Problem: You are given two integers n and k. Find k-th smallest divisor of n, or report that it doesn't exist.

Divisor of n is any such natural number, that n can be divided by it without remainder.

Input

The first line contains two integers n and k (1 ≤ n ≤ 1015, 1 ≤ k ≤ 109).

Output

If n has less than k divisors, output -1.

Otherwise, output the k-th smallest divisor of n.

Examples

Input

4 2


Output

2


Input

5 3


Output

-1


Input

12 5


Output

6

Note

In the first example, number 4 has three divisors: 1, 2 and 4. The second one is 2.

In the second example, number 5 has only two divisors: 1 and 5. The third divisor doesn't exist, so the answer is -1.

Solution (in JAVA):

Solution:
function main(){
	var numbers = readline().split(" ").map(Number);
	
	var num = numbers[0];
	var kthdiv = numbers[1];
	var divs = [];

	if(numbers[1] === 1)
		return 1;

	if(numbers[0] === 1 && numbers[1] !== 1)
        return -1;

	divs.push(1);

	var numDiv = 1;

	for(var i = 2; i <= Math.sqrt(num); i++)
		if(num % i === 0 && ++numDiv === kthdiv)
			return i;
		else if(num % i === 0)
			divs.push(i);


	for(i = divs.length-1; i >= 0; i--)
        if(num / divs[i] !== divs[i])
            divs.push(num/divs[i]);
    
	if(kthdiv <= divs.length)
		return divs[kthdiv-1];

	return -1;
}

print(main());