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<stdio.h>
typedef long long ll;
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
struct pr{
	ll x,y;
	pr(ll a,ll b){
		ll g=gcd(a,b);
		x=a/g;
		y=b/g;
	}
};
pr operator-(pr a,pr b){
	if(a.x*b.y<a.y*b.x)return pr(-1,1);
	return pr(a.x*b.y-a.y*b.x,a.y*b.y);
};
int main(){
	ll n,i,j;
	pr t(0,1);
	scanf("%lld",&n);
	for(i=1;i<=3500;i++){
		for(j=1;j<=3500;j++){
			t=pr(4,n)-pr(1,i)-pr(1,j);
			if(t.x==1){
				printf("%lld %lld %lld\n",i,j,t.y);
				return 0;
			}
		}
	}
}