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)

from random import randint 
mod=10**9+7
def ways(n,k,arr):
	dp=[[0]*(k+1) for _ in range(n)]
	for i in range(arr[0]+1):
		dp[0][i]=1
	for i in range(1,n):
		s=0
		start=0
		for j in range(k+1):
			s+=dp[i-1][j]
			if s>mod:
				s-=mod
			dp[i][j]=s
			if j-start==arr[i]:
				s-=dp[i-1][start]
				if s<0:
					s+=mod
				start+=1

	return dp[n-1][k]
			

# with open ('input.txt') as f :
n,k=map(int,input().split())
arr=list(map(int,input().split()))
res=ways(n,k,arr)
# res=ways(100,10**5,[randint(0,10**5) for _ in range(100)])
print(res)