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
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        int K = Integer.parseInt(sc.next());
        int mod = 1_000_000_007;
        long[][] dp = new long[N+1][K+1];
        int[] a = new int[N];
        for (int i=0;i<N;i++) {
            a[i] = Integer.parseInt(sc.next());
        }
        dp[0][0] = 1;
        for (int i=0;i<N;i++) {
            for (int j=0;j<K+1;j++) {
                long tmp = 0;
                // for (int k=Math.max(0, j-a[i]);k<=j;k++) {
                //     tmp = (tmp+dp[i][k])%mod;
                // }
                if (j-1>=0) tmp = (tmp+dp[i+1][j-1])%mod;
                tmp = (tmp+dp[i][j])%mod;
                if (j-a[i]-1>=0) tmp -= dp[i][j-a[i]-1];
                if (tmp<0) tmp+=mod;
                dp[i+1][j] = tmp;
            }
        }
        System.out.println(dp[N][K]);
    }
}