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;
const int mod=1e9+7;
int dp[102][100005],n;
int a[102],k;
signed main()
{
    cin>>n>>k;
    for(int i=1;i<=n;++i)
    {
        cin>>a[i];
    }
    dp[0][0]=1;
    for(int j=0;j<=k;j++)
    {
    for(int i=1;i<=n;i++)
    {
            dp[i][j]=dp[i-1][j];
            if(j)
                dp[i][j]+=dp[i][j-1];
                dp[i][j]%=mod;
            if(j-a[i]-1>=0)
            dp[i][j]=(dp[i][j]+mod-dp[i-1][j-a[i]-1])%mod;
            dp[i][j]%=mod;
    }
    }
    cout<<dp[n][k]<<endl;
	return 0;
}
