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>
using namespace std;
using ll = long long;

const int MAX_N = 102, MAX_K = 1e5+2, MOD = 1e9+7;
int N, K;
int a[MAX_N];
ll dp[MAX_N][MAX_K];

void solve()
{
	dp[0][0]=1;
	for(int i=0;i<N;++i){
	    ll psum = 0;
		for(int j=0;j<=K;++j){
		    (psum += dp[i][j])%=MOD;
            (dp[i+1][j] += psum)%=MOD;
            if(j>=a[i]) psum = (psum-dp[i][j-a[i]]+MOD)%MOD;
		}
	}
	ll ans = dp[N][K];
	cout << ans << '\n';
}

int main()
{
	cin >> N >> K;
	for(int i=0;i<N;++i) cin >> a[i];
	solve();
	return 0;
}