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
#dp[i][j] denotes number of ways to distribute j candies among first i
l=input().split()
n=int(l[0])
k=int(l[1])
l=input().split()
li=[int(i) for i in l]
dp=[[0 for i in range(k+1)]for i in range(n+1)]
for i in range(n+1):
    dp[i][0]=1
for i in range(1,k+1):
    dp[0][i]=0
pref=[0 for i in range(k+1)]
sumi=0
for i in range(k+1):
    sumi+=dp[0][i]
    pref[i]=sumi
    pref[i]%=1000000007
for i in range(1,n+1):
    for j in range(1,k+1):
        howmany=li[i-1]
        left=max(0,j-howmany)
        right=j
        if(left==0):
            dp[i][j]=pref[j]
        else:
            dp[i][j]=pref[j]-pref[left-1]
        dp[i][j]%=1000000007
    sumi=0
    for j in range(k+1):
        sumi+=dp[i][j]
        pref[j]=sumi
        pref[j]%=1000000007
print(dp[n][k])
