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;
const ll mod = 1e9 + 7;

int n,k;
int a[100005];
ll dp[105][100005];
ll sum[100005];
int main() {
    scanf("%d%d",&n,&k);
    for(int i = 1;i<=n;i++) scanf("%d",&a[i]);
    for(int i = 0;i<=n;i++) dp[i][0] = 1;
    for(int i = 1;i<=n;i++) {
        sum[0] = 0;
        for(int j = 1;j<=k+1;j++) sum[j] = sum[j-1] + dp[i-1][j-1];
        for(int j = 1;j<=k;j++) 
            dp[i][j] = (sum[j+1] - sum[max(0,j-a[i])] + mod) % mod;
    }
    printf("%lld\n",dp[n][k]);
    return 0;
}