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>
#define ll long long
#define mod 1000000007

using namespace std;

int n,k;
int a[110];
int dp[110][100010];

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(0);

	cin>>n>>k;
	for(int i=1;i<=n;i++)
        cin>>a[i];

    dp[0][0]=1;
    int suma;
    for(int i=1;i<=n;i++)
    {
        suma=0;
        for(int j=0;j<=k;j++)
        {
            suma=(suma+dp[i-1][j]-(j-a[i]-1>=0?dp[i-1][j-a[i]-1]:0))%mod;
            dp[i][j]=(suma+mod)%mod;
        }
    }
    cout<<dp[n][k];
	return 0;
}
