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 Lua (Lua 5.3.5) (judge verdict: Accepted)

local n,k=io.read("n","n")
local t={}
for i=0,k-1 do
    t[i]=0
end
for i=1,n do
    t[i%k]=t[i%k]+1
end

local counter=0
for a=0,k-1 do
    local b=(k-a)%k
    local c=(k-a)%k
    if (b+c)%k==0 then
        counter=counter+t[a]*t[b]*t[c]
    end
end
print(counter)