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)

macro_rules !input {(source =$s :expr ,$($r :tt ) *) =>{let mut iter =$s .split_whitespace () ;let mut next =||{iter .next () .unwrap () } ;input_inner !{next ,$($r ) *} } ;($($r :tt ) *) =>{let stdin =std ::io ::stdin () ;let mut bytes =std ::io ::Read ::bytes (std ::io ::BufReader ::new (stdin .lock () ) ) ;let mut next =move ||->String {bytes .by_ref () .map (|r |r .unwrap () as char ) .skip_while (|c |c .is_whitespace () ) .take_while (|c |!c .is_whitespace () ) .collect () } ;input_inner !{next ,$($r ) *} } ;}
macro_rules !input_inner {($next :expr ) =>{} ;($next :expr ,) =>{} ;($next :expr ,$var :ident :$t :tt $($r :tt ) *) =>{let $var =read_value !($next ,$t ) ;input_inner !{$next $($r ) *} } ;}
macro_rules !read_value {($next :expr ,($($t :tt ) ,*) ) =>{($(read_value !($next ,$t ) ) ,*) } ;($next :expr ,[$t :tt ;$len :expr ] ) =>{(0 ..$len ) .map (|_ |read_value !($next ,$t ) ) .collect ::<Vec <_ >>() } ;($next :expr ,chars ) =>{read_value !($next ,String ) .chars () .collect ::<Vec <char >>() } ;($next :expr ,usize1 ) =>{read_value !($next ,usize ) -1 } ;($next :expr ,$t :ty ) =>{$next () .parse ::<$t >() .expect ("Parse error" ) } ;}

const MOD: usize = 1000000007;

fn main() {
   input! {
      n: usize,
      k: usize,
      a: [usize; n]
   }
   let mut dp = vec![vec![0usize; k + 2]; n + 1];
   dp[0].add(0, 1);
   for i in 0..n {
      for j in 0..k + 1 {
         let c = if j >= a[i] {
            dp[i].range(j - a[i], j + 1)
         } else {
            dp[i].range(0, j + 1)
         } % MOD;
         dp[i + 1].add(j, c);
      }
   }
   let ans = dp[n].range(k, k + 1) % MOD;
   println!("{}", ans);
}

use std::ops::{AddAssign, Sub};
trait BIT<T: Copy + Clone + Sub + AddAssign> {
   fn add(&mut self, idx: usize, w: T);
   fn sum(&self, idx: usize) -> T;
   fn range(&self, l: usize, r: usize) -> T;
}
impl<T: Copy + Clone + Sub<Output = T> + AddAssign> BIT<T> for [T] {
   /// let mut bit = vec![0; n+1];
   /// for (i, w) in 0..q {
   ///    bit.add(i, w);
   /// }
   fn add(&mut self, idx: usize, w: T) {
      let mut j = (idx + 1) as i64;
      while j < self.len() as i64 {
         self[j as usize] += w;
         j += j & -j;
      }
   }
   /// [0, r]
   fn sum(&self, idx: usize) -> T {
      let mut i = (idx + 1) as i64;
      let mut sum = self[0];
      while i != 0 {
         sum += self[i as usize];
         i -= i & -i;
      }
      sum
   }
   /// [l, r)
   fn range(&self, l: usize, r: usize) -> T {
      match (l, r) {
         (0, _) => self.sum(r - 1),
         _ => self.sum(r - 1) - self.sum(l - 1),
      }
   }
}