Problem:
Score : 200 points

Problem Statement

Snuke has come to a store that sells boxes containing balls. The store sells the following three kinds of boxes:

Red boxes, each containing R red balls

Green boxes, each containing G green balls

Blue boxes, each containing B blue balls

Snuke wants to get a total of exactly N balls by buying r red boxes, g green boxes and b blue boxes.
How many triples of non-negative integers (r,g,b) achieve this?

Constraints

All values in input are integers.

1 \leq R,G,B,N \leq 3000

Input

Input is given from Standard Input in the following format:

R G B N

Output

Print the answer.

Sample Input 1

1 2 3 4

Sample Output 1

4

Four triples achieve the objective, as follows:

(4,0,0)

(2,1,0)

(1,0,1)

(0,2,0)

Sample Input 2

13 1 4 3000

Sample Output 2

87058

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

PROGRAM ATCODER

implicit none
integer :: r,g,b,n,x,y,z,max_r,max_g,max_b,i,j,count=0

read*, r,g,b,n

max_r = n/r ; max_g = n/g ; max_b = n/b

do i = 0, max_r, 1
  do j = 0, max_g, 1
    x = i ; y = j ; z = (n - x*r - y*g)/b
    if ( mod(n - x*r - y*g,b) == 0 .and. z >=0 .and. z <= max_b ) then
      count = count + 1
    end if
  end do
end do

print'(i0)',  count

END PROGRAM ATCODER