var calc_root(m) {
  int base = 1;
  repeat(70) { base *= 10; }
  var (a, b, c) = (1, 0, - m);
  var (p1, q1, p2, q2) = (1, 0, 0, 1);
  do {
    int k = -1;
    var (a1, b1, c1) = (0, 0, 0);
    do {
      k += 1;
      (a1, b1, c1) = (a, b, c);
      c += b;
      c += b += a;
    } until (c > 0);
    (a, b, c) = (- c1, - b1, - a1);
    (p1, q1) = (k * p1 + q1, p1);
    (p2, q2) = (k * p2 + q2, p2);
  } until (p1 > base);
  return (p1, q1, p2, q2);
}