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)

#![allow(unused)]

use std::cmp::{min, max};
use std::io::Write;

macro_rules! dbg {
    ($($a:expr),*) => {
        writeln!(
            std::io::stderr(),
            concat!($(stringify!($a), " = {:?}, "),*),
            $($a),*);
    }
}

//
// Based on EbTech's Scanner https://stackoverflow.com/q/56449027
//
struct Scanner<'a, R: std::io::BufRead> {
    reader: R,
    buf: String,
    iter: std::str::SplitWhitespace<'a>,
}

impl<'a, R: std::io::BufRead> Scanner<'a, R> {
    fn new(reader: R) -> Scanner<'a, R> {
        Scanner { reader: reader, buf: String::new(), iter: "".split_whitespace() }
    }

    fn get_str(&mut self) -> &str {
        if let Some(t) = self.iter.next() {
            return t;
        }
        self.buf.clear();
        self.reader.read_line(&mut self.buf).expect("I/O error");
        self.iter = unsafe { std::mem::transmute(self.buf.split_whitespace()) };
        self.get_str()
    }

    fn get<T: std::str::FromStr>(&mut self) -> T {
        self.get_str().parse().ok().expect("Parse error")
    }
}

fn main() {
    let stdin = std::io::stdin();
    solve(Scanner::new(stdin.lock()));
}

const M: i64 = 1000000007;

fn solve<R: std::io::BufRead>(mut sc: Scanner<R>) {
    let n: usize = sc.get();
    let k: usize = sc.get();
    let xs: Vec<usize> = (0..n).map(|_| sc.get()).collect();

    //
    // dp[p][c] = 最初の p + 1 人で飴ちょうど c 個を分ける配り方の数
    //
    let mut dp: Vec<i64> = vec![0; k + 1];
    dp[0] = 1;

    for p in 0..n {
        dp = (0..(k + 1)).scan(0, |a, c| {
            let dec = if c > xs[p] { dp[c - xs[p] - 1] } else { 0 };
            *a = (*a + dp[c] - dec + M) % M;
            Some(*a)
        }).collect();
    }

    println!("{}", dp[k]);
}