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.Scanner;

public class Main {

    static int MOD = 1_000_000_007;
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int K = sc.nextInt();
        int[] A = new int[N+1];
        for(int i = 1; i <= N; i++) A[i] = sc.nextInt();
        // dp[i][j]：ｉ人目まででｊ個の飴を分ける分け方 % MOD
        long[][] dp = new long[N+1][K+1];
        dp[0][0] = 0;
        int sum = 0;
        for(int i = 1; i <= N; i++){
            sum += A[i];
            for(int j = 0; j <= K; j++){
                if(j == 0) dp[i][j] = 1;
                else if(j <= A[i]) dp[i][j] = (dp[i-1][j] + dp[i][j-1]) % MOD;
                else if(j <= sum) dp[i][j] = (dp[i-1][j] + dp[i][j-1] - dp[i-1][j - A[i] -1] + MOD) % MOD;
            }
        }
        System.out.println(dp[N][K]);
        sc.close();
    }

}
