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; ll dp[105][100005], MOD = 1e9 + 7;
int main() {int n,k;scanf("%i%i",&n,&k);dp[0][0]=1;for(int x=1; x<=n; x++) {ll a;scanf("%lli",&a);for(int y=0;y<=k;y++){dp[x][y]+=dp[x-1][y]-(y-a>0?dp[x-1][y-a-1]:0);if(y>0)dp[x][y]+=dp[x][y-1];dp[x][y]%=MOD;dp[x][y]+=MOD;dp[x][y]%=MOD;}}printf("%lli\n",dp[n][k]%MOD);}
