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:
import sys
import math

from functools import reduce

def factors(n):
        return (reduce(list.__add__,([i, n//i] for i in range(1, int(n**0.5) + 1) if not n % i)))

val = raw_input();
val = val.split(' ');
n = int(val[0]);
k = int(val[1]);

if n != 0:
    l = factors(n)
    l.sort()
    l = list(dict.fromkeys(l))
if n == 0 or (k  > len(l)) or (n == 1 and k > 1):
    print('-1')
else:
    print(l[k - 1])