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: Time Limit Exceeded)

N, K = map(int, input().split())
a = tuple(map(int, input().split()))

def main():
    l = [1 if a[0] >= j else 0 for j in range(K+1)]
    s = a[0]
    for i in range(1,N):
        t = 0
        lt = l
        l = [0] * (K + 1)
        s += a[i]
        for j in range(min(K+1, s+1)):
            if j == 0:
                t = 1
                l[j] = 1
            else:
                if j <= a[i]:
                    t += lt[j]
                else:
                    t += (lt[j] - lt[j - a[i] - 1])
                l[j] += t
    return l[-1] % (10 ** 9 + 7)
            
print(main())