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::cmp::*;
use std::io;

fn main(){
    let mut t_cases = 1;
    for i in 0..t_cases{
        solve();
    }
}
fn solve(){
    let MOD = 10i32.pow(9)+7;
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    let mut iter = buf.trim().split_whitespace().map(|x| x.parse::<usize>().unwrap());
    let n = iter.next().unwrap();
    let k = iter.next().unwrap();
    // buf.clear();
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    let a = buf.trim().split_whitespace().map(|x| x.parse::<usize>().unwrap()).collect::<Vec<_>>();
    let mut dp = vec![0i32;k+1];
    dp[0] = 1;
    for item in a{
        let mut tdp = dp.clone();
        let mut s = dp[0];
        for i in 1..(k+1){
            s+=dp[i];
            if i > (item){
                s-=dp[i-item-1];
            }
            s = (s)%MOD;
            tdp[i] = (s+MOD)%MOD;
        }
        dp = tdp;
        // println!("{:?}",dp);
    }
    println!("{}",dp[k]);
    // println!("{}",(-6)%5);
}