from operator import xor
from functools import reduce
 
class LFSR(object):
    def __init__(self, taps, func, init):
        self.func = func
        self.state = int(init, 2)
        self.width = len(init)
        self.taps = [self.width - t - 1 for t in taps]
 
    def _bit(self, b):
        return (self.state & 1 << b) >> b
 
    def step(self):
        shift = reduce(self.func, (self._bit(t) for t in self.taps)) & 1
        self.state >>= 1
        if shift:
            self.state |= 1 << (self.width - 1)
 
    def __str__(self):
        return '{:0{}b}'.format(self.state, self.width)
 
def xnor(a, b):
    return ~xor(a, b)
 
def run(challenge):
    taps, func, start, count = challenge.split()
    taps = list(map(int, taps[1:-1].split(',')))
    func = xor if func == 'XOR' else xnor
    count = int(count)
 
    reg = LFSR(taps, func, start)
    print(0, reg)
    for i in range(1, count + 1):
        reg.step()
        print(i, reg)
 
if __name__ == '__main__':
    for challenge in ['[1,2] XOR 001 7',
                      '[0,2] XNOR 001 7',
                      '[1,2,3,7] XOR 00000001 16',
                      '[1,5,6,31] XOR 00000000000000000000000000000001 16']:
        run(challenge)
        print()

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