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
/*input
4 100000
100000 100000 100000 100000
*/
#include<bits/stdc++.h>
using namespace std;
const int mod = 1e9+7;
int main()
{
	int N,K;cin>>N>>K;
	vector<int> a(N+1);
	for(int i=1;i<=N;i++) cin>>a[i];

	vector<int> dp2(K+1,0);
	vector<int> pf(K+1,1);

	for(int i=1;i<=N;i++)
	{
		for(int j=0;j<=K;j++)
		{
			// dp2[j] = dp1[j-a[i]] .... dp1[j];
			dp2[j] = pf[j] - (j-a[i]-1>=0?pf[j-a[i]-1]:0);
			dp2[j]%=mod;
			if(dp2[j]<0) dp2[j]+=mod;
		}

		for(int j=0;j<=K;j++) pf[j]=((j-1>=0?pf[j-1]:0)+dp2[j])%mod;
	}

	cout<<dp2[K]<<"\n";

	return 0;
}
