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.Arrays;
import java.util.Scanner;

public class Main {
    static final Scanner sc  = new Scanner(System.in);
    static final int     MOD = (int) 1E9 + 7;
    
    public static void main(String[] args) {
        int N = nint();
        int K = nint();
        int[] a = nints(N, 1, 0);
        
        int[][] dp = new int[N+1][K+1];
        
        for (int n = 0; n <= N; n++) {
            dp[n][0] = 1;
        }
        
        for (int n = 1; n <= N; n++) {
            int[] c = new int[K+2];
            for (int i = 1; i <= K+1; i++) {
                c[i] = (c[i-1]+dp[n-1][i-1]) % MOD;
            }
            
            for (int k = 1; k <= K; k++) {
                dp[n][k] = (c[k+1] - c[max(0, k - a[n])] + MOD) % MOD;
            }
        }
        System.out.println(dp[N][K]);
    }
    
    private static int nint() {
        return sc.nextInt();
    }

    private static int[] nints(int n) {
        return nints(n, 0, 0);
    }

    private static int[] nints(int n, int padL, int padR) {
        int[] a = new int[padL + n + padR];
        for (int i = 0; i < n; i++)
            a[padL + i] = nint();
        return a;
    }

    private static long nlong() {
        return sc.nextLong();
    }

    private static long[] nlongs(int n) {
        return nlongs(n, 0, 0);
    }

    private static long[] nlongs(int n, int padL, int padR) {
        long[] a = new long[padL + n + padR];
        for (int i = 0; i < n; i++)
            a[padL + i] = nlong();
        return a;
    }

    private static double ndouble() {
        return sc.nextDouble();
    }

    private static double[] ndoubles(int n) {
        return ndoubles(n, 0, 0);
    }

    private static double[] ndoubles(int n, int padL, int padR) {
        double[] d = new double[n + padL + padR];
        for (int i = 0; i < n; i++) {
            d[padL + i] = ndouble();
        }
        return d;
    }

    private static String nstr() {
        return sc.next();
    }

    private static char[] nchars() {
        return sc.next().toCharArray();
    }

    private static char[] nchars(int padL, int padR) {
        char[] temp = sc.next().toCharArray();
        char[] ret = new char[temp.length + padL + padR];
        System.arraycopy(temp, 0, ret, padL, temp.length);
        return ret;
    }

    private static char[][] nchars2(int h, int w) {
        return nchars2(h, w, 0, 0);
    }

    private static char[][] nchars2(int h, int w, int padLU, int padRD) {
        char[][] a2 = new char[h + padLU + padRD][w + padLU + padRD];
        for (int i = 0; i < h; i++)
            System.arraycopy(nchars(), 0, a2[padLU + i], padLU, w);
        return a2;
    }

    private static long min(long... ls) {
        return Arrays.stream(ls).min().getAsLong();
    }

    private static int min(int... is) {
        return Arrays.stream(is).min().getAsInt();
    }

    private static long max(long... ls) {
        return Arrays.stream(ls).max().getAsLong();
    }

    private static int max(int... is) {
        return Arrays.stream(is).max().getAsInt();
    }

    private static long abs(long a, long b) {
        return Math.abs(a - b);
    }
}
