k-th divisor
题目描述
A. k-th divisor
time limit per test
2 secondsmemory limit per test
256 megabytesinput
standard inputoutput
standard outputYou 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.
题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 371 题。保留原作者与原赛事署名。