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 PYTHON3):

Solution:
import sys
input=sys.stdin.readline
def read():return list(map(int,input().split()))
n,k=read()
i=2
div=[1]
if n>1:
    div.append(n)
while i*i<=n:
    if n%i==0:
        div.append(i)
        if n//i!=i:
            div.append(n//i)
    i += 1
div.sort()
if k > len(div):
    print(-1)
else:
    print(div[k-1])