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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program atcoder
    implicit none
    integer(8) :: i,j,n,k,modd
    integer(8),allocatable,dimension(:,:) :: dp
    integer(8),allocatable,dimension(:) :: a
    read*,n,k
    allocate(dp(0:n,0:k))
    allocate(a(0:n))
    read(*,*)(a(i),i=1,n)
    modd = 1000000007
    do i = 0,n
        dp(i,0) = 1
    enddo
    do i = 1,n
        do j = 1,k
            if(j-a(i)-1 >= 0 ) then
                dp(i,j) = dp(i,j-1)+dp(i-1,j)-dp(i-1,j-a(i)-1)
            else
                dp(i,j) = dp(i,j-1)+dp(i-1,j)
            end if
            dp(i,j) = mod(mod(dp(i,j),modd)+modd,modd)
        enddo
    enddo
    write(*,'(I0)')dp(n,k)
    stop 
!---------------------------------------
contains

end program atcoder