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:
n,k=map(int,input().split())
ct=0

num=int(n**(0.5))
i=1
ct=0
arr=[]
ch=0
l=0
while(i<=num):
    if(n%i==0):
        if(i*i!=n):
            arr.append(n//i)
            l+=1
        arr.append(i)
        ct+=1
        l+=1
    if(ct==k):
        print(i)
        ch=1
        break
    i+=1
if(ch==0):
    if(l<k):
        print(-1)
    else:
        arr.sort()
        print(arr[k-1])