Baltic OI '03 P5 - Lamps

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Points: 15 (partial)
Time limit: 3.0s
Memory limit: 64M

Problem types
Baltic Olympiad in Informatics: 2003 Day 2, Problem 2

There is a castle with a circular main hall. There are N lamps numbered from 1 to N on the wall of the hall. Each of the lamps can be either on or off. At each second the lamp number i changes its state if the lamp number i+1 is on, except the lamp number N changes its state if the lamp number 1 is on.

Your task is, given the initial states of all lamps at some moment, to find their states after M seconds.

Input Specification

The first line of the input contains two integers N (0 < N \le 10^6) and M (0 \le M \le 10^9). The next N lines contain the initial states of the lamps, starting with the lamp number 1. A line containing 0 means that the lamp is off and 1 means that the lamp is on.

Output Specification

The output must contain exactly N lines describing the states of the lamps after M seconds, starting with the lamp number 1.

Sample Input

3 1
0
0
1

Sample Output

0
1
1

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