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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

N,K = map(int,input().split())
A = list(map(int,input().split()))
dp = []
for i in range(N):
  L = [0]*(K+1)
  dp.append(L)
for i in range(A[0]+1):
  dp[0][i] = 1
for i in range(1,N):
  cur = [0]*(K+2)
  for j in range(K+1):
    cur[j+1] = (cur[j]+dp[i-1][j])%(10**9+7)
  for k in range(K+1):
    if k > A[i]:
      dp[i][k] = cur[k+1]-cur[k-A[i]]
    else:
      dp[i][k] = cur[k+1]
print(dp[N-1][K]%(10**9+7))