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 Lua (LuaJIT 2.1.0) (judge verdict: Accepted)

local n,k=io.read("n","n")
local a={}
for i=1,n do
    a[i]=io.read("n")
end

local dp={}
for i=1,n+1 do
    dp[i]={}
    dp[i][1]=1
    for j=2,k+1 do
        dp[i][j]=0
    end
end

local mod=1000000007
for i=1,n do
    for j=2,k+1 do
        if j-1-a[i]>0 then
            dp[i+1][j]=(dp[i+1][j-1]+dp[i][j]-dp[i][j-1-a[i]])%mod
        else
            dp[i+1][j]=(dp[i+1][j-1]+dp[i][j])%mod
        end
    end
end
print(dp[n+1][k+1])