#pragma GCC optimize("O2") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define int ll #define INT128_MAX (__int128)(((unsigned __int128) 1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1) #define INT128_MIN (-INT128_MAX - 1) #define clock chrono::steady_clock::now().time_since_epoch().count() #ifdef DEBUG #define dbg(x) cout << (#x) << " = " << x << '\n' #else #define dbg(x) #endif namespace R = std::ranges; namespace V = std::views; using namespace std; using ll = long long; using ull = unsigned long long; using ldb = long double; using pii = pair; using pll = pair; //#define double ldb template ostream& operator<<(ostream& os, const pair pr) { return os << pr.first << ' ' << pr.second; } template ostream& operator<<(ostream& os, const array &arr) { for(const T &X : arr) os << X << ' '; return os; } template ostream& operator<<(ostream& os, const vector &vec) { for(const T &X : vec) os << X << ' '; return os; } template ostream& operator<<(ostream& os, const set &s) { for(const T &x : s) os << x << ' '; return os; } //note: inversion only works when MOD is a prime struct mint { static long long MOD; long long _val; mint(long long init = 0) { _val = init % MOD; (*this).norm(); } mint POW(long long index) { if (index == 0) return mint(1ll); mint base = *this; mint res = (base == 0ll ? 0ll : 1ll); while(index) { if (index & 1) res *= base; base *= base, index >>= 1; } return res; } mint inv() { return (*this).POW(MOD - 2); } mint& norm() { if (_val >= MOD) _val -= MOD; if (_val < 0) _val += MOD; return *this; } mint& operator+=(mint b) { _val += b._val; return (*this).norm(); } mint& operator-=(mint b) { _val -= b._val; return (*this).norm(); } mint& operator*=(mint b) { _val = (_val * b._val) % MOD; return *this; } mint& operator/=(mint b) { _val = (_val * b.inv()._val) % MOD; return *this; } mint& operator++() { _val += 1; return (*this).norm(); } mint& operator--() { _val -= 1; return (*this).norm(); } mint operator++(signed) { mint tmp = *this; ++(*this); return tmp; } mint operator--(signed) { mint tmp = *this; --(*this); return tmp; } mint operator-() { return mint(-_val); } bool operator==(mint b) { return _val == b._val; } bool operator!=(mint b) { return _val != b._val; } friend mint operator+(mint a, mint b) { return a += b; } friend mint operator-(mint a, mint b) { return a -= b; } friend mint operator*(mint a, mint b) { return a *= b; } friend mint operator/(mint a, mint b) { return a /= b; } friend ostream& operator<<(ostream& os, const mint& b) { return os << b._val; } friend istream& operator>>(istream& is, mint& b) { long long val; is >> val; b = mint(val); return is; } }; ll mint::MOD = 2; const int C = 100000001; vector prime; int mpf[C]; void sieve() { for(int i = 1; i < C; i++) mpf[i] = i; for(int i = 2; i < C; i++) { if (mpf[i] == i) prime.emplace_back(i); for(int P : prime) { if (P > mpf[i] or i * P >= C) break; mpf[i * P] = P; } } } vector factorize(int val) { vector res; while(val > 1) { int p = mpf[val]; res.emplace_back(p, 0); while(val % p == 0) res.back().second += 1, val /= p; } return res; } vector factors(int val) { vector res(1, 1); for(auto [p, idx] : factorize(val)) { vector tmp; for(int i = 0, base = 1; i <= idx; i++, base *= p) for(int X : res) tmp.emplace_back(X * base); res.swap(tmp); } return res; } mt19937 rng(clock); uniform_int_distribution unif(5000000, 5761454); signed main() { ios::sync_with_stdio(false), cin.tie(NULL); sieve(); int n, q, k; cin >> n >> q >> k; while(k % (mint::MOD = unif(rng)) == 0); dbg(mint::MOD); vector a(n + 1); for(mint &x : a | V::drop(1)) cin >> x; mint tmp = k; for(int i = 1; i <= n; i++) a[i] *= tmp, tmp *= k; partial_sum(a.begin(), a.end(), a.begin()); while(q--) { int l, r; cin >> l >> r; cout << (a[r] - a[l - 1] == 0 ? "No\n" : "Yes\n"); } return 0; }