codeforces 743-C. Vladik and fractions（构造）

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.
Input

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

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.
Examples
Input

3

Output

2 7 42

Input

7

Output

7 8 56

题目大意：
给你一个n，找出一组最小的三个数x、y、z，满足x< y< z，并且2/n=1/x+1/y+1/z。

解题思路：
构造出

2/n = 1/n + 1/(n+1) + 1/(n*(n+1))

即此时x、y、z是最小的。
但是有两种情况应该排除在外，第一种n=1的时候，不能构造，第二种n=3的时候，可以构造成 2/3 = 1/2 + 1/7 + 1/42

#include<iostream>using namespace std;int main(){    int n;    while(cin>>n)    {        if(n==1)          cout<<-1<<endl;        else        {            if(n==3)              cout<<2<<" "<<7<<" "<<42<<endl;            else              cout<<n<<" "<<n+1<<" "<<n*(n+1)<<endl;        }    }    return 0;}