C.cpp

int main() {
  double r;
  int n;
  while (cin >> r >> n, r) {
    vector<double> h(60, 0.0);
    auto height = h.begin() + 30;
    REP(i,n) {
      int xl, xr;
      double y;
      cin >> xl >> xr >> y;
      for (int j = xl; j < xr; j++) {
        height[j] = max(height[j], y);
      }
    }
    double res = 1e5;
    for (int i = -30; i < 30; i++) {
      if (abs(i) >= r) continue;
      double he = min(height[i-1], height[i]);
      res = min(res, r - sqrt(r*r - i*i) + he);
    }
    cout << setprecision(10) << fixed << res << endl;
  }
  return 0;
}