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 <stdio.h>
#include <algorithm>
#include <string>
#include <vector>
using namespace std;

const long long mod = 1000000007;
int N,K; long long D[100100],S[100100];

int main()
{
	scanf ("%d %d",&N,&K); D[0] = 1;
	for (int i=0;i<N;i++){
		int a; scanf ("%d",&a);
		S[0] = D[0];
		for (int j=1;j<=K;j++) S[j] = (S[j-1] + D[j]) % mod;
		for (int j=0;j<=K;j++){
			D[j] = S[j];
			if (j > a) D[j] = (D[j] + mod - S[j-a-1]) % mod;
		}
	}

	printf ("%lld\n",D[K]);

	return 0;
}