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: Time Limit Exceeded)

import java.util.Scanner;

class Main {
	public static void main(String args[]) {
		Scanner scanner = new Scanner(System.in);
		long numbef = scanner.nextInt();//要素数
		long numaft = scanner.nextInt();//要素数
		
		
		insertionSort(numbef, numaft);
		
		scanner.close();
	}

	public static void insertionSort( long numbef, long numaft){
		long subbef = numbef / 2;
		long subaft = numbef / 2;
		long sub = 0;
		long gcd = 1 ; 
		
		//重複しないために
		if( numbef == numaft ){
			System.out.println(numbef);
			return;
		}else if( subaft > subbef ){
			sub = subbef + 1;
		}else{
			sub = subaft + 1;
		}
		
		//最大公約数探し
		for(int i = 1; i <= sub; i ++ ){
			if( numbef % i == 0 && numaft % i == 0){
				gcd = i;
			}
		}
		
		System.out.println(gcd);
	}
}