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 math
a=list(map(int,input().split()))
s=[]
for i in range(1,int(math.sqrt(a[0]))+1):
    if(a[0]%i==0):
        s.append(i)
        if(i*i!=a[0]):
            s.append(a[0]//i)
s.sort()
if(len(s)<a[1]):
    print(-1)
else:
    print(s[a[1]-1])