結果
問題 | No.2305 [Cherry 5th Tune N] Until That Day... |
ユーザー |
![]() |
提出日時 | 2023-05-19 22:35:27 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
TLE
|
実行時間 | - |
コード長 | 29,175 bytes |
コンパイル時間 | 6,893 ms |
コンパイル使用メモリ | 241,360 KB |
実行使用メモリ | 65,720 KB |
最終ジャッジ日時 | 2024-12-20 00:57:23 |
合計ジャッジ時間 | 37,007 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge5 |
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ファイルパターン | 結果 |
---|---|
other | AC * 19 TLE * 2 |
ソースコード
#include <algorithm>#include <array>#include <bitset>#include <cassert>#include <chrono>#include <cmath>#include <complex>#include <deque>#include <forward_list>#include <fstream>#include <functional>#include <iomanip>#include <ios>#include <iostream>#include <limits>#include <list>#include <map>#include <numeric>#include <queue>#include <random>#include <set>#include <sstream>#include <stack>#include <string>#include <tuple>#include <type_traits>#include <unordered_map>#include <unordered_set>#include <utility>#include <vector>using namespace std;using lint = long long;using pint = pair<int, int>;using plint = pair<lint, lint>;struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;#define ALL(x) (x).begin(), (x).end()#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)#define REP(i, n) FOR(i,0,n)#define IREP(i, n) IFOR(i,0,n)template <typename T, typename V>void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os <<']'; return os; }template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v<< ','; os << ']'; return os; }template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);},tpl); return is; }template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) {((os << args << ','), ...);}, tpl); return os << ')'; }template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os<< v << ','; os << '}'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os <<']'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}';return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os <<'}'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v <<','; os << '}'; return os; }template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for(auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }#ifdef HITONANODE_LOCALconst string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET<< std::endl#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " <<__FILE__ << COLOR_RESET << std::endl : std::cerr)#else#define dbg(x) ((void)0)#define dbgif(cond, x) ((void)0)#endif#include <iostream>#include <set>#include <vector>template <int md> struct ModInt {#if __cplusplus >= 201402L#define MDCONST constexpr#else#define MDCONST#endifusing lint = long long;MDCONST static int mod() { return md; }static int get_primitive_root() {static int primitive_root = 0;if (!primitive_root) {primitive_root = [&]() {std::set<int> fac;int v = md - 1;for (lint i = 2; i * i <= v; i++)while (v % i == 0) fac.insert(i), v /= i;if (v > 1) fac.insert(v);for (int g = 1; g < md; g++) {bool ok = true;for (auto i : fac)if (ModInt(g).pow((md - 1) / i) == 1) {ok = false;break;}if (ok) return g;}return -1;}();}return primitive_root;}int val_;int val() const noexcept { return val_; }MDCONST ModInt() : val_(0) {}MDCONST ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; }MDCONST ModInt(lint v) { _setval(v % md + md); }MDCONST explicit operator bool() const { return val_ != 0; }MDCONST ModInt operator+(const ModInt &x) const {return ModInt()._setval((lint)val_ + x.val_);}MDCONST ModInt operator-(const ModInt &x) const {return ModInt()._setval((lint)val_ - x.val_ + md);}MDCONST ModInt operator*(const ModInt &x) const {return ModInt()._setval((lint)val_ * x.val_ % md);}MDCONST ModInt operator/(const ModInt &x) const {return ModInt()._setval((lint)val_ * x.inv().val() % md);}MDCONST ModInt operator-() const { return ModInt()._setval(md - val_); }MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; }MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; }MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; }MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; }friend MDCONST ModInt operator+(lint a, const ModInt &x) {return ModInt()._setval(a % md + x.val_);}friend MDCONST ModInt operator-(lint a, const ModInt &x) {return ModInt()._setval(a % md - x.val_ + md);}friend MDCONST ModInt operator*(lint a, const ModInt &x) {return ModInt()._setval(a % md * x.val_ % md);}friend MDCONST ModInt operator/(lint a, const ModInt &x) {return ModInt()._setval(a % md * x.inv().val() % md);}MDCONST bool operator==(const ModInt &x) const { return val_ == x.val_; }MDCONST bool operator!=(const ModInt &x) const { return val_ != x.val_; }MDCONST bool operator<(const ModInt &x) const {return val_ < x.val_;} // To use std::map<ModInt, T>friend std::istream &operator>>(std::istream &is, ModInt &x) {lint t;return is >> t, x = ModInt(t), is;}MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) {return os << x.val_;}MDCONST ModInt pow(lint n) const {ModInt ans = 1, tmp = *this;while (n) {if (n & 1) ans *= tmp;tmp *= tmp, n >>= 1;}return ans;}static std::vector<ModInt> facs, facinvs, invs;MDCONST static void _precalculation(int N) {int l0 = facs.size();if (N > md) N = md;if (N <= l0) return;facs.resize(N), facinvs.resize(N), invs.resize(N);for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;facinvs[N - 1] = facs.back().pow(md - 2);for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];}MDCONST ModInt inv() const {if (this->val_ < std::min(md >> 1, 1 << 21)) {if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0};while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return invs[this->val_];} else {return this->pow(md - 2);}}MDCONST ModInt fac() const {while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return facs[this->val_];}MDCONST ModInt facinv() const {while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return facinvs[this->val_];}MDCONST ModInt doublefac() const {lint k = (this->val_ + 1) / 2;return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac()): ModInt(k).fac() * ModInt(2).pow(k);}MDCONST ModInt nCr(const ModInt &r) const {return (this->val_ < r.val_) ? 0 : this->fac() * (*this - r).facinv() * r.facinv();}MDCONST ModInt nPr(const ModInt &r) const {return (this->val_ < r.val_) ? 0 : this->fac() * (*this - r).facinv();}ModInt sqrt() const {if (val_ == 0) return 0;if (md == 2) return val_;if (pow((md - 1) / 2) != 1) return 0;ModInt b = 1;while (b.pow((md - 1) / 2) == 1) b += 1;int e = 0, m = md - 1;while (m % 2 == 0) m >>= 1, e++;ModInt x = pow((m - 1) / 2), y = (*this) * x * x;x *= (*this);ModInt z = b.pow(m);while (y != 1) {int j = 0;ModInt t = y;while (t != 1) j++, t *= t;z = z.pow(1LL << (e - j - 1));x *= z, z *= z, y *= z;e = j;}return ModInt(std::min(x.val_, md - x.val_));}};template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};using mint = ModInt<998244353>;// Integer convolution for arbitrary mod// with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class.// We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`.// input: a (size: n), b (size: m)// return: vector (size: n + m - 1)template <typename MODINT>std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner);constexpr int nttprimes[3] = {998244353, 167772161, 469762049};// Integer FFT (Fast Fourier Transform) for ModInt class// (Also known as Number Theoretic Transform, NTT)// is_inverse: inverse transform// ** Input size must be 2^n **template <typename MODINT> void ntt(std::vector<MODINT> &a, bool is_inverse = false) {int n = a.size();if (n == 1) return;static const int mod = MODINT::mod();static const MODINT root = MODINT::get_primitive_root();assert(__builtin_popcount(n) == 1 and (mod - 1) % n == 0);static std::vector<MODINT> w{1}, iw{1};for (int m = w.size(); m < n / 2; m *= 2) {MODINT dw = root.pow((mod - 1) / (4 * m)), dwinv = 1 / dw;w.resize(m * 2), iw.resize(m * 2);for (int i = 0; i < m; i++) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv;}if (!is_inverse) {for (int m = n; m >>= 1;) {for (int s = 0, k = 0; s < n; s += 2 * m, k++) {for (int i = s; i < s + m; i++) {MODINT x = a[i], y = a[i + m] * w[k];a[i] = x + y, a[i + m] = x - y;}}}} else {for (int m = 1; m < n; m *= 2) {for (int s = 0, k = 0; s < n; s += 2 * m, k++) {for (int i = s; i < s + m; i++) {MODINT x = a[i], y = a[i + m];a[i] = x + y, a[i + m] = (x - y) * iw[k];}}}int n_inv = MODINT(n).inv().val();for (auto &v : a) v *= n_inv;}}template <int MOD>std::vector<ModInt<MOD>> nttconv_(const std::vector<int> &a, const std::vector<int> &b) {int sz = a.size();assert(a.size() == b.size() and __builtin_popcount(sz) == 1);std::vector<ModInt<MOD>> ap(sz), bp(sz);for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i];ntt(ap, false);if (a == b)bp = ap;elsentt(bp, false);for (int i = 0; i < sz; i++) ap[i] *= bp[i];ntt(ap, true);return ap;}long long garner_ntt_(int r0, int r1, int r2, int mod) {using mint2 = ModInt<nttprimes[2]>;static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];static const long long m0_inv_m1 = ModInt<nttprimes[1]>(nttprimes[0]).inv().val();static const long long m01_inv_m2 = mint2(m01).inv().val();int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * m01_inv_m2;return (r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val()) % mod;}template <typename MODINT>std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner) {if (a.empty() or b.empty()) return {};int sz = 1, n = a.size(), m = b.size();while (sz < n + m) sz <<= 1;if (sz <= 16) {std::vector<MODINT> ret(n + m - 1);for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) ret[i + j] += a[i] * b[j];}return ret;}int mod = MODINT::mod();if (skip_garner orstd::find(std::begin(nttprimes), std::end(nttprimes), mod) != std::end(nttprimes)) {a.resize(sz), b.resize(sz);if (a == b) {ntt(a, false);b = a;} else {ntt(a, false), ntt(b, false);}for (int i = 0; i < sz; i++) a[i] *= b[i];ntt(a, true);a.resize(n + m - 1);} else {std::vector<int> ai(sz), bi(sz);for (int i = 0; i < n; i++) ai[i] = a[i].val();for (int i = 0; i < m; i++) bi[i] = b[i].val();auto ntt0 = nttconv_<nttprimes[0]>(ai, bi);auto ntt1 = nttconv_<nttprimes[1]>(ai, bi);auto ntt2 = nttconv_<nttprimes[2]>(ai, bi);a.resize(n + m - 1);for (int i = 0; i < n + m - 1; i++)a[i] = garner_ntt_(ntt0[i].val(), ntt1[i].val(), ntt2[i].val(), mod);}return a;}template <typename MODINT>std::vector<MODINT> nttconv(const std::vector<MODINT> &a, const std::vector<MODINT> &b) {return nttconv<MODINT>(a, b, false);}// Berlekamp–Massey algorithm// https://en.wikipedia.org/wiki/Berlekamp%E2%80%93Massey_algorithm// Complexity: O(N^2)// input: S = sequence from field K// return: L = degree of minimal polynomial,// C_reversed = monic min. polynomial (size = L + 1, reversed order, C_reversed[0] = 1))// Formula: convolve(S, C_reversed)[i] = 0 for i >= L// Example:// - [1, 2, 4, 8, 16] -> (1, [1, -2])// - [1, 1, 2, 3, 5, 8] -> (2, [1, -1, -1])// - [0, 0, 0, 0, 1] -> (5, [1, 0, 0, 0, 0, 998244352]) (mod 998244353)// - [] -> (0, [1])// - [0, 0, 0] -> (0, [1])// - [-2] -> (1, [1, 2])template <typename Tfield>std::pair<int, std::vector<Tfield>> find_linear_recurrence(const std::vector<Tfield> &S) {int N = S.size();using poly = std::vector<Tfield>;poly C_reversed{1}, B{1};int L = 0, m = 1;Tfield b = 1;// adjust: C(x) <- C(x) - (d / b) x^m B(x)auto adjust = [](poly C, const poly &B, Tfield d, Tfield b, int m) -> poly {C.resize(std::max(C.size(), B.size() + m));Tfield a = d / b;for (unsigned i = 0; i < B.size(); i++) C[i + m] -= a * B[i];return C;};for (int n = 0; n < N; n++) {Tfield d = S[n];for (int i = 1; i <= L; i++) d += C_reversed[i] * S[n - i];if (d == 0)m++;else if (2 * L <= n) {poly T = C_reversed;C_reversed = adjust(C_reversed, B, d, b, m);L = n + 1 - L;B = T;b = d;m = 1;} elseC_reversed = adjust(C_reversed, B, d, b, m++);}return std::make_pair(L, C_reversed);}// Calculate ^N \bmod f(x)$// Known as `Kitamasa method`// Input: f_reversed: monic, reversed (f_reversed[0] = 1)// Complexity: (K^2 \log N)$ ($: deg. of $)// Example: (4, [1, -1, -1]) -> [2, 3]// ( x^4 = (x^2 + x + 2)(x^2 - x - 1) + 3x + 2 )// Reference: http://misawa.github.io/others/fast_kitamasa_method.html// http://sugarknri.hatenablog.com/entry/2017/11/18/233936template <typename Tfield>std::vector<Tfield> monomial_mod_polynomial(long long N, const std::vector<Tfield> &f_reversed) {assert(!f_reversed.empty() and f_reversed[0] == 1);int K = f_reversed.size() - 1;if (!K) return {};int D = 64 - __builtin_clzll(N);std::vector<Tfield> ret(K, 0);ret[0] = 1;auto self_conv = [](std::vector<Tfield> x) -> std::vector<Tfield> {int d = x.size();std::vector<Tfield> ret(d * 2 - 1);for (int i = 0; i < d; i++) {ret[i * 2] += x[i] * x[i];for (int j = 0; j < i; j++) ret[i + j] += x[i] * x[j] * 2;}return ret;};for (int d = D; d--;) {ret = nttconv(ret, ret);for (int i = 2 * K - 2; i >= K; i--) {for (int j = 1; j <= K; j++) ret[i - j] -= ret[i] * f_reversed[j];}ret.resize(K);if ((N >> d) & 1) {std::vector<Tfield> c(K);c[0] = -ret[K - 1] * f_reversed[K];for (int i = 1; i < K; i++) { c[i] = ret[i - 1] - ret[K - 1] * f_reversed[K - i]; }ret = c;}}return ret;}// Guess k-th element of the sequence, assuming linear recurrence// initial_elements: 0-ORIGIN// Verify: abc198f https://atcoder.jp/contests/abc198/submissions/21837815template <typename Tfield>Tfield guess_kth_term(const std::vector<Tfield> &initial_elements, long long k) {assert(k >= 0);if (k < static_cast<long long>(initial_elements.size())) return initial_elements[k];const auto f = find_linear_recurrence<Tfield>(initial_elements).second;const auto g = monomial_mod_polynomial<Tfield>(k, f);Tfield ret = 0;for (unsigned i = 0; i < g.size(); i++) ret += g[i] * initial_elements[i];return ret;}#include <chrono>#include <random>#include <vector>template <typename ModInt> std::vector<ModInt> gen_random_vector(int len) {static std::mt19937 mt(std::chrono::steady_clock::now().time_since_epoch().count());static std::uniform_int_distribution<int> rnd(1, ModInt::mod() - 1);std::vector<ModInt> ret(len);for (auto &x : ret) x = rnd(mt);return ret;};// Probabilistic algorithm to find a solution of linear equation Ax = b if exists.// Complexity: O(n T(n) + n^2)// Reference:// [1] W. Eberly, E. Kaltofen, "On randomized Lanczos algorithms," Proc. of international symposium on// Symbolic and algebraic computation, 176-183, 1997.template <typename Matrix, typename T>std::vector<T> linear_system_solver_lanczos(const Matrix &A, const std::vector<T> &b) {assert(A.height() == int(b.size()));const int M = A.height(), N = A.width();const std::vector<T> D1 = gen_random_vector<T>(N), D2 = gen_random_vector<T>(M),v = gen_random_vector<T>(N);auto applyD1 = [&D1](std::vector<T> v) {for (int i = 0; i < int(v.size()); i++) v[i] *= D1[i];return v;};auto applyD2 = [&D2](std::vector<T> v) {for (int i = 0; i < int(v.size()); i++) v[i] *= D2[i];return v;};auto applyAtilde = [&](std::vector<T> v) -> std::vector<T> {v = applyD1(v);v = A.prod(v);v = applyD2(v);v = A.prod_left(v);v = applyD1(v);return v;};auto dot = [&](const std::vector<T> &vl, const std::vector<T> &vr) -> T {return std::inner_product(vl.begin(), vl.end(), vr.begin(), T(0));};auto scalar_vec = [&](const T &x, std::vector<T> vec) -> std::vector<T> {for (auto &v : vec) v *= x;return vec;};auto btilde1 = applyD1(A.prod_left(applyD2(b))), btilde2 = applyAtilde(v);std::vector<T> btilde(N);for (int i = 0; i < N; i++) btilde[i] = btilde1[i] + btilde2[i];std::vector<T> w0 = btilde, v1 = applyAtilde(w0);std::vector<T> wm1(w0.size()), v0(v1.size());T t0 = dot(v1, w0), gamma = dot(btilde, w0) / t0, tm1 = 1;std::vector<T> x = scalar_vec(gamma, w0);while (true) {if (!t0 or !std::count_if(w0.begin(), w0.end(), [](T x) { return x != T(0); })) break;T alpha = dot(v1, v1) / t0, beta = dot(v1, v0) / tm1;std::vector<T> w1(N);for (int i = 0; i < N; i++) w1[i] = v1[i] - alpha * w0[i] - beta * wm1[i];std::vector<T> v2 = applyAtilde(w1);T t1 = dot(w1, v2);gamma = dot(btilde, w1) / t1;for (int i = 0; i < N; i++) x[i] += gamma * w1[i];wm1 = w0, w0 = w1;v0 = v1, v1 = v2;tm1 = t0, t0 = t1;}for (int i = 0; i < N; i++) x[i] -= v[i];return applyD1(x);}// Probabilistic algorithm to calculate determinant of matrices// Complexity: O(n T(n) + n^2)// Reference:// [1] D. H. Wiedmann, "Solving sparse linear equations over finite fields,"// IEEE Trans. on Information Theory, 32(1), 54-62, 1986.template <class Matrix, class Tp> Tp blackbox_determinant(const Matrix &M) {assert(M.height() == M.width());const int N = M.height();std::vector<Tp> b = gen_random_vector<Tp>(N), u = gen_random_vector<Tp>(N),D = gen_random_vector<Tp>(N);std::vector<Tp> uMDib(2 * N);for (int i = 0; i < 2 * N; i++) {uMDib[i] = std::inner_product(u.begin(), u.end(), b.begin(), Tp(0));for (int j = 0; j < N; j++) b[j] *= D[j];b = M.prod(b);}auto ret = find_linear_recurrence<Tp>(uMDib);Tp det = ret.second.back() * (N % 2 ? -1 : 1);Tp ddet = 1;for (auto d : D) ddet *= d;return det / ddet;}// Complexity: O(n T(n) + n^2)template <class Matrix, class Tp>std::vector<Tp> reversed_minimal_polynomial_of_matrix(const Matrix &M) {assert(M.height() == M.width());const int N = M.height();std::vector<Tp> b = gen_random_vector<Tp>(N), u = gen_random_vector<Tp>(N);std::vector<Tp> uMb(2 * N);for (int i = 0; i < 2 * N; i++) {uMb[i] = std::inner_product(u.begin(), u.end(), b.begin(), Tp());b = M.prod(b);}auto ret = find_linear_recurrence<Tp>(uMb);return ret.second;}// Calculate A^k b// Complexity: O(n^2 log k + n T(n))// Verified: https://www.codechef.com/submit/COUNTSEQ2template <class Matrix, class Tp>std::vector<Tp> blackbox_matrix_pow_vec(const Matrix &A, long long k, std::vector<Tp> b) {assert(A.width() == int(b.size()));assert(k >= 0);std::vector<Tp> rev_min_poly = reversed_minimal_polynomial_of_matrix<Matrix, Tp>(A);std::vector<Tp> remainder = monomial_mod_polynomial<Tp>(k, rev_min_poly);std::vector<Tp> ret(b.size());for (Tp c : remainder) {for (int d = 0; d < int(b.size()); ++d) ret[d] += b[d] * c;b = A.prod(b);}return ret;}// Sparse matrixtemplate <typename Tp> struct sparse_matrix {int H, W;std::vector<std::vector<std::pair<int, Tp>>> vals;sparse_matrix(int H = 0, int W = 0) : H(H), W(W), vals(H) {}int height() const { return H; }int width() const { return W; }void add_element(int i, int j, Tp val) {assert(i >= 0 and i < H);assert(j >= 0 and i < W);vals[i].emplace_back(j, val);}std::vector<Tp> prod(const std::vector<Tp> &vec) const {assert(W == int(vec.size()));std::vector<Tp> ret(H);for (int i = 0; i < H; i++) {for (const auto &p : vals[i]) ret[i] += p.second * vec[p.first];}return ret;}std::vector<Tp> prod_left(const std::vector<Tp> &vec) const {assert(H == int(vec.size()));std::vector<Tp> ret(W);for (int i = 0; i < H; i++) {for (const auto &p : vals[i]) ret[p.first] += p.second * vec[i];}return ret;}std::vector<std::vector<Tp>> vecvec() const {std::vector<std::vector<Tp>> ret(H, std::vector<Tp>(W));for (int i = 0; i < H; i++) {for (auto p : vals[i]) ret[i][p.first] += p.second;}return ret;}};int main() {int N;cin >> N;vector<int> P(N + 1, -1);vector<vector<int>> child(N + 1);FOR(i, 1, N + 1) cin >> P.at(i), child.at(P.at(i)).push_back(i);vector<mint> W(N + 1);FOR(i, 1, N + 1) cin >> W.at(i);int Q;cin >> Q;sparse_matrix<mint> trans(N + 1 + Q, N + 1 + Q);REP(i, N + 1) {if (child.at(i).empty()) {trans.add_element(0, i, 1);} else {mint wsum = 0;for (int j : child.at(i)) wsum += W.at(j);for (int j : child.at(i)) trans.add_element(j, i, W.at(j) / wsum);}}vector<tuple<int, int, int>> kaqs;REP(q, Q) {int a, k;cin >> a >> k;kaqs.emplace_back(k, a, q);trans.add_element(N + 1 + q, a, 1);trans.add_element(N + 1 + q, N + 1 + q, 1);}vector<mint> init(N + 1);init.front() = 1;for (auto [k, a, q] : kaqs) init.push_back(a == 0 ? -1 : 0);vector<mint> ret(Q);sort(ALL(kaqs));int klast = -1;const auto rev_min_poly = reversed_minimal_polynomial_of_matrix<decltype(trans), mint>(trans);for (auto [k_, a, q] : kaqs) {auto dk = k_ - klast;dbg(make_tuple(k_, dk, a, q));klast = k_;if (dk) {auto remainder = monomial_mod_polynomial<mint>(dk, rev_min_poly);std::vector<mint> tmp(init.size());for (auto c : remainder) {for (int d = 0; d < int(init.size()); ++d) tmp[d] += init[d] * c;init = trans.prod(init);}init = tmp;}ret.at(q) = init.at(N + 1 + q);}for (auto x : ret) cout << x << endl;}