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

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