Time Limit : sec, Memory Limit : KB

# 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 xy (secondarily).

## Constraints

• 1 ≤ a, b ≤ 109

## Sample Input 1

4 12


## Sample Output 1

1 0


## Sample Input 2

3 8


## Sample Output 2

3 -1