Circle of Life

This is a simplified version of Conway's Game of Life played on a circular arrangement of segments. The circle is divided into N segments, numbered 1 to N in clockwise order. Each segment is either alive (denoted by 1) or dead (denoted by 0).

The game evolves automatically for T rounds. In each round, every segment updates its state simultaneously according to the following rule:

New State = \(\begin{cases} 1 & \text{if exactly one adjacent segment is alive,}\\ 0 & \text{otherwise.} \end{cases}\)

Here, the two adjacent segments of a segment are the ones immediately clockwise and anticlockwise. Note that the circle is cyclic; thus, segment 1 is adjacent to segment N and segment 2, and segment N is adjacent to segment N-1 and segment 1.

Given the initial configuration of the circle, simulate the game for T rounds and output the final state as a string of N digits.

inputFormat

The input consists of two lines:

• The first line contains two integers N and T (1 ≤ N, T ≤ some limit), where N is the number of segments and T is the number of rounds.
• The second line is a string of N characters, each of which is either 0 or 1, representing the initial state of the segments in order.

outputFormat

Output a single line containing the final state of the circle after T rounds, as a string of N digits.

sample

8 1
01010101

00000000