Blink

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.

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

• 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).

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

Input Details

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

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