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)

N, K = map(int, input().split())
M=10**9+7
As = list(map(int, input().split()))
dp = [[0]*(K+1)for _ in range(N+1)]
dp2 = [[1]*(K+1)for _ in range(N+1)]
dp[0][0] = 1

for i in range(1, N+1):
    for j in range(K+1):
#        print(i,j, dp[i][j-1] - dp2[i][j-1] + dp[i-1][j], j-As[i-1])
        dp[i][j] = 1 if j==0 else (dp[i][j-1] - dp2[i][j-1] + dp[i-1][j])%M
        dp2[i][j] = 0 if j-As[i-1] <0 else dp[i-1][j-As[i-1]]%M
#        dp[i][j] = sum(dp[i-1][max(0, j-As[i])...j])
#        sum(dp[i][0...j]) = sum(dp[i-1][max(0,j-As[i])...j])
#        dp[i][j] = dp[i-1][j] + dp[i-1][j-1] + ... dp[i-1][max(0, j-As[i])]
#print(dp,dp2)
print(dp[N][K])