Educational Codeforces Round 17 |
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Finished |

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math

number theory

*1400

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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* ≤ 10^{15}, 1 ≤ *k* ≤ 10^{9}).

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.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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