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:
from math import *
n,k=map(int,raw_input().split())
count=0
i=1
ans=-1
while(i<=sqrt(n)):
    if(n%i==0):
        count+=1
        if(count==k):
            ans=i
            break
    #print(count,i)
    i+=1
if(count<k):
    if(ceil(sqrt(n))==floor(sqrt(n))):
        i-=2
    else:
        i-=1
    while(i>=1):
        if(n%i==0):
            count+=1
            if(count==k):
                ans=n/i
                break
        i-=1
print(ans)