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 LuaJIT (2.0.4) (judge verdict: Accepted)

local mod = 1000000007
local function badd(x, y) return (x + y) % mod end
local function bsub(x, y) return y <= x and x - y or x + mod - y end
local n, k = io.read("*n", "*n")
local dp1, dp2 = {1}, {0}
for i = 2, k + 1 do
  dp1[i] = 0
  dp2[i] = 0
end
for i = 1, n do
  local src = i % 2 == 1 and dp1 or dp2
  local dst = i % 2 == 1 and dp2 or dp1
  for j = 1, k + 1 do
    dst[j] = 0
  end
  local a = io.read("*n") + 1
  local sum = 0
  for j = 1, k + 1 do
    sum = badd(sum, src[j])
    if a < j then
      sum = bsub(sum, src[j - a])
    end
    dst[j] = badd(dst[j], sum)
  end
end
local ret = n % 2 == 1 and dp2 or dp1
print(ret[k + 1])