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 <vector>
using namespace std;
const int mod = 1e9+7;

int main(){
  int N, K;
  cin >> N >> K;
  vector<int> A(N);
  for(int i = 0; i < N; ++i) cin >> A[i];
  vector<int> dp(K+1,0);
  dp[0] = 1;
  for(int i = 0; i < N; ++i){
    vector<int> dp_(K+1,0);
    int s = 0;
    for(int j = 0; j <= K; ++j){
      s += dp[j], s %= mod;
      if(j > A[i]) s += mod - dp[j-A[i]-1], s %= mod;
      dp_[j] += s, dp_[j] %= mod;
    }
    dp = dp_;
  }
  cout << dp[K] << endl;
}
