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 (1.15.1) (judge verdict: Accepted)

use std::io::*;
const MOD: u64 = 1_000_000_007;

mod fenwick_tree {
    use std::ops::*;
    pub struct FenwickTree<T> {
        size: usize,
        data: Vec<T>,
        identity: T,
    }
    impl<T: Copy + Clone + AddAssign + Sub<Output = T>> FenwickTree<T> {
        pub fn new(size: usize, id: T) -> FenwickTree<T> {
            FenwickTree {
                size: size,
                data: vec![id; size + 2],
                identity: id,
            }
        }
        pub fn query(&self, i: usize) -> T {
            let mut res = self.identity;
            let mut idx = i as isize - 1;
            while idx >= 0 {
                res += self.data[idx as usize];
                idx = (idx & (idx + 1)) - 1;
            }
            res
        }
        pub fn update(&mut self, i: usize, x: T) {
            let mut idx = i;
            while idx <= self.size {
                self.data[idx] += x;
                idx |= idx + 1;
            }
        }
    }
}

fn main() {
    let mut s: String = String::new();
    std::io::stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let n: usize = itr.next().unwrap().parse().unwrap();
    let k: usize = itr.next().unwrap().parse().unwrap();
    let a: Vec<usize> = (0..n)
        .map(|_| itr.next().unwrap().parse().unwrap())
        .collect();

    let mut dp: Vec<fenwick_tree::FenwickTree<u64>> = (0..n + 1)
        .map(|_| fenwick_tree::FenwickTree::new(k + 1, 0))
        .collect();
    dp[0].update(0, 1);
    for i in 1..n + 1 {
        for j in (0..k + 1).rev() {
            let mut tmp = (dp[i - 1].query(j + 1) % MOD
                - dp[i - 1].query(j - std::cmp::min(j, a[i - 1])) % MOD
                + MOD)
                % MOD;
            tmp %= MOD;
            dp[i].update(j, tmp);
        }
    }
    println!(
        "{}",
        (dp[n].query(k + 1) % MOD - dp[n].query(k) % MOD + MOD) % MOD
    );
}