Problem:
Score : 300 points

Problem Statement

You are given integers N and K. Find the number of triples (a,b,c) of positive integers not greater than N such that a+b,b+c and c+a are all multiples of K.
The order of a,b,c does matter, and some of them can be the same.

Constraints

1 \leq N,K \leq 2\times 10^5

N and K are integers.

Input

Input is given from Standard Input in the following format:

N K

Output

Print the number of triples (a,b,c) of positive integers not greater than N such that a+b,b+c and c+a are all multiples of K.

Sample Input 1

3 2

Sample Output 1

9

(1,1,1),(1,1,3),(1,3,1),(1,3,3),(2,2,2),(3,1,1),(3,1,3),(3,3,1) and (3,3,3) satisfy the condition.

Sample Input 2

5 3

Sample Output 2

1

Sample Input 3

31415 9265

Sample Output 3

27

Sample Input 4

35897 932

Sample Output 4

114191

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

main = map read . words <$> getLine >>= \[n, k] -> print (patterns n k)
patterns n k  
  | even k    =   6 * length  [() | 
                              a <- [k `div` 2, k .. n], 
                              b <- [a + k `div` 2, a + k .. n], 
                              c <- [b + k `div` 2, b + k .. n],
                              (a + b) `mod` k == 0,
                              (b + c) `mod` k == 0,
                              (c + a) `mod` k == 0] +
                  6 * length  [() |
                              ab <- [k `div` 2, k .. n],
                              c  <- [ab + k `div` 2, ab + k .. n],
                              (ab + ab) `mod` k == 0,
                              (ab + c) `mod` k == 0] +
                  length      [() |
                              abc <- [k `div` 2, k .. n],
                              (abc + abc) `mod` k == 0]
  | otherwise =   6 * length  [() | 
                              a <- [k, k + k .. n], 
                              b <- [a + k, a + k + k .. n], 
                              c <- [b + k, b + k + k .. n],
                              (a + b) `mod` k == 0,
                              (b + c) `mod` k == 0,
                              (c + a) `mod` k == 0] +
                  6 * length  [() |
                              ab <- [k, k + k .. n],
                              c  <- [ab + k, ab + k + k .. n],
                              (ab + ab) `mod` k == 0,
                              (ab + c) `mod` k == 0] +
                  length      [() |
                              abc <- [k, k + k .. n],
                              (abc + abc) `mod` k == 0]