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>
#define int long long
using namespace std;
const int Maxn=1e2+10,Maxk=1e5+10,MOD=1e9+7;
int N,K;
vector<int> S(Maxk);
int Dp[Maxn][Maxk];
signed main()
{
	cin>>N>>K;
	Dp[0][0]=1;
	for(int i=1;i<=N;i++)
	{
		int A;
		cin>>A;
		for(int j=0;j<=K;j++)
		{
			S[j+1]=(S[j]+Dp[i-1][j])%MOD;
		}
		for(int j=0;j<=K;j++)
		{
			Dp[i][j]=(S[j+1]-S[max(0LL,j-A)]+MOD)%MOD;
		}
	}
	cout<<Dp[N][K]<<endl;
	return 0;
}