
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
 1 ≤ a, b ≤ 109
Sample Input 1
4 12
Sample Output 1
1 0
Sample Input 2
3 8
Sample Output 2
3 -1
