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())
c=2
if n==1:
    c=1
for i in range(2,int(n**0.5)+1):
    if n%i==0:
        c+=1
        if n//i!=i:
            c+=1
if k>c:
    print(-1)
else:
    t=0
    for i in range(1,int(n**0.5)+1):
        if n%i==0:
            t+=1
            if t==k:
                print(i)
                break
            elif c-t+1==k:
                print(n//i)
                break