There are N children, numbered 1, 2, \ldots, N.

They have decided to share K candies among themselves. Here, for each i (1 \leq i \leq N), Child i must receive between 0 and a_i candies (inclusive). Also, no candies should be left over.

Find the number of ways for them to share candies, modulo 10^9 + 7. Here, two ways are said to be different when there exists a child who receives a different number of candies.

Constraints

* All values in input are integers.
* 1 \leq N \leq 100
* 0 \leq K \leq 10^5
* 0 \leq a_i \leq K

Input

Input is given from Standard Input in the following format:


N K
a_1 a_2 \ldots a_N


Output

Print the number of ways for the children to share candies, modulo 10^9 + 7.

Examples

Input

3 4
1 2 3


Output

5


Input

1 10
9


Output

0


Input

2 0
0 0


Output

1


Input

4 100000
100000 100000 100000 100000


Output

665683269
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i,a) for(int i=0;i<(a);i++)
const ll MOD=1000000007;

int N,K,A[101010];
ll to[101010], from[101010];

int main(){
  cin>>N>>K;
  rep(i,N) cin>>A[i];
  from[0]=1;
  rep(i,N){
    fill(to,to+101010,0);
    for(int j=0;j<=K;j++){
      int k=min(K+1,j+A[i]+1);
      (to[j]+=from[j])%=MOD;
      to[k]=(to[k]-from[j]+MOD)%MOD;
    }
    rep(j,K) (to[j+1]+=to[j])%=MOD;
    swap(from,to);
  }
  cout<<from[K]<<endl;
  return 0;
}
