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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

'use strict'

const mod = 1e9 + 7

function solve(N, K, A) {
  if (K === 0) {
    return 1
  }
  var dp = new Array(K+1).fill(0)
  var prefix = new Array(N).fill(0).map(e => new Array(K+1).fill(0))

  for (var i = 0; i < N; i++) {
    for (var j = 0; j <= K; j++) {
      if (i === 0) {
        dp[j] = j <= A[i] ? 1 : 0
        prefix[i][j] = j > 0 ? ((prefix[i][j-1] + dp[j]) % mod) : (dp[j] % mod)
      } else {
        dp[j] = (j-1 - A[i]) >= 0 ? ((prefix[i-1][j] - prefix[i-1][j - A[i] - 1]) % mod) : (prefix[i-1][j] % mod)
        prefix[i][j] = j > 0 ? ((prefix[i][j-1] + dp[j]) % mod) : (dp[j] % mod)
      }
    }
  }
  return dp[K] % mod
}

function main(input) {
  var lines = input.split("\n")
  var NK = lines[0].split(' ').map(l => parseInt(l))
  var N = NK[0]
  var K = NK[1]
  var A = lines[1].split(' ').map(l => parseInt(l))
  var ans = solve(N, K, A)
  console.log(ans)
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));