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)

def exgcd(x,y):
  a0,a1=1,0
  b0,b1=0,1
  while y>0:
    q=x//y
    a2=a0-q*a1
    b2=b0-q*b1
    x,y=y,x%y
    a0,a1=a1,a2
    b0,b1=b1,b2
  return [a0,b0]
  
x,y=map(int,input().split())
ans=exgcd(x,y)
print(ans[0],ans[1])