Submission #28870025

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Source Code Expand

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

#ifndef ONLINE_JUDGE
  #include "debug.h"
#endif

#define fast { ios :: sync_with_stdio(false); cin.tie(0); cout.tie(0); }
#define pb push_back
#define eb emplace_back
#define ll long long
#define ld long double
#define vll vector<ll>
#define infl LONG_LONG_MAX
#define infd LDBL_MAX
#define F first
#define S second
#define pll pair<ll,ll>
#define G(a,b) get<a>(b)
#define ALL(v) v.begin(),v.end()
#define MP make_pair
#define MT make_tuple
#define f(i,a,b) for(ll i=a;i<b;i++)
#define fi(i,a,b) for(ll i=(b-1);i>=a;i--)
#define nl cout<<"\n";
#define sz(x) (ll)x.size()
#define rem_dup(v) v.resize(unique(v.begin(), v.end()) - v.begin()) 

template<class T>
using min_heap = priority_queue<T,vector<T>,greater<T> >;

clock_t startTime;
double getCurrentTime() {
  return (double)(clock() - startTime) / CLOCKS_PER_SEC;
}

const ll N=1e5+5,p=998244353;

ll pow_mod_p(ll a,ll b)
{
   a=a%p;
   ll res=1;
   while(b>0)
   {
     if(b&1) res=(res*a)%p;
     b=b>>1;
     a=(a*a)%p;
   }
   return res;
}

inline ll mod_inv(ll x)
{
   return pow_mod_p(x,p-2);
}


ll n,k,a[N],fac[N],faci[N];

ll nCr(ll x,ll y){
  if(x<y) return 0;
  else if(x==y) return 1;
  ll den1=y,den2=x-y;
  if(den1<den2) swap(den1,den2);
  ll ans=1;
  f(i,den1+1,x+1){
    ans=(ans*i)%p;
  }
  ans=(ans*faci[den2])%p;
  return ans;
}

void func()
{
  cin>>n>>k;
  f(i,1,n+1) cin>>a[i];
  fac[0]=1;
  f(i,1,k+1) fac[i]=(fac[i-1]*i)%p;
  faci[k]=mod_inv(fac[k]);
  fi(i,0,k) faci[i]=(faci[i+1]*(i+1))%p;
  ll s=0;
  f(i,2,n+1){
    s+=a[i];
  }
  if(a[1]<s+k){
    cout<<"0\n";
    return;
  }
  ll rem=a[1]-s-k,ans=nCr(k+rem-1,rem);
  f(i,2,n+1) ans=(ans*nCr(k+a[i]-1,a[i]))%p;
  cout<<ans<<"\n";
} 


int main()
{
  startTime = clock();
  fast
  //#ifndef ONLINE_JUDGE
  //freopen("input.txt", "r", stdin);
  //freopen("output.txt", "w", stdout);
  //#endif // ONLINE_JUDGE
  cout<<fixed<<setprecision(10);

  int ntc=1;
  // cin>>ntc;

  f(i,1,ntc+1)
  {
    // cout<<"Case #"<<i<<": ";
    func();
    // clr();
  }
  // cout<<getCurrentTime()<<"\n";

  return 0;
}

Submission Info

Judge Result