Codeforces 743C Vladik and fractions（数学）

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本文介绍了一个关于将特定形式的分数拆分为三个不同正分数之和的问题，并提供了一种有效的解决方案。通过设定特定的x、y、z值，能够满足题目要求的条件，即对于任意正整数n，找到x、y、z使得分数1/n可以表示为它们的和。

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 $\text{[math]}$ as a sum of three distinct positive fractions in form $\text{[math]}$ .

Help Vladik with that, i.e for a given n find three distinct positive integers x, y and z such that $\text{[math]}$ . 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

题意：给定 n 值，输出符合的 x, y, z 。

思路：

即 x = n， y = n+1, z = n*(n+1)

ac code：

#include<stdio.h>
#include<cstring>
#include<cmath>
#include<algorithm>
#define HardBoy main()
#define ForMyLove return 0;
using namespace std;
const int MYDD = 1103;

int HardBoy {
	int n;
	scanf("%d", &n);
	if(n == 1){
		puts("-1");
	} else {
		printf("%d %d %d\n", n, n+1, n*(n+1)); 
	} 
	ForMyLove
}