Problem:
Greatest Common Divisor

Write a program which finds the greatest common divisor of two natural numbers a and b

Input

a and b are given in a line sparated by a single space.

Output

Output the greatest common divisor of a and b.

Constrants

1 ≤ a, b ≤ 109

Hint

You can use the following observation:

For integers x and y, if x ≥ y, then gcd(x, y) = gcd(y, x%y)

Sample Input 1

54 20

Sample Output 1

2

Sample Input 2

147 105

Sample Output 2

21

Solution in JAVA (judge verdict: Accepted)

import java.util.Scanner;

/**
 * 素数判定
 * @author nobu
 * @see <a href="http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_1_B&lang=ja">ALDS1_1_B</a>
 */
public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int x = sc.nextInt();
		int y = sc.nextInt();

		System.out.println(gcd(x, y));

		sc.close();
	}

	private static int gcd(int x, int y) {
		if (x < y) {
			int tmp = x;
			x = y;
			y = tmp;
		}

		while (0 < y) {
			int r = x % y;
			x = y;
			y = r;
		}

		return x;
	}

}