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: Accepted)


MOD = int(1e9)+7


def main():
    n, K = map(int, input().split())
    a = list(map(int, input().split()))

    # dp[i][j] is the number of ways to distribute j candies to first i people
    dp = [[0]*(K+1) for i in range(n+1)]
    prefix = [[0]*(K+1) for i in range(n+1)]
    prefix[0] = [1]*(K+1)
    for i in range(1, n+1):
        for j in range(K+1):
            start = j - min(a[i-1], j)-1
            end = j
            dp[i][j] = (prefix[i-1][end] - \
                (prefix[i-1][start] if start >= 0 else 0))%MOD
            prefix[i][j] = (prefix[i][j-1] + dp[i][j]) % MOD

    print(dp[n][K]%MOD)


if __name__ == "__main__":
    main()