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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

import sys
n, k = [int(i) for i in sys.stdin.readline().split()]
a_ls = [int(i) for i in sys.stdin.readline().split()]
memo_ls = [[0 for i in range(k+1)] for j in range(n)]
memo_ls[0][0] = 1
for i in range(n):
    for j in range(k+1):
        if i == 0:
            if j <= a_ls[i]:
                memo_ls[i][j] = 1
            continue
        if j == 0:
            memo_ls[i][j] = 1
            continue
        if a_ls[i] < j:
            memo_ls[i][j] = (- memo_ls[i-1][max(0,j-a_ls[i]-1)] + memo_ls[i][j-1] + memo_ls[i-1][j]) % (10**7+9) #sum(memo_ls[i-1][max(0,j - a_ls[i]):j+1]) % (10**9 + 7)
        else:
            memo_ls[i][j] = (memo_ls[i][j-1] + memo_ls[i-1][j]) % (10**9+7)
print(memo_ls[-1][-1])