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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;

const M: u64 = 1000_000_007;

fn calc(n: usize, k: usize, a: &Vec<usize>) -> u64 {
    let mut dp = vec![vec![0; k + 1]; n];
    for j in 0..=a[0] {
        dp[0][j] = 1;
    }
    for j in (a[0] + 1)..=k {
        dp[0][j] = 0;
    }
    for i in 1..n {
        let mut cum = vec![0; k + 2];
        for j in 1..=(k + 1) {
            cum[j] = (cum[j - 1] + dp[i - 1][j - 1]) % M;
        }
        for j in 0..=k {
            let ks = if a[i] > j { 0 } else {j - a[i]};
            dp[i][j] = (cum[j + 1] + M - cum[ks]) % M;
        }
    }
    dp[n - 1][k]
}

fn main() {
    input! {
        n: usize,
        k: usize,
        a: [usize; n],
    }

    println!("{}", calc(n, k, &a));
}