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 Pascal (FPC 2.6.2) (judge verdict: Runtime Error)

var n,k,i:longint;
a:array[1..3]of longint;
b:array[1..200000]of longint;
count,m:longint;
procedure dfs(x:integer);
var j:longint;
begin 
	if x>3 then 
	begin 
		if (a[1]+a[3]) mod k=0 then inc(count);
		exit;
	end;
	for j:=1 to m do 
		if ((b[j]-a[x-1])<=n) and ((b[j]-a[x-1])>0) then 
		begin 
			a[x]:=b[j]-a[x-1];
			dfs(x+1);
		end
		else if b[j]-a[x-1]>n then exit;
end;
begin 
	read(n,k);
	m:=2*n div k;
	for i:=1 to m do b[i]:=i*k;
	for i:=1 to n do 
	begin 
		a[1]:=i;
		dfs(2);
	end;
	write(count);
end.