結果
問題 | No.2580 Hyperinflation |
ユーザー |
👑 ![]() |
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 |
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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 nachianamespace 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 nachianamespace nachia{int Popcount(unsigned long long c) noexcept {#ifdef __GNUC__return __builtin_popcountll(c);#elsec = (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 != 0int MsbIndex(unsigned long long x) noexcept {#ifdef __GNUC__return 63 - __builtin_clzll(x);#elseusing 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) & 0xfreturn q;#endif}// please ensure x != 0int LsbIndex(unsigned long long x) noexcept {#ifdef __GNUC__return __builtin_ctzll(x);#elsereturn 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 nachianamespace 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 nachianamespace 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 2Elem 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 - srcLFps 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-fFps 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 nachianamespace 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 nachiausing 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 NACHIAint T; cin >> T; for(int t=0; t<T; T!=++t?(cout<<'\n'),0:0)#endiftestcase();return 0;}