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 Ruby (judge verdict: Accepted)

def egcd(x,y)
	return [x,1,0] if y==0
	g,a,b=egcd(y,x%y)
	[g,b,a-x/y*b]
end
puts egcd(*gets.split.map(&:to_i))[1,2]*' '