Blink               blink.X

Unhappy with the dim lighting in his barn, Farmer John has just installed a
fancy new chandelier consisting of N (3 <= N <= 16) lights bulbs arranged
in a circle.  

The cows are fascinated by this new light fixture, and enjoy playing the
following game: at time T, they toggle the state of each light bulb if its
neighbor to the left was turned on at time T-1.  They continue this game
for B units of time (1 <= B <= 10^15).  Note that B might be too large to
fit into a standard 32-bit integer, but a long integer will be OK.

Given the initial states of the light bulbs, please determine their final
states after B units of time have elapsed.

PROBLEM NAME: blink

INPUT FORMAT:

* Line 1: Two space-separated integers, N and B.

* Lines 2..1+N: Line i+1 contains the initial state of bulb i, either
        0 (off) or 1 (on).

SAMPLE INPUT:

5 6
1
0
0
0
0

INPUT DETAILS:

There are five light bulbs.  The first is initially on, and the others are off.

OUTPUT FORMAT:

* Lines 1..N: Line i should contain the final state of bulb i, either
        0 (off) or 1 (on).

SAMPLE OUTPUT:

1
1
1
0
1

OUTPUT DETAILS:

The light bulb states are as follows:
Time T=0: 1 0 0 0 0
Time T=1: 1 1 0 0 0
Time T=2: 1 0 1 0 0
Time T=3: 1 1 1 1 0
Time T=4: 1 0 0 0 1
Time T=5: 0 1 0 0 1
Time T=6: 1 1 1 0 1