Sharing the Candy

Time limit2sMemory limit64 MB

Summary

For each X in [A,B], the number of even splits equals the number of divisors of X; find the maximum divisor count and all X achieving it.

Level: Medium6 of 10
Topics: Number theory, Math, Implementation, Brute force
Solved: No attempts yet

Problem

Ivica invited all of his friends to a big party. A party without candy is no party at all.

Ivica is afraid the candy will run short, so he will not buy fewer than $A$ pieces. His money is enough for at most $B$ pieces. Not every friend will come, so Ivica does not know how many people the party will have. He therefore wants to buy an amount that can be split evenly in as many ways as possible. A split is even when every friend who takes part receives the same number of pieces and none of the candy is left over. For example, if Ivica buys $6$ pieces, there are four even splits: $1+1+1+1+1+1$ , $2+2+2$ , $3+3$ , $6$ .

Write a program that tells Ivica how many pieces of candy to buy.

Input

The first and only line contains two natural numbers $A$ and $B$ , separated by one space. ( $1 \le A \le B \le 2\,000\,000$ )

Output

Let $M$ be the largest number of even splits Ivica can reach. Let $S$ be the set of all integers $X$ in the interval $[A, B]$ such that buying $X$ pieces of candy allows exactly $M$ even splits, and let $N$ be the number of elements of $S$ .

Print $M$ and $N$ on the first line, separated by one space. On each of the next $N$ lines print one element of $S$ , in increasing order.

Examples3

Example 1
Input
```
1 10
```
Expected output
```
4 3
6
8
10
```
Example 2
Input
```
13 15
```
Expected output
```
4 2
14
15
```

Example 3

Input

9125 1912412

Expected output