結果
| 問題 | No.2580 Hyperinflation |
| ユーザー |
👑  Nachia
|
| 提出日時 | 2023-12-08 23:53:28 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 667 ms / 4,000 ms |
| コード長 | 26,811 bytes |
| コンパイル時間 | 1,920 ms |
| コンパイル使用メモリ | 132,144 KB |
| 最終ジャッジ日時 | 2025-02-18 09:41:09 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 31 |
ソースコード
#ifdef NACHIA
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <utility>
#include <queue>
#include <array>
#include <cmath>
#include <atcoder/modint>
using namespace std;
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(i64 i=0; i<(i64)(n); i++)
#define repr(i,n) for(i64 i=(i64)(n)-1; i>=0; i--)
const i64 INF = 1001001001001001001;
const char* yn(bool x){ return x ? "Yes" : "No"; }
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
template<typename A> using nega_queue = priority_queue<A,vector<A>,greater<A>>;
using Modint = atcoder::static_modint<998244353>;
#include <iterator>
#include <functional>
template<class Elem> struct vec;
template<class Iter>
struct seq_view{
using Ref = typename std::iterator_traits<Iter>::reference;
using Elem = typename std::iterator_traits<Iter>::value_type;
Iter a, b;
Iter begin() const { return a; }
Iter end() const { return b; }
int size() const { return (int)(b-a); }
seq_view(Iter first, Iter last) : a(first), b(last) {}
seq_view sort() const { std::sort(a, b); return *this; }
Ref& operator[](int x){ return *(a+x); }
template<class F = std::less<Elem>, class ret = vec<int>> ret sorti(F f = F()) const {
ret x(size()); for(int i=0; i<size(); i++) x[i] = i;
x().sort([&](int l, int r){ return f(a[l],a[r]); });
return x;
}
template<class ret = vec<Elem>> ret col() const { return ret(begin(), end()); }
template<class F = std::equal_to<Elem>, class ret = vec<std::pair<Elem, int>>>
ret rle(F eq = F()) const {
auto x = ret();
for(auto& a : (*this)){
if(x.size() == 0 || !eq(x[x.size()-1].first, a)) x.emp(a, 1); else x[x.size()-1].second++;
} return x;
}
template<class F> seq_view sort(F f) const { std::sort(a, b, f); return *this; }
Iter uni() const { return std::unique(a, b); }
Iter lb(const Elem& x) const { return std::lower_bound(a, b, x); }
Iter ub(const Elem& x) const { return std::upper_bound(a, b, x); }
int lbi(const Elem& x) const { return lb(x) - a; }
int ubi(const Elem& x) const { return ub(x) - a; }
seq_view bound(const Elem& l, const Elem& r) const { return { lb(l), lb(r) }; }
template<class F> Iter lb(const Elem& x, F f) const { return std::lower_bound(a, b, x, f); }
template<class F> Iter ub(const Elem& x, F f) const { return std::upper_bound(a, b, x, f); }
template<class F> Iter when_true_to_false(F f) const {
if(a == b) return a;
return std::lower_bound(a, b, *a,
[&](const Elem& x, const Elem&){ return f(x); });
}
seq_view same(Elem x) const { return { lb(x), ub(x) }; }
template<class F> auto map(F f) const {
vec<typename Iter::value_type> r;
for(auto& x : *this) r.emp(f(x));
return r;
}
Iter max() const { return std::max_element(a, b); }
Iter min() const { return std::min_element(a, b); }
template<class F = std::less<Elem>>
Iter min(F f) const { return std::min_element(a, b, f); }
seq_view rev() const { std::reverse(a, b); return *this; }
};
template<class Elem>
struct vec {
using Base = typename std::vector<Elem>;
using Iter = typename Base::iterator;
using CIter = typename Base::const_iterator;
using View = seq_view<Iter>;
using CView = seq_view<CIter>;
vec(){}
explicit vec(int n, const Elem& value = Elem()) : a(0<n?n:0, value) {}
template <class I2> vec(I2 first, I2 last) : a(first, last) {}
vec(std::initializer_list<Elem> il) : a(std::move(il)) {}
vec(Base b) : a(std::move(b)) {}
operator Base() const { return a; }
Iter begin(){ return a.begin(); }
CIter begin() const { return a.begin(); }
Iter end(){ return a.end(); }
CIter end() const { return a.end(); }
int size() const { return a.size(); }
bool empty() const { return a.empty(); }
Elem& back(){ return a.back(); }
const Elem& back() const { return a.back(); }
vec sortunied(){ vec x = *this; x().sort(); x.a.erase(x().uni(), x.end()); return x; }
Iter operator()(int x){ return a.begin() + x; }
CIter operator()(int x) const { return a.begin() + x; }
View operator()(int l, int r){ return { (*this)(l), (*this)(r) }; }
CView operator()(int l, int r) const { return { (*this)(l), (*this)(r) }; }
View operator()(){ return (*this)(0,size()); }
CView operator()() const { return (*this)(0,size()); }
Elem& operator[](int x){ return a[x]; }
const Elem& operator[](int x) const { return a[x]; }
Base& operator*(){ return a; }
const Base& operator*() const { return a; }
vec& push(Elem args){
a.push_back(std::move(args));
return *this;
}
template<class... Args>
vec& emp(Args &&... args){
a.emplace_back(std::forward<Args>(args) ...);
return *this;
}
template<class Range>
vec& app(Range& x){ for(auto& v : a) emp(v); }
Elem pop(){
Elem x = std::move(a.back());
a.pop_back(); return x;
}
bool operator==(const vec& r) const { return a == r.a; }
bool operator!=(const vec& r) const { return a != r.a; }
bool operator<(const vec& r) const { return a < r.a; }
bool operator<=(const vec& r) const { return a <= r.a; }
bool operator>(const vec& r) const { return a > r.a; }
bool operator>=(const vec& r) const { return a >= r.a; }
vec<vec<Elem>> pile(int n) const { return vec<vec<Elem>>(n, *this); }
template<class F> vec& filter(F f){
int p = 0;
for(int q=0; q<size(); q++) if(f(a[q])) std::swap(a[p++],a[q]);
a.resize(p); return *this;
}
private: Base a;
};
template<class IStr, class U, class T>
IStr& operator>>(IStr& is, vec<std::pair<U,T>>& v){ for(auto& x:v){ is >> x.first >> x.second; } return is; }
template<class IStr, class T>
IStr& operator>>(IStr& is, vec<T>& v){ for(auto& x:v){ is >> x; } return is; }
template<class OStr, class T>
OStr& operator<<(OStr& os, const vec<T>& v){
for(int i=0; i<v.size(); i++){
if(i){ os << ' '; } os << v[i];
} return os;
}
#include <cassert>
namespace nachia{
template<unsigned int MOD>
struct PrimitiveRoot{
using u64 = unsigned long long;
static constexpr u64 powm(u64 a, u64 i) {
u64 res = 1, aa = a;
while(i){
if(i & 1) res = res * aa % MOD;
aa = aa * aa % MOD;
i /= 2;
}
return res;
}
static constexpr bool ExamineVal(unsigned int g){
unsigned int t = MOD - 1;
for(u64 d=2; d*d<=t; d++) if(t % d == 0){
if(powm(g, (MOD - 1) / d) == 1) return false;
while(t % d == 0) t /= d;
}
if(t != 1) if(powm(g, (MOD - 1) / t) == 1) return false;
return true;
}
static constexpr unsigned int GetVal(){
for(unsigned int x=2; x<MOD; x++) if(ExamineVal(x)) return x;
return 0;
}
static const unsigned int val = GetVal();
};
} // namespace nachia
namespace nachia{
template<class Modint>
class Comb{
private:
static constexpr int MOD = Modint::mod();
std::vector<Modint> F;
std::vector<Modint> iF;
public:
void extend(int newN){
int prevN = (int)F.size() - 1;
if(newN >= MOD) newN = MOD - 1;
if(prevN >= newN) return;
F.resize(newN+1);
iF.resize(newN+1);
for(int i=prevN+1; i<=newN; i++) F[i] = F[i-1] * Modint::raw(i);
iF[newN] = F[newN].inv();
for(int i=newN; i>prevN; i--) iF[i-1] = iF[i] * Modint::raw(i);
}
Comb(int n = 1){
F.assign(2, Modint(1));
iF.assign(2, Modint(1));
extend(n);
}
Modint factorial(int n) const { return F[n]; }
Modint invFactorial(int n) const { return iF[n]; }
Modint invOf(int n) const { return iF[n] * F[n-1]; }
Modint comb(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return F[n] * iF[r] * iF[n-r];
}
Modint invComb(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return iF[n] * F[r] * F[n-r];
}
Modint perm(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return F[n] * iF[n-r];
}
Modint invPerm(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return iF[n] * F[n-r];
}
Modint operator()(int n, int r) const { return comb(n,r); }
};
} // namespace nachia
namespace nachia{
int Popcount(unsigned long long c) noexcept {
#ifdef __GNUC__
return __builtin_popcountll(c);
#else
c = (c & (~0ull/3)) + ((c >> 1) & (~0ull/3));
c = (c & (~0ull/5)) + ((c >> 2) & (~0ull/5));
c = (c & (~0ull/17)) + ((c >> 4) & (~0ull/17));
c = (c * (~0ull/257)) >> 56;
return c;
#endif
}
// please ensure x != 0
int MsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
return 63 - __builtin_clzll(x);
#else
using u64 = unsigned long long;
int q = (n >> 32) ? 32 : 0;
auto m = n >> q;
constexpr u64 hi = 0x8888'8888;
constexpr u64 mi = 0x1111'1111;
m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 35;
m = (((m | ~(hi - (n & ~hi))) & hi) * mi) >> 31;
q += (m & 0xf) << 2;
q += 0x3333'3333'2222'1100 >> (((n >> q) & 0xf) << 2) & 0xf
return q;
#endif
}
// please ensure x != 0
int LsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
return __builtin_ctzll(x);
#else
return MsbIndex(x & -x);
#endif
}
}
namespace nachia {
template<class mint>
struct NttInterface{
template<class Iter>
void Butterfly(Iter, int) const {}
template<class Iter>
void IButterfly(Iter, int) const {}
template<class Iter>
void BitReversal(Iter a, int N) const {
for(int i=0, j=0; j<N; j++){
if(i < j) std::swap(a[i], a[j]);
for(int k = N>>1; k > (i^=k); k>>=1);
}
}
};
} // namespace nachia
namespace nachia{
constexpr int bsf_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
template <class mint>
struct NttFromAcl : NttInterface<mint> {
using u32 = unsigned int;
using u64 = unsigned long long;
static int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (u32)(n)) x++;
return x;
}
struct fft_info {
static constexpr u32 g = nachia::PrimitiveRoot<mint::mod()>::val;
static constexpr int rank2 = bsf_constexpr(mint::mod()-1);
std::array<mint, rank2+1> root;
std::array<mint, rank2+1> iroot;
std::array<mint, std::max(0, rank2-1)> rate2;
std::array<mint, std::max(0, rank2-1)> irate2;
std::array<mint, std::max(0, rank2-2)> rate3;
std::array<mint, std::max(0, rank2-2)> irate3;
fft_info(){
root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
iroot[rank2] = root[rank2].inv();
for(int i=rank2-1; i>=0; i--){
root[i] = root[i+1] * root[i+1];
iroot[i] = iroot[i+1] * iroot[i+1];
}
mint prod = 1, iprod = 1;
for(int i=0; i<=rank2-2; i++){
rate2[i] = root[i+2] * prod;
irate2[i] = iroot[i+2] * iprod;
prod *= iroot[i+2];
iprod *= root[i+2];
}
prod = 1; iprod = 1;
for(int i=0; i<=rank2-3; i++){
rate3[i] = root[i+3] * prod;
irate3[i] = iroot[i+3] * iprod;
prod *= iroot[i+3];
iprod *= root[i+3];
}
}
};
template<class RandomAccessIterator>
void Butterfly(RandomAccessIterator a, int n) const {
int h = ceil_pow2(n);
static const fft_info info;
int len = 0;
while(len < h){
if(h-len == 1){
int p = 1 << (h-len-1);
mint rot = 1;
for(int s=0; s<(1<<len); s++){
int offset = s << (h-len);
for(int i=0; i<p; i++){
auto l = a[i+offset];
auto r = a[i+offset+p] * rot;
a[i+offset] = l+r;
a[i+offset+p] = l-r;
}
if(s+1 != (1<<len)) rot *= info.rate2[LsbIndex(~(u32)(s))];
}
len++;
} else {
int p = 1 << (h-len-2);
mint rot = 1, imag = info.root[2];
for(int s=0; s<(1<<len); s++){
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
int offset = s << (h-len);
for(int i=0; i<p; i++){
auto mod2 = 1ULL * mint::mod() * mint::mod();
auto a0 = 1ULL * a[i+offset].val();
auto a1 = 1ULL * a[i+offset+p].val() * rot.val();
auto a2 = 1ULL * a[i+offset+2*p].val() * rot2.val();
auto a3 = 1ULL * a[i+offset+3*p].val() * rot3.val();
auto a1na3imag = 1ULL * mint(a1 + mod2 - a3).val() * imag.val();
auto na2 = mod2 - a2;
a[i+offset] = a0 + a2 + a1 + a3;
a[i+offset+1*p] = a0 + a2 + (2 * mod2 - (a1 + a3));
a[i+offset+2*p] = a0 + na2 + a1na3imag;
a[i+offset+3*p] = a0 + na2 + (mod2 - a1na3imag);
}
if(s+1 != (1<<len)) rot *= info.rate3[LsbIndex(~(u32)(s))];
}
len += 2;
}
}
}
template<class RandomAccessIterator>
void IButterfly(RandomAccessIterator a, int n) const {
int h = ceil_pow2(n);
static const fft_info info;
constexpr int MOD = mint::mod();
int len = h;
while(len){
if(len == 1){
int p = 1 << (h-len);
mint irot = 1;
for(int s=0; s<(1<<(len-1)); s++){
int offset = s << (h-len+1);
for(int i=0; i<p; i++){
auto l = a[i+offset];
auto r = a[i+offset+p];
a[i+offset] = l+r;
a[i+offset+p] = (u64)(MOD + l.val() - r.val()) * irot.val();
}
if(s+1 != (1<<(len-1))) irot *= info.irate2[LsbIndex(~(u32)(s))];
}
len--;
} else {
int p = 1 << (h-len);
mint irot = 1, iimag = info.iroot[2];
for(int s=0; s<(1<<(len-2)); s++){
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
int offset = s << (h-len+2);
for(int i=0; i<p; i++){
auto a0 = 1ULL * a[i+offset+0*p].val();
auto a1 = 1ULL * a[i+offset+1*p].val();
auto a2 = 1ULL * a[i+offset+2*p].val();
auto a3 = 1ULL * a[i+offset+3*p].val();
auto a2na3iimag = 1ULL * mint((MOD + a2 - a3) * iimag.val()).val();
a[i+offset] = a0 + a1 + a2 + a3;
a[i+offset+1*p] = (a0 + (MOD - a1) + a2na3iimag) * irot.val();
a[i+offset+2*p] = (a0 + a1 + (MOD - a2) + (MOD - a3)) * irot2.val();
a[i+offset+3*p] = (a0 + (MOD - a1) + (MOD - a2na3iimag)) * irot3.val();
}
if(s+1 != (1<<(len-2))) irot *= info.irate3[LsbIndex(~(u32)(s))];
}
len -= 2;
}
}
}
};
} // namespace nachia
namespace nachia {
template<class Elem, class NttInst = NttFromAcl<Elem>>
struct FpsNtt {
public:
using Fps = FpsNtt;
using ElemTy = Elem;
static constexpr unsigned int MOD = Elem::mod();
static constexpr int CONV_THRES = 30;
static const NttInst nttInst;
static const unsigned int zeta = nachia::PrimitiveRoot<MOD>::GetVal();
private:
using u32 = unsigned int;
static Elem ZeroElem() noexcept { return Elem(0); }
static Elem OneElem() noexcept { return Elem(1); }
static Comb<Elem> comb;
std::vector<Elem> a;
int RSZ(int& sz) const { return sz = (sz < 0 ? size() : sz); }
public:
int size() const noexcept { return a.size(); }
Elem& operator[](int x) noexcept { return a[x]; }
const Elem& operator[](int x) const noexcept { return a[x]; }
Elem getCoeff(int x) const noexcept { return (0 <= x && x < size()) ? a[x] : ZeroElem(); }
static Comb<Elem>& GetComb() { return comb; }
static int BestNttSize(int x) noexcept { assert(x); return 1 << MsbIndex(x*2-1); }
Fps move(){ return std::move(*this); }
Fps& set(int i, Elem c){ a[i] = c; return *this; }
Fps& removeLeadingZeros(){
int newsz = size();
while(newsz && a[newsz-1].val() == 0) newsz--;
a.resize(newsz);
if((int)a.capacity() / 4 > newsz) a.shrink_to_fit();
return *this;
}
FpsNtt(){}
FpsNtt(int sz) : a(sz, ZeroElem()) {}
FpsNtt(int sz, Elem e) : a(sz, e) {}
FpsNtt(std::vector<Elem>&& src) : a(std::move(src)) {}
FpsNtt(const std::vector<Elem>& src) : a(src) {}
Fps& ntt() {
capSize(BestNttSize(size()));
nttInst.Butterfly(a.begin(), size());
return *this;
}
Fps& intt() {
nttInst.IButterfly(a.begin(), a.size());
return times(Elem::raw(size()).inv());
}
Fps nttDouble(Fps vanilla) const {
int n = size();
assert(n == (n&-n)); // n is a power of 2
Elem q = Elem::raw(zeta).pow((Elem::mod() - 1) / (n*2));
Elem qq = OneElem();
for(int i=0; i<n; i++){ vanilla[i] *= qq; qq *= q; }
vanilla.ntt();
Fps res = clip(0, n*2);
for(int i=0; i<n; i++) res[n+i] = vanilla[i];
return res;
}
Fps nttDouble() const { return nttDouble(clip().intt().move()); }
// Fps res(resSz);
// for(int j=0; j<resSz-destL && j+srcL < srcR; j++) res[j+destL] = a.getCoeff(j+srcL)
// if srcR is unspecified -> srcR = max(srcL, size());
// if resSz is unspecified -> resSz = destL + srcR - srcL
Fps clip(int srcL, int srcR = -1, int destL = 0, int resSz = -1) const {
srcR = RSZ(srcR);
if(resSz < 0) resSz = destL + srcR - srcL;
int rj = std::min(std::min(srcR, size()) - srcL, resSz - destL);
Fps res(resSz);
for(int j=std::max(0, -srcL); j<rj; j++) res[j+destL] = a[j+srcL];
return res;
}
Fps clip() const { return *this; }
Fps& capSize(int l, int r) {
if(r <= (int)size()) a.resize(r);
if(size() <= l) a.resize(l, ZeroElem());
return *this;
}
Fps& capSize(int z){ a.resize(RSZ(z), ZeroElem()); return *this; }
Fps& times(Elem x){ for(int i=0; i<size(); i++){ a[i] *= x; } return *this; }
Fps& timesFactorial(int z = -1){ comb.extend(RSZ(z)); for(int i=0; i<z; i++){ a[i] *= comb.factorial(i); } return *this; }
Fps& timesInvFactorial(int z = -1){ comb.extend(RSZ(z)); for(int i=0; i<z; i++){ a[i] *= comb.invFactorial(i); } return *this; }
Fps& clrRange(int l, int r){ for(int i=l; i<r; i++){ a[i] = ZeroElem(); } return *this; }
Fps& negate(){ for(auto& e : a){ e = -e; } return *this; }
Fps& mulEach(const Fps& other, int maxi = -1){
maxi = std::min(RSZ(maxi), std::min(size(), other.size()));
for(int i=0; i<maxi; i++) a[i] *= other[i];
return *this;
}
Fps& reverse(int sz = -1){ RSZ(sz); std::reverse(a.begin(), a.begin() + sz); return *this; }
static Fps convolution(const Fps& a, const Fps& b, int sz = -1){
if(std::min(a.size(), b.size()) <= CONV_THRES){
if(a.size() > b.size()) return convolution(b, a, sz);
if(sz < 0) sz = std::max(0, a.size() + b.size() - 1);
std::vector<Elem> res(sz);
for(int i=0; i<a.size(); i++) for(int j=0; j<b.size() && i+j<sz; j++) res[i+j] += a[i] * b[j];
return res;
}
int Z = BestNttSize(a.size() + b.size() - 1);
return a.clip(0, Z).ntt().mulEach(b.clip(0, Z).ntt()).intt().capSize(sz).move();
}
Fps convolve(const Fps& r, int sz = -1) const { return convolution(*this, r, sz); }
// 1
// ----- = 1 + f + f^2 + f^3 + ...
// 1-f
Fps powerSum(int sz) const {
RSZ(sz);
if(sz == 0) return {};
int q = std::min(sz, 32);
Fps x = Fps(q).set(0, OneElem()).move();
for(int i=1; i<q; i++) for(int j=1; j<=std::min(i,(int)a.size()-1); j++) x[i] += x[i-j] * a[j];
while(x.size() < sz){
int hN = x.size(), N = hN*2;
Fps a = x.clip(0, N).ntt().move();
Fps b = clip(0, N).ntt().mulEach(a).intt().clrRange(0,hN).ntt().mulEach(a).intt().move();
for(int i=0; i<hN; i++) b[i] = x[i];
std::swap(b, x);
}
return x.capSize(sz).move();
}
Fps inv(int sz = -1) const {
RSZ(sz);
Elem iA0 = a[0].inv();
return clip(0, std::min(sz, size())).times(-iA0).set(0, ZeroElem()).powerSum(sz).times(iA0).move();
}
Fps& difference(){
if(size() == 0) return *this;
for(int i=0; i+1<size(); i++) a[i] = a[i+1] * Elem::raw(i+1);
return capSize(size()-1);
}
Fps& integral(){
if(size() == 0) return capSize(1);
capSize(size()+1);
comb.extend(size());
for(int i=size()-1; i>=1; i--) a[i] = a[i-1] * comb.invOf(i);
return set(0, ZeroElem());
}
Fps& EgfToOgf(){
comb.extend(size());
for(int i=0; i<size(); i++) a[i] *= comb.factorial(i);
return *this;
}
Fps& OgfToEgf(){
comb.extend(size());
for(int i=0; i<size(); i++) a[i] *= comb.invFactorial(i);
return *this;
}
Fps log(int sz = -1){
RSZ(sz);
assert(sz != 0);
assert(a[0].val() == 1);
return convolution(inv(sz), clip().difference(), sz-1).integral();
}
Fps exp(int sz = -1){
RSZ(sz);
Fps res = Fps(1).set(0, OneElem());
while(res.size() < sz){
auto z = res.size();
auto tmp = res.capSize(z*2).log().set(0, -OneElem()).move();
for(int i=0; i<z*2 && i<size(); i++) tmp[i] -= a[i];
auto resntt = res.clip().ntt().mulEach(tmp.ntt()).intt().move();
for(int i=z; i<z*2; i++) res[i] = -resntt[i];
}
return res.capSize(0, sz).move();
}
Fps pow(unsigned long long k, int sz = -1){
int n = RSZ(sz);
if(k == 0) return Fps(n).set(0, OneElem()).move();
int ctz = 0;
while(ctz<n && a[ctz].val() == 0) ctz++;
if((unsigned long long)ctz >= (n-1) / k + 1) return Fps(n);
Elem a0 = a[ctz];
return clip(ctz, ctz+n-ctz*k).times(a0.inv()).log().times(Elem(k)).exp().times(a0.pow(k)).clip(0, -1, ctz*k);
}
auto begin(){ return a.begin(); }
auto end(){ return a.end(); }
auto begin() const { return a.begin(); }
auto end() const { return a.end(); }
std::string toString(std::string beg = "[ ", std::string delim = " ", std::string en = " ]") const {
std::string res = beg;
bool f = false;
for(auto x : a){ if(f){ res += delim; } f = true; res += std::to_string(x.val()); }
res += en;
return res;
}
std::vector<Elem> getVectorMoved(){ return std::move(a); }
Fps& operator+=(const Fps& r){
capSize(std::max(size(), r.size()));
for(int i=0; i<r.size(); i++) a[i] += r[i];
return *this;
}
Fps& operator-=(const Fps& r){
capSize(std::max(size(), r.size()));
for(int i=0; i<r.size(); i++) a[i] -= r[i];
return *this;
}
Fps operator+(const Fps& r) const { return (clip(0, std::max(size(), r.size())) += r).move(); }
Fps operator-(const Fps& r) const { return (clip(0, std::max(size(), r.size())) -= r).move(); }
Fps operator-() const { return (clip().negate()).move(); }
Fps operator*(const Fps& r) const { return convolve(r).removeLeadingZeros().move(); }
Fps& operator*=(const Fps& r){ return (*this) = operator*(r); }
Fps& operator*=(Elem m){ return times(m); }
Fps operator*(Elem m) const { return (clip() *= m).move(); }
Elem eval(Elem x) const {
Elem res = 0;
for(int i=size()-1; i>=0; i--) res = res * x + a[i];
return res;
}
};
template<class Elem, class NttInst> Comb<Elem> FpsNtt<Elem, NttInst>::comb;
template<class Elem, class NttInst> const NttInst FpsNtt<Elem, NttInst>::nttInst;
} // namespace nachia
#include <tuple>
namespace nachia{
template<class Fps>
Fps PolynomialTaylorShift(Fps f, typename Fps::ElemTy c){
int n = f.size();
Fps C = Fps(n).set(0,1);
for(int i=1; i<n; i++) C[i] = C[i-1] * c;
return f.EgfToOgf().convolve(C.OgfToEgf().reverse()).clip(n-1,2*n-1).OgfToEgf().move();
}
} // namespace nachia
namespace nachia {
template<class Elem>
std::vector<Elem> MontmortNumberMod(int maxN){
std::vector<Elem> A(maxN+1);
A[0] = Elem(1);
for(int i=2; i<=maxN; i++) A[i] = (A[i-1] + A[i-2]) * Elem(i-1);
return A;
}
template<class Elem>
FpsNtt<Elem> PartitionFunctionMod(int maxN){
FpsNtt<Elem> A(maxN+1);
Elem One = Elem::raw(1);
for(long long i=-2; i*(3*i-1)/2<=maxN; i-=2) A[i*(3*i-1)/2] += One;
for(long long i=-1; i*(3*i-1)/2<=maxN; i-=2) A[i*(3*i-1)/2] -= One;
for(long long i=0; i*(3*i-1)/2<=maxN; i+=2) A[i*(3*i-1)/2] += One;
for(long long i=1; i*(3*i-1)/2<=maxN; i+=2) A[i*(3*i-1)/2] -= One;
return A.inv();
}
template<class Elem>
FpsNtt<Elem> BernoulliNumberMod(int maxN){
using Fps = FpsNtt<Elem>;
Fps::GetComb().extend(maxN+1);
Fps A(maxN+1);
for(int i=0; i<=maxN; i++) A[i] = Fps::GetComb().invFactorial(i+1);
A = A.inv();
for(int i=1; i<=maxN; i++) A[i] *= Fps::GetComb().factorial(i);
return A;
}
} // namespace nachia
using Fps = nachia::FpsNtt<Modint>;
pair<string, int> modBigint(string s, int d){
string res;
int f = 0;
for(char c : s){
f = f * 10 + (c-'0');
if(f >= d || !res.empty()) res.push_back('0' + f/d);
f %= d;
}
return make_pair(move(res), f);
}
void testcase(){
int N; cin >> N;
vec<int> A(N-1); cin >> A;
string M; cin >> M;
Fps dp = Fps(1).set(0,1);
Fps B = nachia::BernoulliNumberMod<Modint>(N+5).OgfToEgf().move();
int D = 1;
for(int a : A){
int d = 0;
tie(M, d) = modBigint(move(M), a);
dp = nachia::PolynomialTaylorShift(dp, d+1);
Modint q = 1;
for(int i=1; i<dp.size(); i++){ q *= a; dp[i] *= q; }
dp.EgfToOgf().reverse();
dp *= B.clip(0, D+1);
dp = dp.capSize(D+1).reverse().OgfToEgf().set(0,0).move();
D++;
}
Modint x = 0;
for(char c : M) x = x * 10 + (c-'0');
cout << dp.eval(x+1).val() << endl;
}
int main(){
ios::sync_with_stdio(false); cin.tie(nullptr);
#ifdef NACHIA
int T; cin >> T; for(int t=0; t<T; T!=++t?(cout<<'\n'),0:0)
#endif
testcase();
return 0;
}