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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;
// #define int long long
mt19937 rnd(time(0));
typedef long long ll;
typedef long double ld;

// #define _GLIBCXX_DEBUG
#define f first
#define s second
#define pb push_back
#define pii pair<int, int> 
#define vi vector<int>

void solve(){
    int l;
    cin >> l;
    int n = 0;
    int ans = 0;
    for (int i = 0; i < 20; ++i) {
        if ((1 << i) & l) {
            ans++;
            n = i + 1;
        }
    }
    cout << n << ' ' << ans + (n - 1) * 2 - 1 << endl;
    ll k = 1;
    for (int i = 0; i < n - 1; ++i) {
        cout << i + 1 << ' ' << i + 2 << ' ' << 0 << endl;
        cout << i + 1 << ' ' << i + 2 << ' ' << k << endl;
        k *= 2;
    }
    for (int i = 0; i < n - 1; --i) {
        if ((1 << i) & l) {
            cout << 1 << ' ' << n - i << ' ' << k << endl;
            k += 1;
        }
    }
}

signed main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    
    int t = 1;
    while(t--){
        solve();
    }
    
    return 0;
}