Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

3 4
1 2 3

Sample Output 1

5

There are five ways for the children to share candies, as follows:

(0, 1, 3)

(0, 2, 2)

(1, 0, 3)

(1, 1, 2)

(1, 2, 1)

Here, in each sequence, the i-th element represents the number of candies that Child i receives.

Sample Input 2

1 10
9

Sample Output 2

0

There may be no ways for the children to share candies.

Sample Input 3

2 0
0 0

Sample Output 3

1

There is one way for the children to share candies, as follows:

(0, 0)

Sample Input 4

4 100000
100000 100000 100000 100000

Sample Output 4

665683269

Be sure to print the answer modulo 10^9 + 7.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author silviase
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        MCandies solver = new MCandies();
        solver.solve(1, in, out);
        out.close();
    }

    static class MCandies {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            int k = in.nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = in.nextInt();
            ModInt[][] dp = new ModInt[n + 1][k + 1];
            Arrays.fill(dp[0], new ModInt(0));
            dp[0][0] = new ModInt(1);
            for (int i = 0; i < n; i++) {
                ModInt syakSum = new ModInt(0);
                for (int j = 0; j < a[i]; j++) {
                    syakSum = syakSum.add(dp[i][j]);
                    dp[i + 1][j] = syakSum;
                }
                for (int j = a[i]; j <= k; j++) {
                    syakSum = syakSum.add(dp[i][j]);
                    // 尺取り
                    dp[i + 1][j] = syakSum;
                    syakSum = syakSum.sub(dp[i][j - a[i]]);
                }
            }

            out.println(dp[n][k].getVal());

        }

    }

    static class ModInt {
        long val;
        int MOD = (int) 1e9 + 7;

        public ModInt(long i) {
            this.val = (i + MOD) % MOD;
        }

        public ModInt add(ModInt m) {
            return new ModInt(this.val + m.getVal());
        }

        public ModInt sub(ModInt m) {
            return new ModInt(this.val - m.getVal());
        }

        public long getVal() {
            return val;
        }

        public String toString() {
            return Long.toString(val);
        }

    }
}