C. Line （扩展欧几里得）

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

 1 #include <bits/stdc++.h>
 2 using namespace std;
 3 const int maxn = 1e5 + 10;
 4 const int mod = 1e9 + 7;
 5 typedef long long LL;
 6 LL exgcd(LL a, LL b, LL &x, LL &y) {
 7     if (b == 0) {
 8         x = 1, y = 0;
 9         return a;
10     }
11     LL g = exgcd(b, a % b, x, y);
12     LL t;
13     t = x, x = y, y = t - (a / b) * y;
14     return g;
15 }
16 int main() {
17     LL a, b, c, x, y;
18     cin >> a >> b >> c;
19     LL t = exgcd(a, b, x, y);
20     if (c % t == 0) printf("%lld %lld
", -x * c / t, -y * c / t);
21     else printf("-1
");
22     return 0;
23 }