#include <bits/stdc++.h>
const long double eps = 1e-12;
int main() {
#ifdef ONLINE_JUDGE
	std::ios::sync_with_stdio(false);
	std::cin.tie(nullptr), std::cout.tie(nullptr);
	std::freopen("tiii.in", "r", stdin);
	std::freopen("tiii.out", "w", stdout);
#else
	std::freopen(".in", "r", stdin);
	std::freopen(".out", "w", stdout);
#endif
	int T;
	for (std::cin >> T; T--; ) {
		int v, n;
		std::cin >> v >> n;
		std::vector<std::pair<int, int> > a(n + 1);
		for (int i = 1; i <= n; ++i)
			std::cin >> a[i].first;
		for (int i = 1; i <= n; ++i)
			std::cin >> a[i].second;
		a.emplace_back(0, 0), ++n;
		std::sort(a.begin() + 1, a.end());
		int p = std::lower_bound(a.begin() + 1, a.end(), std::make_pair(0, 0)) - a.begin();
		std::sort(a.begin() + 1, a.begin() + p, [](std::pair<int, int> x, std::pair<int, int> y) { return x.second == y.second ? x.first < y.first : x.second > y.second; });
		std::sort(a.begin() + p + 1, a.end(), [](std::pair<int, int> x, std::pair<int, int> y) { return x.second == y.second ? x.first < y.first : x.second < y.second; });
		std::vector<std::vector<long double> > f(n + 1, std::vector<long double> (n + 1, 1e18));
		f[1][n] = 0.;
		auto at = [&](int i, long double t) {
			return std::fabs(a[i].first + t * a[i].second * (i < p ? -1 : 1));
		};
		auto calc = [&](int i, long double t) {
			return at(i, t) / (v - a[i].second);
		};
		// for (int i = 1; i <= n; ++i)
		// 	printf("%d: (%d, %d)\n", i, a[i].first, a[i].second);
		for (int i = 1; i <= p; ++i)
			for (int j = n; j >= p; --j) {
				if (i == p && j == p)
					break;
				long double d = 0.;
				// printf("[%d, %d]: %lf\n", i, j, f[i][j]);
				for (int k = i; k < p; ++k) {
					if (at(k, f[i][j]) >= at(i, f[i][j]) - eps)
						d = std::max(d, calc(k, f[i][j]));
					// printf("  k1 = %d, d = %lf\n", k, d);
					f[k + 1][j] = std::min(f[k + 1][j], f[i][j] + d + (k != j - 1) * d);
				}
				d = 0.;
				for (int k = j; k > p; --k) {
					if (at(k, f[i][j]) >= at(j, f[i][j]) - eps)
						d = std::max(d, calc(k, f[i][j]));
					// printf("  k2 = %d, d = %lf\n", k, d);
					f[i][k - 1] = std::min(f[i][k - 1], f[i][j] + d + (k != i + 1) * d);
				}
			}
		{
			static int casetot = 0;
			std::cout << "Case #" << ++casetot << ": ";
		}
		std::cout << std::fixed << std::setprecision(9) << f[p][p] << '\n';
	}
	return 0;
}