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.

Examples

Input

3 4
1 2 3


Output

5


Input

1 10
9


Output

0


Input

2 0
0 0


Output

1


Input

4 100000
100000 100000 100000 100000


Output

665683269
n,k=map(int,input().split())
l=[int(x) for x in input().split()]
dp=[0 for i in range(k+1)]
dp[0]=1
M=10**9+7
for i in range(len(l)):
	p=[0]*(k+1)
	for j in range(k-1,-1,-1):
		li= j+1
		ri=j+min(l[i],k-j)+1
		if li<=ri:
			p[j+1]+=dp[j]
		if ri<=k:
			p[j+min(l[i],k-j)+1]-=dp[j]
		'''for o in range(j+1,j+min(l[i],k-j)+1):
			dp[o]+=dp[j]'''
	su=0
	for i in range(k+1):
		su=(su+p[i])%M
		dp[i]=(dp[i]+su)%M
print(dp[k]%(10**9+7))
#print(dp[0][n-1])