Teleport Route

A planetary system has 2^n planets numbered from 0 to 2^n - 1. Think of the planets as lying on one line in increasing order of their numbers.

Stancho first reaches planet k by using a space stop. There is also one teleport for each number from 1 to 2^n - 1. A teleport numbered t can be used at most once, and from the current planet m it can move to planet m + t or planet m - t if that planet exists.

Find an order for using teleports so that Stancho visits as many distinct planets as possible. The starting planet k is not counted.

The single line of standard input contains the positive integer n and the integer k, separated by a space.

On the first line, print the maximum number p of planets Stancho can visit, excluding planet k.

On the second line, print the numbers of the p teleports to use, in order. A teleport that moves from a larger-numbered planet to a smaller-numbered planet must be printed as a negative number.

If several valid orders are possible, print any one of them.

• 1 <= n <= 20
• 0 <= k <= 2^n - 1