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 FOR(i,a,b) for(int i = (a); i < (b); i++)
#define ll long long
#define M 1000000007
#define N 105
#define K 100010
using namespace std;

ll n,k,a[N],cnt[K],dp[N][K];

int main()
{
    cin>>n>>k; FOR(i,1,n+1) cin>>a[i];
    dp[0][0]=1;
    FOR(i,1,n+1)
    {
        memset(cnt,0,sizeof(cnt));
        FOR(j,0,k+1) cnt[j]=dp[i-1][j];
        FOR(j,1,k+1) cnt[j]=(cnt[j]+cnt[j-1])%M;
        FOR(j,0,k+1) dp[i][j]=(j<=a[i])?cnt[j]:(cnt[j]-cnt[j-a[i]-1]+M)%M;
    }
    cout<<dp[n][k]<<'\n';

    return 0;
}