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 <cstdio>
#include <algorithm>

using namespace std;

const int MAX_N = 105;
const int MAX_K = 100005;
const int MOD = 1000000007;

int n,k,a[MAX_N];
int dp[MAX_N][MAX_K],sum[MAX_K];

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