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 ll long long int
#define mod 1000000007
using namespace std;

int main()
{ 
	ll n,k,x;
	cin>>n>>k;

	ll dp[k+1];
	memset(dp,0,sizeof(dp));
	dp[0]=1;

	for(ll i=0;i<n;i++)
	{
		cin>>x;

		vector<ll> pre(k+1,0);
		pre[0]=1;

		for(ll j=1;j<=k;j++)
			pre[j]=(pre[j-1]+dp[j])%mod;

		for(ll j=0;j<=k;j++)
		{
			ll z=pre[j];

			if(j-x>=1)
			z=(z-pre[j-x-1]+mod)%mod;

			dp[j]=z;
		}
	}
	cout<<dp[k]<<endl;
}
