This problem is worth 30% of the 100 points allocated to S5

Consider an array of length ~N~, filled with positive integers from the range ~1~ to ~N~, inclusive (the array does not necessarily need to contain every number, however).

An array with maximum element ~x_i~ is considered happy under the following conditions:

1. All of its elements lie in the range ~1~ to ~x_i~
2. Each number from the range ~1~ to ~x_i~ occur at least once in the array
3. The first occurence of the positive integer ~i (1 \leq i < x_i)~ lies before the first occurence of the positive integer ~i+1~.

Brian hands you over the length ~N~, and tells you to find the ~M^{th}~ happy array sorted in ascending lexographical order (as in, starting from the array of all ~1's~).

Input Specification

There is one line of input containing two space-separated integers ~N, M~, representing the number of elements in the array and the happy array you are asked to find. It is guaranteed that there exists such a happy array.

Output Specification

Output a line, containing ~N~ space-separated integers, representing the happy array asked for.

Constraints

Marks Allocated	Bounds on ~N~	Bounds on ~M~
~10\%~	~N = 3~	~1 \leq M \leq 5~
~20\%~	~1 \leq N \leq 10~	~1 \leq M \leq 50~
~70\%~	~1 \leq N \leq 10^5~	~1 \leq M \leq 10^7~

Sample Input 1

4 5

Sample Output 1

1 1 2 3

Sample Explanation 1

The five lexographically least happy arrays, in ascending order are the following: 1 1 1 1 1 1 1 2 1 1 2 1 1 1 2 2 1 1 2 3. Keep in mind that 1 1 1 3 is not a happy array.