Codeforces Round #384 (Div. 2) C. Vladik and fractions 构造题

C. Vladik and fractions

题目链接

http://codeforces.com/contest/743/problem/C

题面

Vladik and Chloe decided to determine who of them is better at math. Vladik claimed that for any positive integer n he can represent fraction as a sum of three distinct positive fractions in form .

Help Vladik with that, i.e for a given n find three distinct positive integers x, y and z such that . Because Chloe can't check Vladik's answer if the numbers are large, he asks you to print numbers not exceeding 109.

If there is no such answer, print -1.

输入

The single line contains single integer n (1 ≤ n ≤ 104).

输出

If the answer exists, print 3 distinct numbers x, y and z (1 ≤ x, y, z ≤ 109, x ≠ y, x ≠ z, y ≠ z). Otherwise print -1.

If there are multiple answers, print any of them.

样例输入

3

样例输出

2 7 42

题意

给你n，让你找到一个x,y,z，使得2/n = 1/x+1/y+1/z

题解

n=1的时候无解，否则可以构造出x=n,y=n+1,z=n(n+1)

代码

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

long long n;
int main()
{
    cin>>n;
    if(n==1)cout<<"-1"<<endl;
    else cout<<n<<" "<<n+1<<" "<<n*(n+1)<<endl;
}