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 long mod = 1_000_000_007;

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int N = in.nextInt(), K = in.nextInt();
		int a[] = new int[N + 1];
		for ( int i = 1; i <= N; i++ ) {
			a[i] = in.nextInt();
		}
		in.close();

		long dp[][] = new long[N + 1][K + 1];
		dp[0][0] = 1;

		for ( int n = 1; n <= N; n++ ) {
			for ( int k = 0; k <= K; k++ ) {
				if ( k == 0 ) {
					dp[n][k] = 1;

				} else {
					dp[n][k] = (dp[n][k - 1] + dp[n - 1][k]) % mod;

				}

				if ( a[n] < k ) {
					dp[n][k] = (dp[n][k - 1] + dp[n - 1][k] - dp[n - 1][k - a[n] - 1]) % mod;

				}
			}
		}
		System.out.println((dp[N][K] + mod) % mod);
	}
}
