Universal Ruler#2432

Universal Ruler

2 seconds
256 megabytes
Medium

To measure a segment using a ruler, place the ruler so that one end of the segment aligns with a mark on the ruler, and the other end aligns with another mark. The length of the segment is then the difference between the numbers corresponding to these two marks.

You are given a plain ruler of sufficient length without any marks. Your goal is to add the fewest marks possible so that you can measure any integer segment length from to .

Input

The first line contains two integers and (1 \leq l \leq r \leq 23).

Output

On the first line, print the minimum number of marks required to measure all segment lengths from to . On the second line, list the required marks in ascending order. All numbers must be integers and must not exceed in absolute value.

Examples

Example 1

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