D. Ehab and the Expected XOR Problemtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputGiven two integers n and x, construct an array that satisfies the following conditions:   for any element a_i in the array, 1 \le a_i<2^n;  there is no non-empty subsegment with bitwise XOR equal to 0 or x,  its length l should be maximized. A sequence b is a subsegment of a sequence a if b can be obtained from a by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.InputThe only line contains two integers n and x (1 \le n \le 18, 1 \le x<2^{18}).OutputThe first line should contain the length of the array l.If l is positive, the second line should contain l space-separated integers a_1, a_2, \dots, a_l (1 \le a_i < 2^n) — the elements of the array a.If there are multiple solutions, print any of them.ExamplesInput
3 5
Output
3
6 1 3Input
2 4
Output
3
1 3 1 Input
1 1
Output
0
NoteIn the first example, the bitwise XOR of the subsegments are \{6,7,4,1,2,3\}.
3 5

3 6 1 3
['bitmasks', 'constructive algorithms', '*1900']