Euclid Problem

The Problem

From Euclid it is known that for any positive integers A and B there exist such integers X and Y that AX+BY=D, where D is the greatest common divisor of A and B. The problem is to find for given A and B corresponding X, Y and D.

The Input

The input will consist of a set of lines with the integer numbers A and B, separated with space (A,B<1000000001).

The Output

For each input line the output line should consist of three integers X, Y and D, separated with space. If there are several such X and Y, you should output that pair for which |X|+|Y| is the minimal (primarily) and X<=Y (secondarily).

Sample Input

4 6
17 17

Sample Output

-1 1 2
0 1 17

#include <stdio.h>
int gcd(int a, int b) {
    int tmp, flag = 0;
    int x1 = 1, y1 = 0, x2 = 0, y2 = 1;
    while(a%b) {
        if(flag) {
            x2 -= a/b*x1;
            y2 -= a/b*y1;
        } else {
            x1 -= a/b*x2;
            y1 -= a/b*y2;
        }
        tmp = a, a = b, b = tmp%b;
        flag ^= 1;
    }
    if(flag)
        printf("%d %d", x1, y1);
    else
        printf("%d %d", x2, y2);
    printf(" %d\n", b);
    return b;
}
int main() {
    int A, B;
    while(scanf("%d %d", &A, &B) == 2) {
        gcd(A, B);
    }
    return 0;
}