C. Line （扩展欧几里得）

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.

Examples

input

Copy

2 5 3

output

Copy

6 -3

ax+by+c=0，化为ax+by=-c/gcd(a,b)*gcd(a,b)，

套拓展欧几里得就可以解出了

 #include <bits/stdc++.h>
 using namespace std;
 const int maxn = 1e5 + ;
 const int mod = 1e9 + ;
 typedef long long LL;
 LL exgcd(LL a, LL b, LL &x, LL &y) {
     if (b == ) {
         x = , y = ;
         return a;
     }
     LL g = exgcd(b, a % b, x, y);
     LL t;
     t = x, x = y, y = t - (a / b) * y;
     return g;
 }
 int main() {
     LL a, b, c, x, y;
     cin >> a >> b >> c;
     LL t = exgcd(a, b, x, y);
     if (c % t == ) printf("%lld %lld\n", -x * c / t, -y * c / t);
     else printf("-1\n");
     return ;
 }