結果

問題 No.1861 Required Number
ユーザー ytqm3ytqm3
提出日時 2022-11-13 16:48:35
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 44 ms / 2,500 ms
コード長 18,224 bytes
コンパイル時間 5,622 ms
コンパイル使用メモリ 298,104 KB
実行使用メモリ 26,972 KB
最終ジャッジ日時 2024-09-14 23:03:34
合計ジャッジ時間 10,785 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
このコードへのチャレンジ
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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 39 ms
26,732 KB
testcase_01 AC 41 ms
26,764 KB
testcase_02 AC 38 ms
26,808 KB
testcase_03 AC 43 ms
26,796 KB
testcase_04 AC 44 ms
26,812 KB
testcase_05 AC 39 ms
26,688 KB
testcase_06 AC 38 ms
26,628 KB
testcase_07 AC 41 ms
26,896 KB
testcase_08 AC 39 ms
26,816 KB
testcase_09 AC 40 ms
26,712 KB
testcase_10 AC 39 ms
26,812 KB
testcase_11 AC 40 ms
26,824 KB
testcase_12 AC 41 ms
26,900 KB
testcase_13 AC 42 ms
26,720 KB
testcase_14 AC 40 ms
26,668 KB
testcase_15 AC 39 ms
26,636 KB
testcase_16 AC 40 ms
26,684 KB
testcase_17 AC 41 ms
26,884 KB
testcase_18 AC 40 ms
26,868 KB
testcase_19 AC 41 ms
26,784 KB
testcase_20 AC 41 ms
26,804 KB
testcase_21 AC 39 ms
26,700 KB
testcase_22 AC 42 ms
26,860 KB
testcase_23 AC 39 ms
26,668 KB
testcase_24 AC 41 ms
26,760 KB
testcase_25 AC 43 ms
26,856 KB
testcase_26 AC 40 ms
26,768 KB
testcase_27 AC 41 ms
26,788 KB
testcase_28 AC 41 ms
26,832 KB
testcase_29 AC 40 ms
26,760 KB
testcase_30 AC 41 ms
26,720 KB
testcase_31 AC 44 ms
26,880 KB
testcase_32 AC 41 ms
26,784 KB
testcase_33 AC 43 ms
26,972 KB
testcase_34 AC 43 ms
26,844 KB
testcase_35 AC 44 ms
26,892 KB
testcase_36 AC 42 ms
26,752 KB
testcase_37 AC 41 ms
26,832 KB
testcase_38 AC 43 ms
26,848 KB
testcase_39 AC 42 ms
26,792 KB
testcase_40 AC 44 ms
26,784 KB
testcase_41 AC 43 ms
26,780 KB
testcase_42 AC 42 ms
26,784 KB
testcase_43 AC 41 ms
26,824 KB
testcase_44 AC 38 ms
26,728 KB
04_evil_1.txt AC 526 ms
37,912 KB
04_evil_2.txt AC 522 ms
37,912 KB
04_evil_3.txt AC 520 ms
37,912 KB
04_evil_4.txt AC 520 ms
37,912 KB
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>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif

namespace ttl{

using namespace std;
using f80=long double;
using i64=int64_t;
using u64=uint64_t;

template<int mod> struct mymodint{
  i64 vl;
  static constexpr i64 get_mod(){ return mod; }
  i64 val(){ return vl; }
  mymodint(i64 vl_=0):vl(vl_%mod){}
  mymodint operator-(){ return (vl==0)?0:mod-vl; }
  mymodint operator+(mymodint rhs){ return mymodint(*this)+=rhs; }
  mymodint operator-(mymodint rhs){ return mymodint(*this)-=rhs; }
  mymodint operator*(mymodint rhs){ return mymodint(*this)*=rhs; }
  mymodint operator/(mymodint rhs){ return mymodint(*this)/=rhs; }
  mymodint pow(i64 rhs){
    mymodint res=1,now=(*this);
    while(rhs){
      res*=((rhs&1)?now:1),now*=now,rhs>>=1;
    }
    return res;
  }
  mymodint& operator+=(mymodint rhs){
    vl+=rhs.vl,vl-=((vl>=mod)?mod:0);
    return (*this);
  }
  mymodint& operator-=(mymodint rhs){
    vl+=((vl<rhs.vl)?mod:0),vl-=rhs.vl;
    return (*this);
  }
  mymodint& operator*=(mymodint rhs){
    vl=vl*rhs.vl%mod;
    return (*this);
  }
  mymodint& operator/=(mymodint rhs){ return (*this)*=rhs.pow(mod-2); }
  bool operator==(mymodint rhs){ return vl==rhs.vl; }
  bool operator!=(mymodint rhs){ return vl!=rhs.vl; }
};

template<u64 mod> using modint=
#if __has_include(<atcoder/all>)
  atcoder::static_modint<mod>;
#else
  mymodint<mod>;
#endif

template<int mod> std::ostream& operator<<(std::ostream& os,modint<mod> x){
  return os<<(x.val());
}
template<int mod> std::istream& operator>>(std::istream& is,modint<mod>& x){
  i64 t;
  is>>t,x=t;
  return is;
}

template<class T> void scn_(T& a){ cin>>a; }
template<class T,class U> void scn_(pair<T,U>& a){ scn_(a.first),scn_(a.second); }
template<class T> void scn_(vector<T>& a){
  for(auto& v:a){
    scn_(v);
  }
}
template<class T> void scn_(vector<vector<T>>& a){
  for(auto& v:a){
    for(auto& u:v){
      cin>>u;
    }
  }
}
void scn(){}
template<class T,class... Args> void scn(T& n,Args&... args){ scn_(n),scn(args...); }
template<class T> void prt_(T a){ cout<<a; }
template<class T,class U> void prt_(pair<T,U> a){ cout<<"{"<<a.first<<", "<<a.second<<"}"; }
void prt_(f80 a){ printf("%.15Lf",a); }
template<class T> void prt(vector<T> a){
  for(size_t i=0;i<a.size();++i){
    prt_(a[i]);
    cout<<" \n"[i==a.size()-1];
  }
}
template<class T> void prt(vector<vector<T>> a){
  for(auto& v:a){
    for(size_t i=0;i<v.size();++i){
      cout<<v[i]<<" \n"[i==v.size()-1];
    }
  }
}
template<class T> void prt(T a){ prt_(a),cout<<"\n"; }
template<class T,class... Args> void prt(T a,Args... args){ prt_(a),cout<<" ",prt(args...); }

template<class Head,class... Tail> struct multi_dim_vector{ using type=vector<typename multi_dim_vector<Tail...>::type>; };
template<class T> struct multi_dim_vector<T>{ using type=T; };
template<class T,class Arg> vector<T> mvec(int n,Arg&& arg){ return vector<T>(n,arg); }
template<class T,class... Args> class multi_dim_vector<Args...,T>::type mvec(int n,Args&&... args){
  return typename multi_dim_vector<Args...,T>::type(n,mvec<T>(args...));
}

template<class T> void rev(T& a){ reverse(a.begin(),a.end());}
template<class T> void srt(T& a){ sort(a.begin(),a.end()); }
template<class T> void rsrt(T& a){ sort(a.rbegin(),a.rend()); }
template<class T> T revd(T a){
  reverse(a.begin(),a.end());
  return a;
}
template<class T> T srtd(T a){
  sort(a.begin(),a.end());
  return a;
}
template<class T> T rsrtd(T a){
  sort(a.rbegin(),a.rend());
  return a;
}
template<class T> T summ(vector<T> a){ return accumulate(a.begin(),a.end(),T(0)); }
template<class T> T maxi(vector<T> a){ return *max_element(a.begin(),a.end()); }
template<class T> T mini(vector<T> a){ return *min_element(a.begin(),a.end()); }
template<class T> void chmx(T& a,T b){ a=max(a,b); }
template<class T> void chmn(T& a,T b){ a=min(a,b); }
i64 ppcnt(u64 k){ return __builtin_popcountll(k); }
template<class T> T powe(T a,i64 n){
  T res=1;
  while(n){
    if(n&1){ res*=a; }
    a*=a;
    n/=2;
  }
  return res;
}
i64 powe(i64 a,i64 n,i64 m){
  i64 res=1;
  while(n){
    if(n&1){ res=res*a%m; }
    a=a*a%m;
    n/=2;
  }
  return res;
}
template<class T> void zip(vector<T>& a){
  auto b=srtd(a);
  b.erase(unique(b.begin(),b.end()),b.end());
  map<T,int> mp;
  for(int i=0;i<b.size();++i){
    mp[b[i]]=i;
  }
  for(auto& v:a){
    v=mp[v];
  }
}
i64 sqrf(i64 n){
  i64 ok=0,ng=1e9+5;
  while(std::abs(ok-ng)>1){
    i64 mid=(ok+ng)/2;
    (mid*mid<=n?ok:ng)=mid;
  }
  return ok;
}
i64 sqrc(i64 n){
  i64 ok=1e9+5,ng=0;
  while(std::abs(ok-ng)>1){
    i64 mid=(ok+ng)/2;
    (mid*mid>=n?ok:ng)=mid;
  }
  return ok;
}
i64 dvf(i64 a,i64 b){
  if(b<0){ a*=-1,b*=-1; }
  if(a<0){ return -(-a+b-1)/b; }
  return a/b;
}
i64 dvc(i64 a,i64 b){
  if(b<0){ a*=-1,b*=-1; }
  if(a<0){ return -(-a)/b; }
  return (a+b-1)/b;
}
vector<int> bfs(vector<vector<int>> G,int v){
  int N=G.size();
  vector<int> dst(N,-1);
  queue<int> q;
  dst[v]=0;
  q.emplace(v);
  while(q.size()){
    int t=q.front();
    q.pop();
    for(auto u:G[t]){
      if(dst[u]==-1){
        dst[u]=dst[t]+1;
        q.emplace(u);
      }
    }
  }
  return dst;
}
vector<i64> dijkstra(vector<vector<pair<int,i64>>>& G,int s){
  int N=G.size();
  vector<i64> dst(N,1e18);
  dst[s]=0;
  priority_queue<pair<i64,int>,vector<pair<i64,int>>,greater<pair<i64,int>>> pq;
  pq.emplace(0,s);
  vector<int> f(N);
  while(pq.size()){
    auto [t,u]=pq.top();
    pq.pop();
    if(f[u]){ continue; }
    f[u]=1;
    for(auto [v,w]:G[u]){
      if(dst[v]>dst[u]+w){
        dst[v]=dst[u]+w;
        pq.emplace(dst[v],v);
      }
    }
  }
  return dst;
}
vector<pair<i64,i64>> pfct(i64 n){
  vector<pair<i64,i64>> res;
  for(i64 i=2;i*i<=n;++i){
    if(n%i!=0){ continue; }
    i64 ex=0;
    while(n%i==0){ ex++,n/=i; }
    res.emplace_back(i,ex);
  }
  if(n!=1){ res.emplace_back(n,1); }
  return res;
}
vector<i64> ediv(i64 n){
  vector<i64> res;
  for(i64 i=1;i*i<=n;++i){
    if(n%i!=0){ continue; }
    res.emplace_back(i);
    if(i*i!=n){ res.emplace_back(n/i); }
  }
  srt(res);
  return res;
}
template<class T> struct csm2d{
  int n,m;
  vector<vector<T>> a,c;
  csm2d(vector<vector<T>> a_):n(a_.size()),m(a_[0].size()),a(a_){
    auto b=mvec<T>(n,m+1,0);
    for(int i=0;i<n;++i){
      for(int j=0;j<m;++j){
        b[i][j+1]=b[i][j]+a[i][j];
      }
    }
    c=mvec<T>(n+1,m+1,0);
    for(int j=0;j<m+1;++j){
      for(int i=0;i<n;++i){
        c[i+1][j]=c[i][j]+b[i][j];
      }
    }
  }
  T operator()(int p,int q,int r,int s){
    return c[p][r]-c[p][s]-c[q][r]+c[q][s];
  }
};
template<class T> auto runlng(T a) -> vector<pair<typename decltype(a)::value_type,i64>>{
  int n=a.size();
  vector<pair<typename decltype(a)::value_type,i64>> res;
  typename decltype(a)::value_type now=a[0];
  i64 l=1;
  for(int i=1;i<n;++i){
    if(a[i-1]==a[i]){ l++; }
    else{
      res.emplace_back(now,l);
      now=a[i],l=1;
    }
  }
  res.emplace_back(now,l);
  return res;
}
template<class T> struct cmb{
  vector<T> fac,ifac;
  cmb(int mx=3000000):fac(mx+1,1),ifac(mx+1,1){
    for(int i=1;i<=mx;++i){ fac[i]=fac[i-1]*i; }
    ifac[mx]/=fac[mx];
    for(int i=mx;i>0;--i){ ifac[i-1]=ifac[i]*i; }
  }
  T operator()(i64 n,i64 k){
    if(n<0||k<0||n<k){ return 0; }
    return fac[n]*ifac[k]*ifac[n-k];
  }
  T f(i64 n){
    return n<0?T(0):fac[n];
  }
  T fi(i64 n){
    return n<0?T(0):ifac[n];
  }
};

}

using namespace ttl;

template<class mint> struct Poly{
  vector<mint> val;
  Poly():val({0}){}
  Poly(mint t):val({t}){}
  Poly(int siz):val(max(1,siz)){}
  Poly(initializer_list<mint> init):val(init){}
  Poly(vector<mint> init):val(init){}
  mint &operator[](int i){
    return val[i];
  }
  int size(){
    return val.size();
  }
  void resize(int siz){
    val.resize(siz);
  }
  void shrink(){
    for(int i=val.size()-1;i>0;--i){
      if(val[i]==0){
        val.pop_back();
      }
      else{
        return;
      }
    }
  }
  Poly operator+(Poly rhs){
    return Poly(*this)+=rhs;
  }
  Poly operator-(Poly rhs){
    return Poly(*this)-=rhs;
  }
  Poly operator*(Poly rhs){
    return Poly(*this)*=rhs;
  }
  Poly operator/(Poly rhs){
    return Poly(*this)/=rhs;
  }
  Poly operator%(Poly rhs){
    return Poly(*this)%=rhs;
  }
  Poly operator-(){
    for(mint& v:val){
      v=mint(0)-v;
    }
    return (*this);
  }
  Poly operator+=(Poly rhs){
    resize(max(this->size(),rhs.size()));
    for(int i=0;i<int(rhs.size());++i){
      (*this)[i]+=rhs[i];
    }
    shrink();
    return (*this);
  }
  Poly operator-=(Poly rhs){
    resize(max(this->size(),rhs.size()));
    for(int i=0;i<int(rhs.size());++i){
      (*this)[i]-=rhs[i];
    }
    shrink();
    return (*this);
  }
  Poly operator*=(Poly rhs){
    val=atcoder::convolution(val,rhs.val);
    return (*this);
  }
  Poly operator/=(Poly rhs){
    if(val.size()<rhs.size()){
      val.resize(0);
      return (*this);
    }
    int rsiz=val.size()-rhs.size()+1;
    reverse(val.begin(),val.end());
    reverse(rhs.val.begin(),rhs.val.end());
    val.resize(rsiz),rhs.inv(rsiz);
    (*this)*=rhs;
    val.resize(rsiz);
    reverse(val.begin(),val.end());
    return (*this);
  }
  Poly operator%=(Poly rhs){
    if(val.size()<rhs.size()){
      return (*this);
    }
    (*this)-=(*this)/rhs*rhs;
    val.resize(rhs.size()-1);
    shrink();
    return (*this);
  }
  mint eval(mint a){
    mint t=1,res=0;
    int n=(*this).size();
    for(int i=0;i<n;++i){
      res+=val[i]*t;
      t*=a;
    }
    return res;
  }
  void diffrent(){
    Poly f(val.size()-1);
    for(int i=1;i<val.size();++i){
      f[i-1]=val[i]*i;
    }
    (*this)=f;
  }
  void integral(){
    Poly f(val.size()+1);
    for(int i=0;i<val.size();++i){
      f[i+1]=val[i]/(i+1);
    }
    (*this)=f;
  }
  void inv(int mx){
    Poly g({mint(1)/val[0]});
    int now=1;
    while(now<mx){
      now<<=1;
      Poly t=(*this);
      t.resize(now);
      t*=g,t=-t;
      t[0]+=2,g*=t;
      g.resize(now);
    }
    g.resize(mx);
    (*this)=g;
  }
  vector<mint> MultiEval(vector<mint> a){
    int siz=1;
    while(siz<int(a.size())){
      siz<<=1;
    }
    vector<Poly> t(siz*2-1,{1});
    for(int i=0;i<int(a.size());++i){
      t[i+siz-1]={-a[i],1};
    }
    for(int i=siz-2;i>=0;--i){
      t[i]=t[2*i+1]*t[2*i+2];
    }
    vector<Poly> g(siz*2-1);
    g[0]=(*this)%t[0];
    for(int i=1;i<siz*2-1;++i){
      g[i]=g[(i-1)/2]%t[i];
    }
    vector<mint> res(a.size());
    for(int i=0;i<int(a.size());++i){
      res[i]=g[i+siz-1][0];
    }
    return res;
  }
  void TaylorShift(mint c){
    cmb<mint> C(val.size());
    vector<mint> g(val.size());
    mint now=1;
    for(size_t i=0;i<val.size();++i){
      val[i]*=C.dat[i];
      g[i]=now*C.idat[i];
      now*=c;
    }
    reverse(val.begin(),val.end());
    g=atcoder::convolution(val,g);
    g.resize(val.size());
    reverse(g.begin(),g.end());
    for(size_t i=0;i<val.size();++i){
      g[i]*=C.idat[i];
    }
    val=g;
  }
  void LagrangeInterpolation(vector<mint> x,vector<mint> y){
    int N=x.size();
    vector<Poly> h(N);
    for(int i=0;i<N;++i){
      h[i]={-x[i],1};
    }
    auto g=Product(h);
    auto g_=g;
    g_.diffrent();
    vector<mint> t=g_.MultiEval(x);
    for(int i=0;i<N;++i){
      t[i]=y[i]/t[i];
    }
    vector<Poly> den(2*N-1),num(2*N-1,{1});
    for(int i=0;i<N;++i){
      den[i+N-1]={-x[i],1};
      num[i+N-1]={t[i]};
    }
    for(int i=N-2;i>=0;--i){
      den[i]=den[2*i+1]*den[2*i+2];
      num[i]=num[2*i+1]*den[2*i+2]+num[2*i+2]*den[2*i+1];
    }
    (*this)=num[0];
  }
};

template<class mint> struct FPS{
  vector<mint> val;
  FPS():val({0}){}
  FPS(mint t):val({t}){}
  FPS(int siz):val(max(1,siz)){}
  FPS(initializer_list<mint> init):val(init){}
  FPS(vector<mint> init):val(init){}
  mint &operator[](int i){
    return val[i];
  }
  int size(){
    return val.size();
  }
  void resize(int siz){
    val.resize(siz);
  }
  FPS& resize_(int siz){
    auto tmp=val;
    tmp.resize(siz);
    return (*this)=tmp;
  }
  FPS operator-(){
    for(mint& v:val){
      v=mint(0)-v;
    }
    return (*this);
  }
  FPS& operator+=(mint rhs){
    val[0]+=rhs;
    return (*this);
  }
  FPS& operator-=(mint rhs){
    val[0]-=rhs;
    return (*this);
  }
  FPS& operator*=(mint rhs){
    for(auto& v:val){
      v*=rhs;
    }
    return (*this);
  }
  FPS& operator/=(mint rhs){
    for(auto& v:val){
      v/=rhs;
    }
    return (*this);
  }
  FPS operator+(mint rhs){
    return FPS(*this)+=rhs;
  }
  FPS operator-(mint rhs){
    return FPS(*this)-=rhs;
  }
  FPS operator*(mint rhs){
    return FPS(*this)*=rhs;
  }
  FPS operator/(mint rhs){
    return FPS(*this)/=rhs;
  }
  FPS& operator+=(FPS rhs){
    resize(max(this->size(),rhs.size()));
    for(size_t i=0;i<rhs.size();++i){
      (*this)[i]+=rhs[i];
    }
    return (*this);
  }
  FPS& operator-=(FPS rhs){
    resize(max(this->size(),rhs.size()));
    for(size_t i=0;i<rhs.size();++i){
      (*this)[i]-=rhs[i];
    }
    return (*this);
  }
  FPS& operator*=(FPS rhs){
    val=atcoder::convolution(val,rhs.val);
    return (*this);
  }
  FPS& operator/=(FPS rhs){
    return (*this)*=rhs.inv();
  }
  FPS& operator>>=(int k){
    if(int(val.size())<=k){
      return (*this)={0};
    }
    FPS res=val;
    res.val.erase(res.val.begin(),res.val.begin()+k);
    return (*this)=res;
  }
  FPS& operator<<=(int k){
    FPS res=val;
    res.val.insert(res.val.begin(),k,mint(0));
    return (*this)=res;
  }
  FPS operator+(FPS rhs){
    return FPS(*this)+=rhs;
  }
  FPS operator-(FPS rhs){
    return FPS(*this)-=rhs;
  }
  FPS operator*(FPS rhs){
    return FPS(*this)*=rhs;
  }
  FPS operator/(FPS rhs){
    return FPS(*this)/=rhs;
  }
  FPS operator%(FPS rhs){
    return FPS(*this)%=rhs;
  }
  FPS operator<<(int k){
    return FPS(*this)<<=k;
  }
  FPS operator>>(int k){
    return FPS(*this)>>=k;
  }
  FPS shrink(){
    for(int i=val.size()-1;i>0;--i){
      if(val[i]==0){
        val.pop_back();
      }
      else{
        break;
      }
    }
    return (*this);
  }
  FPS diff_(){
    if(val.size()==1){
      return (*this)={0};
    }
    FPS f(val.size()-1);
    for(size_t i=1;i<val.size();++i){
      f[i-1]=val[i]*i;
    }
    return f;
  }
  FPS integral_(){
    FPS f(val.size()+1);
    for(size_t i=0;i<val.size();++i){
      f[i+1]=val[i]/(i+1);
    }
    return f;
  }
  FPS inv_(i64 mx=-1){
    if(mx==-1){
      mx=val.size();
    }
    if(val[0]==0){
      assert(0);
    }
    FPS g({mint(1)/val[0]});
    i64 now=1;
    while(now<mx){
      now<<=1;
      FPS t=(*this);
      t.resize(now);
      t*=g;
      t=-t+mint(2);
      g*=t;
      g.resize(now);
    }
    g.resize(mx);
    return g;
  }
  FPS exp_(i64 mx=-1){
    if(mx==-1){
      mx=val.size();
    }
    if(val[0]!=0){
      assert(0);
    }
    FPS g(mint(1));
    i64 now=1;
    while(now<mx){
      now<<=1;
      FPS t=(*this);
      t.resize(now);
      g*=t-g.log_(now)+mint(1);
      g.resize(now);
    }
    g.resize(mx);
    return g;
  }
  FPS log_(i64 mx=-1){
    if(mx==-1){
      mx=val.size();
    }
    if(val[0]!=1){
      assert(0);
    }
    auto f=(*this);
    f.resize(mx);
    return (f.diff_()/f).integral_().resize_(mx);
  }
  FPS pow_(i64 k,int mx=-1){
    if(mx==-1){
      mx=val.size();
    }
    i64 t=0;
    for(auto v:val){
      if(v==0){
        t++;
      }
      else{
        break;
      }
    }
    if(t==val.size()){
    	FPS res(mx);
    	if(k==0){ res[0]=1; }
    	return res;
    }
    auto f=(*this)>>t;
    if(f[0]==0){
      f={0},f.resize(mx);
      return f;
    }
    mint c=f[0];
    f/=c;
    (f.log(mx)*=mint(k)).exp(mx)*=(c.pow(k));
    if(k==0?true:(t<=mx/k)){
      f<<=t*k;
      f.resize(mx);
      return f;
    }
    else{
      f={0},f.resize(mx);
      return f;
    }
  }
  FPS& diff(){
    return (*this)=diff_();
  }
  FPS& integral(){
    return (*this)=integral_();
  }
  FPS& inv(i64 mx=-1){
    return (*this)=inv_(mx);
  }
  FPS& exp(i64 mx=-1){
    return (*this)=exp_(mx);
  }
  FPS& log(i64 mx=-1){
    return (*this)=log_(mx);
  }
  FPS& pow(i64 k,i64 mx=-1){
    return (*this)=pow_(k,mx);
  }
};


template<typename T> T Product(vector<T> a){
  int siz=1;
  while(siz<int(a.size())){
    siz<<=1;
  }
  vector<T> res(siz*2-1,{1});
  for(size_t i=0;i<a.size();++i){
    res[i+siz-1]=a[i];
  }
  for(int i=siz-2;i>=0;--i){
    res[i]=res[2*i+1]*res[2*i+2];
  }
  return res[0];
}

template<class mint> vector<mint> StirlingNumber2(int N){
  FPS<mint> f(N+1),g(N+1);
  mint fact=1;
  for(int i=0;i<=N;++i){
    f[i]=(mint(i).pow(N))/fact;
    g[i]=(mint(-1).pow(i))/fact;
    fact*=i+1;
  }
  f*=g;
  vector<mint> res(N+1);
  for(int i=0;i<=N;++i){
    res[i]=f[i];
  }
  return res;
}

template<class T> T Even(T f){
  T g((f.size()+1)/2);
  for(size_t i=0;i<(f.size()+1)/2;++i){
    g[i]=f[i*2];
  }
  return g;
}
 
template<class T> T Odd(T f){
  T g(f.size()/2);
  for(size_t i=0;i<f.size()/2;++i){
    g[i]=f[i*2+1];
  }
  return g;
}
 
template<class T> T Minus(T f){
  for(size_t i=1;i<f.size();i+=2){
    f[i]*=-1;
  }
  return f;
}

template<class mint> mint BostanMori(FPS<mint> f,FPS<mint> g,i64 k){
  while(k>0){
    if(k%2==0){
      f=Even(f*Minus(g));
    }
    else{
      f=Odd(f*Minus(g));
    }
    g=Even(g*Minus(g));
    k/=2;
  }
  return f[0]/g[0];
}

template<class mint> vector<mint> SubsetSum(int N,vector<int> A,int T){
  vector<mint> C(T+1);
  for(int i=0;i<N;++i){
    if(A[i]<=T){ C[A[i]]+=1; }
  }
  FPS<mint> f(T+1);
  for(int k=1;k<=T;++k){
    for(int i=1;i*k<=T;++i){
      f[i*k]-=C[k]/i*(i%2?-1:1);
    }
  }
  f.exp();
  vector<mint> res(T+1);
  for(int i=0;i<=T;++i){ res[i]=f[i]; }
  return res;
}


template<class mint> vector<mint> Montmort(int N){
  vector<mint> res(N+1);
  res[0]=1,res[1]=0;
  for(int n=2;n<=N;++n){
    res[n]=(res[n-2]+res[n-1])*(n-1);
  }
  return res;
}

int main(){
  constexpr int mod=998244353;
  using mint=modint<mod>;
  cmb<mint> Cb;
  int N,K;
  scn(N,K);
  vector<int> A(N);
  scn(A);
  auto V=SubsetSum<mint>(N,A,K);
  if(V[K]==0){ prt(-1); return 0; }
  vector<int> B(K+1);
  for(int i=0;i<N;++i){
  	B[A[i]]++;
  }
  int ans=0;
  for(int i=1;i<=K;++i){
  	mint s=0;
  	for(int j=0;i*j<=K;++j){
  		s+=V[K-i*j]*(j&1?-1:1);
  	}
  	if(s==0){ ans+=B[i]; }
  }
  prt(ans);
}
0