結果

問題 No.137 貯金箱の焦り
ユーザー momoyuumomoyuu
提出日時 2023-10-24 18:30:00
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 4,100 ms / 5,000 ms
コード長 11,421 bytes
コンパイル時間 5,235 ms
コンパイル使用メモリ 306,680 KB
実行使用メモリ 16,808 KB
最終ジャッジ日時 2024-09-24 11:31:54
合計ジャッジ時間 26,957 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 23
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include<bits/stdc++.h>
using namespace std;
using ll = long long;

template< int mod >
struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if((x += p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int) (1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while(n > 0) {
      if(n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) {
    return os << p.x;
  }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt< mod >(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt< 1234567891 >;
namespace FastFourierTransform {
  using real = long double;

  struct C {
    real x, y;

    C() : x(0), y(0) {}

    C(real x, real y) : x(x), y(y) {}

    inline C operator+(const C &c) const { return C(x + c.x, y + c.y); }

    inline C operator-(const C &c) const { return C(x - c.x, y - c.y); }

    inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); }

    inline C conj() const { return C(x, -y); }
  };

  const real PI = acosl(-1);
  int base = 1;
  vector< C > rts = { {0, 0},
                     {1, 0} };
  vector< int > rev = {0, 1};


  void ensure_base(int nbase) {
    if(nbase <= base) return;
    rev.resize(1 << nbase);
    rts.resize(1 << nbase);
    for(int i = 0; i < (1 << nbase); i++) {
      rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
    }
    while(base < nbase) {
      real angle = PI * 2.0 / (1 << (base + 1));
      for(int i = 1 << (base - 1); i < (1 << base); i++) {
        rts[i << 1] = rts[i];
        real angle_i = angle * (2 * i + 1 - (1 << base));
        rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
      }
      ++base;
    }
  }

  void fft(vector< C > &a, int n) {
    assert((n & (n - 1)) == 0);
    int zeros = __builtin_ctz(n);
    ensure_base(zeros);
    int shift = base - zeros;
    for(int i = 0; i < n; i++) {
      if(i < (rev[i] >> shift)) {
        swap(a[i], a[rev[i] >> shift]);
      }
    }
    for(int k = 1; k < n; k <<= 1) {
      for(int i = 0; i < n; i += 2 * k) {
        for(int j = 0; j < k; j++) {
          C z = a[i + j + k] * rts[j + k];
          a[i + j + k] = a[i + j] - z;
          a[i + j] = a[i + j] + z;
        }
      }
    }
  }

  vector< int64_t > multiply(const vector< int > &a, const vector< int > &b) {
    int need = (int) a.size() + (int) b.size() - 1;
    int nbase = 1;
    while((1 << nbase) < need) nbase++;
    ensure_base(nbase);
    int sz = 1 << nbase;
    vector< C > fa(sz);
    for(int i = 0; i < sz; i++) {
      int x = (i < (int) a.size() ? a[i] : 0);
      int y = (i < (int) b.size() ? b[i] : 0);
      fa[i] = C(x, y);
    }
    fft(fa, sz);
    C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
    for(int i = 0; i <= (sz >> 1); i++) {
      int j = (sz - i) & (sz - 1);
      C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
      fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
      fa[i] = z;
    }
    for(int i = 0; i < (sz >> 1); i++) {
      C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
      C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];
      fa[i] = A0 + A1 * s;
    }
    fft(fa, sz >> 1);
    vector< int64_t > ret(need);
    for(int i = 0; i < need; i++) {
      ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
    }
    return ret;
  }
};
template< typename T >
struct ArbitraryModConvolution {
  using real = FastFourierTransform::real;
  using C = FastFourierTransform::C;

  ArbitraryModConvolution() = default;

  vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) {
    if(need == -1) need = a.size() + b.size() - 1;
    int nbase = 0;
    while((1 << nbase) < need) nbase++;
    FastFourierTransform::ensure_base(nbase);
    int sz = 1 << nbase;
    vector< C > fa(sz);
    for(int i = 0; i < a.size(); i++) {
      fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15);
    }
    fft(fa, sz);
    vector< C > fb(sz);
    if(a == b) {
      fb = fa;
    } else {
      for(int i = 0; i < b.size(); i++) {
        fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15);
      }
      fft(fb, sz);
    }
    real ratio = 0.25 / sz;
    C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
    for(int i = 0; i <= (sz >> 1); i++) {
      int j = (sz - i) & (sz - 1);
      C a1 = (fa[i] + fa[j].conj());
      C a2 = (fa[i] - fa[j].conj()) * r2;
      C b1 = (fb[i] + fb[j].conj()) * r3;
      C b2 = (fb[i] - fb[j].conj()) * r4;
      if(i != j) {
        C c1 = (fa[j] + fa[i].conj());
        C c2 = (fa[j] - fa[i].conj()) * r2;
        C d1 = (fb[j] + fb[i].conj()) * r3;
        C d2 = (fb[j] - fb[i].conj()) * r4;
        fa[i] = c1 * d1 + c2 * d2 * r5;
        fb[i] = c1 * d2 + c2 * d1;
      }
      fa[j] = a1 * b1 + a2 * b2 * r5;
      fb[j] = a1 * b2 + a2 * b1;
    }
    fft(fa, sz);
    fft(fb, sz);
    vector< T > ret(need);
    for(int i = 0; i < need; i++) {
      int64_t aa = llround(fa[i].x);
      int64_t bb = llround(fb[i].x);
      int64_t cc = llround(fa[i].y);
      aa = T(aa).x, bb = T(bb).x, cc = T(cc).x;
      ret[i] = aa + (bb << 15) + (cc << 30);
    }
    return ret;
  }
};



#include<atcoder/modint>
#include<atcoder/convolution>
using mint = atcoder::modint;

ArbitraryModConvolution< modint > fft;
vector<mint> conv(vector<mint>a,vector<mint>b){
    int n = a.size();
    int m = b.size();
    vector<modint> A(n),B(m);
    for(int i = 0;i<n;i++) A[i] = a[i].val();
    for(int i = 0;i<m;i++) B[i] = b[i].val();
    auto C = fft.multiply(A,B);
    vector<mint> res(n+m-1,0);
    for(int i = 0;i<n+m-1;i++) res[i] = C[i].x;
    return res;
}
ostream& operator<<(ostream& os, const mint& m){
    os << m.val();
    return os;
}

template < typename mint >
struct FPS:vector<mint>{
    FPS(){}
    FPS(int n){
        this->resize(n);
    }
    FPS(vector<mint>a){
        *this = a;
    }
    FPS &operator+=(const FPS&r){
        if(r.size()>this->size()) this->resize(r.size());
        for(int i = 0;i<(int)r.size();i++) (*this)[i] += r[i];
        return *this;
    }
    FPS &operator+=(const mint&r){
        if(this->empty()) this->resize(1);
        (*this)[0] += r;
        return *this;
    }
    FPS &operator-=(const FPS&r){
        if(r.size()>this->size()) this->resize(r.size());
        for(int i = 0;i<(int)r.size();i++) (*this)[i] -= r[i];
        return *this;
    }
    FPS &operator-=(const mint&r){
        if(this->empty()) this->resize(1);
        (*this)[0] -= r;
        return *this;
    }
    FPS &operator*=(const FPS&r){
        vector<mint> nxt = conv(*this,r);
        this->resize(nxt.size());
        for(int i = 0;i<nxt.size();i++) (*this)[i] = nxt[i];
        return *this;
    }
    FPS &operator*=(const mint&r){
        for(int i = 0;i<(int)this->size();i++) (*this)[i] *= r;
        return *this;
    }
    FPS operator+(const FPS&r) const {return FPS(*this)+=r;}
    FPS operator+(const mint&r) const {return FPS(*this)+=r;}
    FPS operator-(const FPS&r) const {return FPS(*this)-=r;}
    FPS operator-(const mint&r) const {return FPS(*this)-=r;}
    FPS operator*(const FPS&r) const {return FPS(*this)*=r;}

    void print(){
        for(int i = 0;i<(int)this->size();i++){
            if(i) cout<<" ";
            cout<<(*this)[i];
        }
        cout<<endl;
    }

    int deg(){return (int)this->size()-1;}

    // f^-1 mod x^n
    FPS<mint> inv(int n){
        assert((*this)[0].val()!=0);
        FPS<mint> g(1);
        g[0] = 1/(*this)[0];
        ll now = 1;
        FPS<mint> tmp(1);
        tmp[0] = 2;
        while(now<n){
            g = g * (tmp-g*(*this));
            now <<= 1;
            if(g.size()>now) g.resize(now);
        }
        g.resize(n);
        return g;
    }

    FPS<mint> diff(){
        FPS<mint>g(this->size()-1);
        for(int i = 0;i+1<this->size();i++) g[i] = mint(i+1) * (*this)[i+1];
        return g;
    }

    FPS<mint> integral(){
        FPS<mint>g(this->size()+1);
        g[0] = 0;
        for(int i = 1;i<=this->size();i++) g[i] = (*this)[i-1] / mint(i);
        return g;
    }

    FPS<mint> log(int n){
        assert((*this)[0].val()==1);
        return ((*this).diff() * (*this).inv(n-1)).integral();
    }

    FPS<mint> exp(int n){
        assert((*this)[0].val()==0);
        FPS<mint> g(1);
        g[0] = 1;
        ll now = 1;
        FPS<mint> tmp(1);
        tmp[0] = 1;
        while(now<n){
            g = g * ((*this) + tmp - g.log(now<<1));
            now <<= 1;
            if(g.size()>now) g.resize(now);
        }
        return g;
    }
    
};

template < typename mint >
FPS<mint> pow(FPS<mint>&a,ll k,int n){
    FPS<mint> ans(n+1);
    ans[0] += 1;
    FPS<mint> tmp = a;
    tmp.resize(n+1);
    while(k){
        if(k&1){
            ans *= tmp;
            ans.resize(n+1);
        }
        tmp *= tmp;
        tmp.resize(n+1);
        k>>=1;
    }
    return ans;
}
//[x^n] P(x)/Q(x)
template< typename mint >
mint Bostan_Mori(FPS<mint>&p,FPS<mint>&q,ll n){
    if(n==0) return p[0];
    int d = q.deg();
    assert(p.deg()<d);
    FPS<mint> qi = q;
    for(int i = 0;i<qi.size();i++) if(i%2==1) qi[i] *= -1;
    p *= qi;
    q *= qi;
    for(int i = 0;i*2<q.size();i++) q[i] = q[i*2];
    q.resize((int)(q.size()+1)/2);
    assert(q.deg()==d);
    if(n%2==0){
        for(int i = 0;i*2<p.size();i++) p[i] = p[i*2];
        p.resize((int)(p.size()+1)/2);
        return Bostan_Mori(p,q,n/2);
    }else{
        for(int i = 0;i*2+1<p.size();i++) p[i] = p[i*2+1];
        p.resize((int)p.size()/2);
        return Bostan_Mori(p,q,(n-1)/2);
    }
}
template < typename mint >
FPS<mint> all_mul(vector<FPS<mint>>&fs){
    while(true){
        int n = fs.size();
        if(n==1) break;
        int m = (n+1)/2;
        for(int i = 0;i<m;i++){
            if(2*i+1==n) fs[i] = fs[2*i];
            else fs[i] = fs[2*i] * fs[2*i+1];
        }
        fs.resize(m);
    }
    return fs[0];
}

int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false); 

    mint::set_mod(1234567891);

    ll n,m;
    cin>>n>>m;
    vector<FPS<mint>> fs;
    for(int i = 0;i<n;i++){
        int a;
        cin>>a;
        FPS<mint> g(a+1);
        g[0] = 1;
        g[a] = -1;
        fs.push_back(g);
    }
    auto f = all_mul(fs);
    FPS<mint> g(1);
    g[0] = 1;
    cout<<Bostan_Mori(g,f,m)<<endl;
}
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