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;
typedef long long ll;
int n, k;
vector<ll> a;
ll dp[110][100010];
ll mod = 1000000007;

int main() {
  cin >> n >> k;
  a.resize(n);
  for (int i = 0; i < n; ++i) cin >> a[i];
  for (int i = 0; i <= n; ++i) dp[i][0] = 1;

  for (int i = 1; i <= n; ++i)
    for (int j = 1; j <= k; ++j)
      dp[i][j] = dp[i - 1][j] + dp[i][j - 1] + mod -
                 (j - a[i - 1] - 1 >= 0 ? dp[i - 1][j - a[i - 1] - 1] : 0),
      dp[i][j] %= mod;
  cout << dp[n][k] << endl;
  return 0;
}