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 + 10;
const int mod = 1e9 + 7;
typedef long long LL;
LL exgcd(LL a, LL b, LL &x, LL &y) {
    if (b == 0) {
        x = 1, y = 0;
        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 == 0) printf("%lld %lld
", -x * c / t, -y * c / t);
    else printf("-1
");
    return 0;
}