扩展欧几里得--解一元线性方程CodeForces -7C

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

#include<stdio.h>
#include<string.h>
#include<math.h>
#include<algorithm>
using namespace std;
typedef long long LL;
LL gcd(LL a,LL b)
{
return b ? gcd(b, a%b) : a;
}
void euclid(LL a, LL b,LL &x, LL &y)
{
if(!b){
x = 1; y = 0 ;return ;
}
euclid(b,a%b,y,x);
y -= x*(a/b);
}
int main()
{
__int64 a, b, c, x, y;
while(scanf("%I64d%I64d%I64d",&a, &b, &c)==3)
{
c = -c;
LL g = gcd(a,b);
if(c%g)
{
printf("-1\n");continue;
}
a/=g;
b/=g;
c/=g;
euclid(a,b,x,y);
printf("%I64d %I64d\n",x*c,y*c);
}
return 0;
}