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;
const int MOD=1e9+7;
const int INF=1e9;

ll dp[101][100001];

int main(){
    int n,k;
    cin>>n>>k;
    int a[n];
    for(int i=0;i<n;i++){
        cin>>a[i];
    }
    dp[0][0]=1;
    for(int i=0;i<n;i++){
        dp[i+1][0]=1;
        for(int j=1;j<=a[i];j++){
            dp[i+1][j]=(dp[i+1][j-1]+dp[i][j])%MOD;
        }
        for(int j=a[i]+1;j<=k;j++){
            dp[i+1][j]=(dp[i+1][j-1]+dp[i][j]-dp[i][j-a[i]-1]+MOD)%MOD;
        }
    }
    cout<<dp[n][k]<<endl;
}