405841: GYM102134 B Traveling Salesman Problem

Nowadays British scientists has been investigating the opportunities to increase the performance of traditional computers. Recent research has shown that changing logical zero to logical right shift (x = x / 2) and logical one to logical negation (x = 1 - x) will lead to a significant architecture enhancement. Thus, new architecture will be able to solve some NP hard problems. Assume that mentioned above basic operations will be new zero and new one, respectively.

For example, well known traveling salesman problem solved in the proposed architecture will be equivalent to obtaining number (fraction) from a number of one (initial state). Therefore, you are required to write a program (sequence of zeros and ones) to solve traveling salesman problem for given a and b.

Single line contains two integer numbers a and b.

1  ≤ b ≤  60,

1  ≤ a < 2^b,

a is odd.

Single line should contain a binary sequence, which is a solution for traveling salesman problem using new architecture. If there are multiple solutions, the minimal length program should be printed.

1 1

0

3 3

0010