Problem:
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

Solution in Python3 (judge verdict: Accepted)

r,s=map(int,input().split())
a=d=1;b=c=0
while s:q=r//s;r,s,a,c,b,d=s,r%s,c,a-q*c,d,b-q*d
print(a,b)