#10104Euclid 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.

Input

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

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. If there are several X and Y satisfying the minimal criteria, output the pair for which X ≤ Y .

4 6
17 17

-1 1 2
0 1 17