string cipher(int k, string s)
{
  int n = (int)s.size(), m = n-k+1, t = k+1;
  string r(m, 0), x(t, 0);
  for (int i = 0; i < m; i++) {
    x[i%t] = x[(i+1)%t] ^ (s[n-1-i]-'0');
    r[m-1-i] = (x[i%t] ^ x[(i+k)%t]) + '0';
  }
  return r;
}