Codeforces 797A

A. k-Factorization

题目链接：http://codeforces.com/problemset/problem/797/A

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Given a positive integer n, find k integers (not necessary distinct) such that all these integers are strictly greater than 1, and their product is equal to n.

Input

The first line contains two integers n and k (2 ≤ n ≤ 100000, 1 ≤ k ≤ 20).

Output

If it's impossible to find the representation of n as a product of k numbers, print -1.

Otherwise, print k integers in any order. Their product must be equal to n. If there are multiple answers, print any of them.

Examples

input

5 1

output

5 

input

5 2

output

-1

input

1024 5

output

2 64 2 2 2 
题目大意：输入两个数n和k,找k个大于1的整数，使他们的乘积为n，输出这k个数（如果有多个，输出任意一组），如果没有，输出-1。
方法：把n分解成质因数的乘积，并把这些质因数保存在数组里。如果质因数的个数c小于k,输出-1；否则，输出前k-1个质因数和k到c个质因数的乘积（这样就刚好k个）。
代码：

#include<iostream>
#include<cstdio>
#include<cmath>
using namespace std;
const int N=1e5;
int main()
{
    int n,k;
    cin>>n>>k;
    int f[N];
    int c=0;
    for(int i=2;i<=n;i++)
    {
        while(n%i==0)
        {
            n/=i;
            f[c++]=i;
        }
    }
    if(c<k)cout<<-1<<endl;
    else 
    {
        for(int i=0;i<k-1;i++)
        cout<<f[i]<<' ';
        int sum=1;
        for(int i=k-1;i<c;i++)
        sum*=f[i];
        cout<<sum<<endl;
    }
    return 0;
}