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  pb push_back
#define nl "\n"
#define fastScan ios_base::sync_with_stdio(0); cin.tie(NULL);
#define int long long int
using namespace std;
int s[123456];
int dp[123][123456];
signed main()
{
	fastScan;
	int n,k;cin>>n>>k;
	for(int i=1;i<=n;i++)
		cin>>s[i];
	dp[0][0]=1;
	int mod=(int)(1e9+7);
	for(int i=1;i<=n;i++)
	{
		int pre=0;
		for(int j=0;j<=k;j++)
		{
			pre+=dp[i-1][j];
			if(j-s[i]-1>=0)
				pre-=dp[i-1][j-s[i]-1];
			pre=(pre%mod+mod)%mod;
			dp[i][j]=pre;
		}
	}
	cout<<dp[n][k]<<nl;
}
