CodeForces 7C Line Exgcd（数论）

题意：给直线AX+BY+C=0，找出直线上的一个整数点，没有则输出-1

思路：exgcd裸题...数论真是博大精深...

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

void gcd(long long a,long long b,long long& d,long long& x,long long& y)
{
    if(!b){d=a,x=1,y=0;}
    else{gcd(b,a%b,d,y,x);y-=x*(a/b);}
}
int main()
{
    long long a,b,c,d,x,y;
    cin>>a>>b>>c;c=-c;
    gcd(a,b,d,x,y);
    if(c%d!=0)return puts("-1"),0;
    else
    {
        printf("%lld %lld\n",x*c/d,y*c/d);
    }
}

Description

A line on the plane is described by an equation Ax + By + C = 0. You are to find any point on this line, whose coordinates are integer numbers from  - 5·10¹⁸ to 5·10¹⁸ inclusive, or to find out that such points do not exist.

Input

The first line contains three integers A, B and C ( - 2·10⁹ ≤ A, B, C ≤ 2·10⁹) — corresponding coefficients of the line equation. It is guaranteed that A² + B² > 0.

Output

If the required point exists, output its coordinates, otherwise output -1.

Sample Input

Input

2 5 3

Output

6 -3

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