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:
# cook your dish here
from math import *
n,k=map(int,input().split())
a=[1]
if(n!=1):
	a.append(n)
for i in range(2,int(sqrt(n)+1)):
	if(n%i==0):
		a.append(i)
		if((n//i)!=i):
			a.append(n//i)
a.sort()
if(k>len(a)):
	print(-1)
else:
	print(a[k-1])