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())




t=[]
p=0
h=0
for j in range(1,int(n**(0.5))+1):

    if n%j==0:
        if j!=n//j:
            t.append(n//j)
        p+=1
        if p==k:
            print(j)
            h+=1
            break



if h==0:
    p-=k

    if abs(p)>len(t):
        print(-1)
    else:
        print(t[p])