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;
#define ll long long
int n,k;
int dp[110][100009];
int s[110][100009];
const int mod=1e9+7;
int main()
{
    scanf("%d%d",&n,&k);
    dp[0][k]=s[0][k]=1;
    for(int i=1;i<=n;i++)
    {
        int x;scanf("%d",&x);
        for(int j=1;j<=k;j++)
            dp[i][j]=(s[i-1][min(k,j+x)]-s[i-1][j-1]+mod)%mod;
        s[i][0]=dp[i][0]=s[i-1][x];
        for(int j=1;j<=k;j++)
            s[i][j]=(s[i][j-1]+dp[i][j])%mod;
    }
    cout<<dp[n][0]<<endl;
    return 0;
}