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;
#define rep(i,n) for(int i = 0; i < (n);i++)
#define sz(x) int(x.size())
typedef long long ll;
typedef pair<int,int> P;
constexpr int mod = 1e9+7;
int main(){
  int n, k;
  cin >> n >> k;
  vector<int> a(n);
  rep(i,n) cin >> a[i];
  
  vector<int> dp(k+2,0);
  dp[0] = 1;
  rep(i,n) {
    vector<int> cum(k+2,0);
    rep(j,k+1) (cum[j+1] =  cum[j] + dp[j]) %= mod;
    rep(j,k+1) (dp[j] = (cum[j+1] - cum[max(0,j-a[i])]) + mod ) %= mod;
  }
  cout << dp[k] << endl;
  return 0;
} 