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;
long long n, k, a[105], dp[105][100005], mod=1000000007;
int main (){
ios::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
cin >> n >> k; dp[0][0]=1;
for (int i=1; i<=n; i++) cin >> a[i];
for (int i=1; i<=n; i++){
	long long sum=0;
	for (int j=0; j<=k; j++){
		sum+=dp[i-1][j];
		if (j>a[i]) sum-=dp[i-1][j-a[i]-1];
		sum = ((sum%mod)+mod)%mod;
		dp[i][j]=sum;
	}
} cout << dp[n][k];
return 0;
}
