2 * r + 1); if (check(f(seg[r], sm))) { sm = f(seg[r], sm); r--; } } return r + 1 - size; } sm = f(seg[r], sm); } while ((r & -r) != r); return 0; } }; #line 93 "main.cpp" int main() { INT(n,b,q); mint::set_mod(b); VEC(ll,a,n); auto prs = prime_factorization(b); vvl cnt(prs.size(),vl(n)); vm rem(n); vi zero_flg(n); rep(i,n) { ll now = a[i]; if(now == 0) { zero_flg[i] = 1; continue; } rep(j,prs.size()) { int p = prs[j].first; while(now % p == 0) { cnt[j][i]++; now /= p; } } rem[i] = now; } vm init(n); rep(i,n) init[i] = a[i]; auto op = [](mint x,mint y) {return x * y;}; segtree seg(init,op,1); rep(i,q) { INT(j); LL(m); INT(l,r); r++; int flg = 1; if(zero_flg[j] == 0) { rep(k,prs.size()) if(cnt[k][j] < prs[k].second) { flg = 0; break; } if(flg && m == b) { mint tmp = 1; rep(k,prs.size()) { cnt[k][j] -= prs[k].second; tmp *= mint(prs[k].first).pow(cnt[k][j]); } tmp *= rem[j]; seg.set(j,tmp); } else { ll now = m; if(now == 0) zero_flg[j] = 1; else { rep(k,prs.size()) { int p = prs[k].first; while(now % p == 0) { cnt[k][j]++; now /= p; } } rem[j] *= now; } seg.set(j,seg.get(j)*m); } } cout << seg.prod(l,r) << '\n'; } }