結果
| 問題 | No.2305 [Cherry 5th Tune N] Until That Day... |
| ユーザー |
 hitonanode
|
| 提出日時 | 2023-05-19 23:04:58 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 36,632 bytes |
| コンパイル時間 | 3,971 ms |
| コンパイル使用メモリ | 243,764 KB |
| 実行使用メモリ | 18,268 KB |
| 最終ジャッジ日時 | 2024-05-10 06:27:54 |
| 合計ジャッジ時間 | 18,306 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 2 ms
5,376 KB |
| testcase_02 | AC | 3 ms
5,376 KB |
| testcase_03 | AC | 19 ms
10,616 KB |
| testcase_04 | AC | 11 ms
6,908 KB |
| testcase_05 | AC | 26 ms
10,632 KB |
| testcase_06 | AC | 166 ms
18,092 KB |
| testcase_07 | AC | 735 ms
18,256 KB |
| testcase_08 | AC | 731 ms
18,268 KB |
| testcase_09 | AC | 405 ms
18,136 KB |
| testcase_10 | AC | 404 ms
18,256 KB |
| testcase_11 | TLE | - |
| testcase_12 | -- | - |
| testcase_13 | -- | - |
| testcase_14 | -- | - |
| testcase_15 | -- | - |
| testcase_16 | -- | - |
| testcase_17 | -- | - |
| testcase_18 | -- | - |
| testcase_19 | -- | - |
| testcase_20 | -- | - |
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_LOCAL
const 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
#endif
using 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;
else
ntt(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 or
std::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);
}
// Formal Power Series (形式的冪級数) based on ModInt<mod> / ModIntRuntime
// Reference: https://ei1333.github.io/luzhiled/snippets/math/formal-power-series.html
template <typename T> struct FormalPowerSeries : std::vector<T> {
using std::vector<T>::vector;
using P = FormalPowerSeries;
void shrink() {
while (this->size() and this->back() == T(0)) this->pop_back();
}
P operator+(const P &r) const { return P(*this) += r; }
P operator+(const T &v) const { return P(*this) += v; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator-(const T &v) const { return P(*this) -= v; }
P operator*(const P &r) const { return P(*this) *= r; }
P operator*(const T &v) const { return P(*this) *= v; }
P operator/(const P &r) const { return P(*this) /= r; }
P operator/(const T &v) const { return P(*this) /= v; }
P operator%(const P &r) const { return P(*this) %= r; }
P &operator+=(const P &r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];
shrink();
return *this;
}
P &operator+=(const T &v) {
if (this->empty()) this->resize(1);
(*this)[0] += v;
shrink();
return *this;
}
P &operator-=(const P &r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];
shrink();
return *this;
}
P &operator-=(const T &v) {
if (this->empty()) this->resize(1);
(*this)[0] -= v;
shrink();
return *this;
}
P &operator*=(const T &v) {
for (auto &x : (*this)) x *= v;
shrink();
return *this;
}
P &operator*=(const P &r) {
if (this->empty() || r.empty())
this->clear();
else {
auto ret = nttconv(*this, r);
*this = P(ret.begin(), ret.end());
}
return *this;
}
P &operator%=(const P &r) {
*this -= *this / r * r;
shrink();
return *this;
}
P operator-() const {
P ret = *this;
for (auto &v : ret) v = -v;
return ret;
}
P &operator/=(const T &v) {
assert(v != T(0));
for (auto &x : (*this)) x /= v;
return *this;
}
P &operator/=(const P &r) {
if (this->size() < r.size()) {
this->clear();
return *this;
}
int n = (int)this->size() - r.size() + 1;
return *this = (reversed().pre(n) * r.reversed().inv(n)).pre(n).reversed(n);
}
P pre(int sz) const {
P ret(this->begin(), this->begin() + std::min((int)this->size(), sz));
ret.shrink();
return ret;
}
P operator>>(int sz) const {
if ((int)this->size() <= sz) return {};
return P(this->begin() + sz, this->end());
}
P operator<<(int sz) const {
if (this->empty()) return {};
P ret(*this);
ret.insert(ret.begin(), sz, T(0));
return ret;
}
P reversed(int deg = -1) const {
assert(deg >= -1);
P ret(*this);
if (deg != -1) ret.resize(deg, T(0));
reverse(ret.begin(), ret.end());
ret.shrink();
return ret;
}
P differential() const { // formal derivative (differential) of f.p.s.
const int n = (int)this->size();
P ret(std::max(0, n - 1));
for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);
return ret;
}
P integral() const {
const int n = (int)this->size();
P ret(n + 1);
ret[0] = T(0);
for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);
return ret;
}
P inv(int deg) const {
assert(deg >= -1);
assert(this->size() and ((*this)[0]) != T(0)); // Requirement: F(0) != 0
const int n = this->size();
if (deg == -1) deg = n;
P ret({T(1) / (*this)[0]});
for (int i = 1; i < deg; i <<= 1) {
auto h = (pre(i << 1) * ret).pre(i << 1) >> i;
auto tmp = (-h * ret).pre(i);
ret.insert(ret.end(), tmp.begin(), tmp.end());
ret.resize(i << 1);
}
ret = ret.pre(deg);
ret.shrink();
return ret;
}
P log(int deg = -1) const {
assert(deg >= -1);
assert(this->size() and ((*this)[0]) == T(1)); // Requirement: F(0) = 1
const int n = (int)this->size();
if (deg == 0) return {};
if (deg == -1) deg = n;
return (this->differential() * this->inv(deg)).pre(deg - 1).integral();
}
P sqrt(int deg = -1) const {
assert(deg >= -1);
const int n = (int)this->size();
if (deg == -1) deg = n;
if (this->empty()) return {};
if ((*this)[0] == T(0)) {
for (int i = 1; i < n; i++)
if ((*this)[i] != T(0)) {
if ((i & 1) or deg - i / 2 <= 0) return {};
return (*this >> i).sqrt(deg - i / 2) << (i / 2);
}
return {};
}
T sqrtf0 = (*this)[0].sqrt();
if (sqrtf0 == T(0)) return {};
P y = (*this) / (*this)[0], ret({T(1)});
T inv2 = T(1) / T(2);
for (int i = 1; i < deg; i <<= 1) ret = (ret + y.pre(i << 1) * ret.inv(i << 1)) * inv2;
return ret.pre(deg) * sqrtf0;
}
P exp(int deg = -1) const {
assert(deg >= -1);
assert(this->empty() or ((*this)[0]) == T(0)); // Requirement: F(0) = 0
const int n = (int)this->size();
if (deg == -1) deg = n;
P ret({T(1)});
for (int i = 1; i < deg; i <<= 1) {
ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);
}
return ret.pre(deg);
}
P pow(long long k, int deg = -1) const {
assert(deg >= -1);
const int n = (int)this->size();
if (deg == -1) deg = n;
if (k == 0) {
P ret(deg);
if (deg >= 1) ret[0] = T(1);
ret.shrink();
return ret;
}
for (int i = 0; i < n; i++) {
if ((*this)[i] != T(0)) {
T rev = T(1) / (*this)[i];
P C = (*this) * rev, D(n - i);
for (int j = i; j < n; j++) D[j - i] = C.coeff(j);
D = (D.log(deg) * T(k)).exp(deg) * (*this)[i].pow(k);
if (__int128(k) * i > deg) return {};
P E(deg);
long long S = i * k;
for (int j = 0; j + S < deg and j < (int)D.size(); j++) E[j + S] = D[j];
E.shrink();
return E;
}
}
return *this;
}
// Calculate f(X + c) from f(X), O(NlogN)
P shift(T c) const {
const int n = (int)this->size();
P ret = *this;
for (int i = 0; i < n; i++) ret[i] *= T(i).fac();
std::reverse(ret.begin(), ret.end());
P exp_cx(n, 1);
for (int i = 1; i < n; i++) exp_cx[i] = exp_cx[i - 1] * c / i;
ret = (ret * exp_cx), ret.resize(n);
std::reverse(ret.begin(), ret.end());
for (int i = 0; i < n; i++) ret[i] /= T(i).fac();
return ret;
}
T coeff(int i) const {
if ((int)this->size() <= i or i < 0) return T(0);
return (*this)[i];
}
T eval(T x) const {
T ret = 0, w = 1;
for (auto &v : *this) ret += w * v, w *= x;
return ret;
}
};
// 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;
} else
C_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/2017/11/18/233936
template <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;
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/21837815
template <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/COUNTSEQ2
template <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 matrix
template <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);
vector<vector<mint>> rems;
REP(d, 30) {
rems.push_back(monomial_mod_polynomial<mint>(1 << d, rev_min_poly));
}
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);
REP(d, 30) {
if ((dk >> d) & 1) {
std::vector<mint> tmp(init.size());
for (auto c : rems.at(d)) {
for (int i = 0; i < int(init.size()); ++i) tmp[i] += init[i] * c;
init = trans.prod(init);
}
init = tmp;
}
}
}
ret.at(q) = init.at(N + 1 + q);
}
for (auto x : ret) cout << x << endl;
}