CF762A第K大约数（k-th divisor）
1178+

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

Copy
4 2
Output
2
Input
5 3
Outpu
-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.

2 seconds 256 megabytes

# 解题思路

n是1015，很大，从1到1015逐个数字枚举会超时；但一个数n的约数，不超过2*√n个，因为不超过√n的约数最多√n个，超过√n的约数跟不超过√n的约数是一一对应的。