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 PYTHON):

Solution:
def prime(n, m) :
    i = 1
    p = 0
    div = []
    while i*i <= n :
        if n % i == 0 :
            if i*i != n :
                div.append(n/i)
                div.append(i)
            else :
                div.append(i)
        i += 1
    div.sort()
    if len(div) >= m :
        return div[m-1]
    return -1

n, m = map(int, raw_input().split())

print prime(n, m)