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;

int a[110];
int dp[2][100010];
int MOD=1000000007;

int main() {
    int n, k;
    cin>>n>>k;
    for (int i=0;i<n;i++) cin>>a[i];
    memset(dp,0,sizeof(dp));
    dp[0][0]=dp[1][0]=1;
    for (int i=0;i<n;i++) {
        int sum=1;
        for (int j=1;j<=k;j++) {
            sum+=dp[i%2][j];
            if (j>a[i]) sum-=dp[i%2][j-a[i]-1];
            sum=(sum%MOD+MOD)%MOD;
            dp[(i+1)%2][j]=sum;
        }
    }
    cout<<dp[n%2][k]<<endl;
}