# Extended Euclid Algorithm

Given positive integers `a` and `b`, find the integer solution (`x`, `y`) to `ax + by = gcd(a, b)`, where `gcd(a, b)` is the greatest common divisor of `a` and `b`.

## Input

`a` `b`

Two positive integers `a` and `b` are given separated by a space in a line.

## Output

Print two integers `x` and `y` separated by a space. If there are several pairs of such `x` and `y`, print that pair for which `|x| + |y|` is the minimal (primarily) and `x` ≤ `y` (secondarily).

## Constraints

## Sample Input 1

4 12

## Sample Output 1

1 0

## Sample Input 2

3 8

## Sample Output 2

3 -1