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

The cows 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).

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출처 올림피아드 > USACO > 2012-2013 > US Open > Bronze