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

n, k = map(int, input().split())
if k > n:
    print(-1)
    exit()
d = list()
found = False
sqrt = int(math.sqrt(n))
for i in range(1, sqrt + 1):
    if n % i == 0:
        d.append(i)
    if len(d) == k:
        found = True
        print(i)
        break

if not found:
    if k <= len(d) * 2:
        if sqrt * sqrt == n:
            if k == len(d) * 2:
                print(-1)
            else:
                print(n // d[-(k - len(d)) - 1])
        else:
            print(n // d[-(k - len(d))])
    else:
        print(-1)