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.*;

class Main{
	public static void main(String args[]){
		Scanner scan = new Scanner(System.in);
		int x = scan.nextInt();
		int y = scan.nextInt();
		int z;
		//??????????????????????????????
		//??´??° x, y(x >= y)??????????????? x ??¨ y ????????§??¬?´???°??? y ??¨ x % y ????????§??¬?´???°???????????????
		//????????§ x % y ??? x ??? y ??§?????£???????????§??????
		do{
			z = Math.max(x, y) % Math.min(x, y);
			if(z == 0){
				System.out.println(Math.min(x, y));
			}
			else{
				if(x > y){x = z;}
				else{y = z;}
			}
		}while(z != 0);
	}
}