Submission #1084117

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Source Code Expand

#include <string>
#include <vector>
#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<stack>
#include<queue>
#include<cmath>
#include<algorithm>
#include<functional>
#include<list>
#include<deque>
#include<bitset>
#include<set>
#include<map>
#include<unordered_map>
#include<unordered_set>
#include<cstring>
#include<sstream>
#include<complex>
#include<iomanip>
#include<numeric>
#include<cassert>
#define X first
#define Y second
#define pb push_back
#define rep(X,Y) for (int (X) = 0;(X) < (Y);++(X))
#define reps(X,S,Y) for (int (X) = S;(X) < (Y);++(X))
#define rrep(X,Y) for (int (X) = (Y)-1;(X) >=0;--(X))
#define repe(X,Y) for ((X) = 0;(X) < (Y);++(X))
#define peat(X,Y) for (;(X) < (Y);++(X))
#define all(X) (X).begin(),(X).end()
#define rall(X) (X).rbegin(),(X).rend()
#define eb emplace_back
#define UNIQUE(X) (X).erase(unique(all(X)),(X).end())
#define Endl endl

using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
template<class T> using vv=vector<vector<T>>;
template<class T> ostream& operator<<(ostream &os, const vector<T> &t) {
os<<"{"; rep(i,t.size()) {os<<t[i]<<",";} os<<"}"<<endl; return os;}
template<class S, class T> ostream& operator<<(ostream &os, const pair<S,T> &t) { return os<<"("<<t.first<<","<<t.second<<")";}
template<class T> inline bool MX(T &l,const T &r){return l<r?l=r,1:0;}
template<class T> inline bool MN(T &l,const T &r){return l>r?l=r,1:0;}
#define out(args...){vector<string> a_r_g_s=s_p_l_i_t(#args, ','); e_r_r(a_r_g_s.begin(), args); }
vector<string> s_p_l_i_t(const string& s, char c) { vector<string> v; stringstream ss(s); string x; while(getline(ss,x,c)) v.emplace_back(x); return move(v);}
void e_r_r(vector<string>::iterator it) {}
template<typename T, typename... Args> void e_r_r(vector<string>::iterator it, T a, Args... args){ if(*it==" 1"||*it=="1") cerr<<endl; else cerr << it -> substr((*it)[0] == ' ', it -> length()) << " = " << a << ", "; e_r_r(++it, args...);}
const ll MOD=1e9+7;

ll dp[2123][2123];
ll sum[2123][2123];
ll modpow(ll r,ll n,ll m=MOD){
  ll re=1,d=r%m;
  if(n<0)(n%=m-1)+=m-1;
  for(;n;n/=2){
    if(n&1)(re*=d)%=m;
    (d*=d)%=m;
  }
  return re;
}

int main(){
  ios_base::sync_with_stdio(false);
  cout<<fixed<<setprecision(0);
  int n,t;
  cin>>n>>t; --t;
  if(n==1){
    cout<<1<<endl;
    return 0;
  }
  int o=max(2,n-t);
  dp[o][1]=modpow(2,o-2);
  fill(sum[o]+1,sum[o]+2023,dp[o][1]);
  reps(i,o+1,n+1)rep(j,i){
    dp[i][j]=sum[i-1][j];
    (sum[i][j]+=dp[i][j])%=MOD;
    (sum[i][j+1]+=sum[i][j])%=MOD;
  }
  //rep(i,n+1){rep(j,n+1)cout<<dp[i][j]<<",";cout<<endl;}cout<<endl;
  // rep(i,n+1){rep(j,n+1)cout<<sum[i][j]<<",";cout<<endl;}
  cout<<sum[n][n-1]<<endl;
  return 0;
}
/*

100 100
676902861
*/
// int main(){
//   ios_base::sync_with_stdio(false);
//   cout<<fixed<<setprecision(0);
//   int n,t;
//   cin>>n>>t; --t;
//   dp[n-t][1]=modpow(2,max(0,n-t-2));
//   fill(sum[n-t]+1,sum[n-t]+2023,dp[n-t][1]);
//   reps(i,n-t+1,n+1)rep(j,i){
//     if(j+1==i){
//       (dp[i][j]+=sum[j][j-1])%=MOD;
//     }else{
//       (dp[i][j]+=dp[i-1][j])%=MOD;
//     }
//     if(j>1) (dp[i][j]+=sum[i-1][j-1])%=MOD;
//     (sum[i][j]+=dp[i][j])%=MOD;
//     (sum[i][j+1]+=sum[i][j])%=MOD;
//   }
//   rep(i,n+1){rep(j,n+1)cout<<dp[i][j]<<",";cout<<endl;}cout<<endl;
//   rep(i,n+1){rep(j,n+1)cout<<sum[i][j]<<",";cout<<endl;}
//   cout<<sum[n][n-1]<<endl;
//   return 0;
// }

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