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