// extended.go
// description: Implementation of Extended GCD Algorithm
// details:
// A simple implementation of Extended GCD algorithm, that returns GCD, a and b
// which solves ax + by = gcd(a, b)
// time complexity: O(log(min(a, b))) where a and b are the two numbers
// space complexity: O(log(min(a, b))) where a and b are the two numbers
// author(s) [Taj](https://github.com/tjgurwara99)
// see extended_test.go

package gcd

// Extended simple extended gcd
func Extended(a, b int64) (int64, int64, int64) {
	if a == 0 {
		return b, 0, 1
	}
	gcd, xPrime, yPrime := Extended(b%a, a)
	return gcd, yPrime - (b/a)*xPrime, xPrime
}