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 <iostream>
#include <cstring>

using namespace std;

typedef long long ll;

int n, k, a[105];
ll dp[100005];
const ll mod = (ll)1e9 + 7;

int main(){
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
cin >> n >> k;
for(int i = 0 ; i < n ; ++i){
	cin >> a[i];
}
dp[k] = 1;
for(int i = 0 ; i < n ; ++i){
	for(int j = k - 1 ; j >= 0 ; --j){
		dp[j] = (dp[j] + dp[j + 1]) % mod;
	}
	for(int j = a[i] + 1 ; j <= k ; ++j){
		dp[j - a[i] - 1] = (dp[j - a[i] - 1] - dp[j] + mod) % mod;
	}
}
cout << dp[0] << endl;

return 0;
}

