Key

Time limit1sMemory limit128 MB

Summary

Find every odd K in [A, B] such that (K-1)! is not a multiple of K^2, where B - A is at most 100 but B can be 10^18.

Level: Medium7 of 10
Topics: Number theory, Math, Probability, Brute force
Solved: No attempts yet

Problem

While cracking the passwords of several data encryption systems, a novice hacker discovered the rule by which encryption keys are formed. An encryption key is an odd integer $K$ that satisfies both of the following conditions:

$K^2$ does not divide $(K-1)!$ ; that is, $(K-1)!$ is not a multiple of $K^2$ .
$A \le K \le B$

Here $(K-1)! = (K-1) \times (K-2) \times \cdots \times 2 \times 1$ .

Find all possible encryption keys $K$ within the range $[A, B]$ .

Input

Two integers $A$ and $B$ are given on a single line, separated by a space. ( $3 \le A < B \le 10^{18}$ , $B - A \le 100$ )

Output

Print all encryption keys $K$ in the range on a single line, in ascending order, separated by single spaces. It is guaranteed that at least one key exists in the range.

Examples2

Example 1
Input
```
3 8
```
Expected output
```
3 5 7
```
Example 2
Input
```
7 14
```
Expected output
```
7 9 11 13
```