CF7C 扩展欧几里得解不定方程

题目链接：http://codeforces.com/problemset/problem/7/C

C. Line

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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 test(s)

input

2 5 3

output

6 -3

扩展欧几里得AX+BY=GCD(A,B)

AX+BY=-C/Z;(-C/Z==GCD(A,B))

AX*Z+BY*Z=-C;

通过扩展欧几里得我们可以求出X,Y来

最后的解为(x*z,y*z);

#include <iostream>
#include <cstdio>
using namespace std;
typedef long long LL;
LL x,y;
LL ex_gcd(LL a,LL b,LL &x,LL &y)
{
    if(!b){
        x=1;
        y=0;
        return a;
    }
    LL result=ex_gcd(b,a%b,x,y);
    LL tmp=x-a/b*y;
    x=y;
    y=tmp;
    return result;
}
int main()
{
    LL a,b,c;
    while(cin>>a>>b>>c){
        LL r=ex_gcd(a,b,x,y);
        if(c%r!=0){
            puts("-1");
        }
        else{
            cout<<-x*(c/r)<<" "<<-y*(c/r)<<endl;
        }
    }
    return 0;
}