#include <string.h>
#include <assert.h>
#include <array>
#include <bitset>
#include <functional>
#include <iostream>
#include <stdlib.h>

using namespace std;

typedef uint32_t State;
const State logState = 16;
const State maxState = 1 << logState;

bitset<8> rule(110);

State update(State s) {
  State r(0);
  bitset<logState> b(s);
  for (unsigned i=0; i<logState; i++)
    r |= rule[1 * b[(i + logState - 1) % logState]
	    + 2 * b[i]                
	    + 4 * b[(i + 1) % logState]] << i;
  return r;
}

typedef array<State, maxState> Trans;

void iterTrans(int times, function<void(int)> f) {
  while (times--)
    for (State s=0; s<maxState; s++)
      f(s);
}

void init(Trans &t) {
  iterTrans(1, [&](int s) { 
      t[s] = update(s); });
}

Trans* findCycle(Trans &t) {
  // forward to t=maxState; now every state is in a cycle
  iterTrans(logState, [&](int s) {
      t[s] = t[t[s]]; });
  // compute loop id (lowest state no): go through the loop again and
  // record the lowest occuring state no
  Trans &c(*new Trans());
  iterTrans(1, [&](int s) { 
      c[s] = t[s]; });
  iterTrans(logState, [&](int s) {
      c[s] = min(c[s], c[t[s]]);
      t[s] = t[t[s]]; });
  return &c;
}

void print(Trans &t) {
  for (auto s : t)
    cout << bitset<logState>(s) << endl;
}

void printTraj(State s, int count) {
  while (count--) {
    cout << bitset<logState>(s) << endl;
    s = update(s);
  }
}

int main(int argc, char **argv) {
  assert(argc >= 2);
  rule = atoi(argv[1]);
  if (!strcmp(argv[2], "traj")) {
    assert(argc == 5);
    printTraj(atoi(argv[3]), atoi(argv[4]));
  }
  if (!strcmp(argv[2], "cycle")) {
    Trans &t = *(new Trans);
    init(t);
    Trans &c(*findCycle(t));
    print(c);
  }
  return 0;
}