Problem:
Score : 300 points

Problem Statement

You are given an integer N.

Find a triple of positive integers h, n and w such that 4/N = 1/h + 1/n + 1/w.

If there are multiple solutions, any of them will be accepted.

Constraints

It is guaranteed that, for the given integer N, there exists a solution such that h,n,w \leq 3500.

Inputs

Input is given from Standard Input in the following format:

N

Outputs

Print a triple of positive integers h, n and w that satisfies the condition, in the following format:

h n w

Sample Input 1

2

Sample Output 1

1 2 2

4/2 = 1/1 + 1/2 + 1/2.

Sample Input 2

3485

Sample Output 2

872 1012974 1539173474040

It is allowed to use an integer exceeding 3500 in a solution.

Sample Input 3

4664

Sample Output 3

3498 3498 3498

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#define ll long long
using namespace std;

struct FS{
	ll x,y;
}n,a,b,c;

FS operator + (FS u,FS v){
	return (FS){ u.x*v.y+v.x*u.y , u.y*v.y };
}
FS operator - (FS u,FS v){
	return (FS){ u.x*v.y-v.x*u.y , u.y*v.y };
}
bool operator < (FS u,FS v){
	return u.x*v.y<v.x*u.y;
}

int main(){
	ll t;cin>>t;n=(FS){4,t};
	for (int i=1;i<=3500;i++){
		a=(FS){1,i};
		for (int j=1;j<=3500;j++){
			b=(FS){1,j};
			c=a+b;
			if (c<n){
				c=n-c;
				if (c.y%c.x==0){
					printf("%d %d %lld",i,j,c.y/c.x);
					return 0;
				}
			}
		}
	}
}