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:
def main():
    a = list(map(int, input().split()))
    delit = [1]
    if a[0] != 1:
        delit.append(a[0])
    count = 1
    for i in range(2, int(a[0] ** 0.5) + 1):
        if a[0] % i == 0:
            delit.append(i)
            b = a[0] // i
            if i != b:
                delit.append(b)
    delit.sort()
    return -1 if len(delit) < a[1] else delit[a[1] - 1]

print(main())