#include <bits/stdc++.h>
using namespace std;

int C, n, a[505], b[505];
double rs;

bool vis[505];
bool check(double p, double t) {
    if (t >= rs) return 0; 
    double t1(0), t2(0);
    for (int i = 1; i <= n; i++) if (!vis[i]) {
        if (a[i] > 0) t1 = max(t1, (a[i] + b[i] * t - p) / (C - b[i]));
        else t2 = max(t2, (p - a[i] + b[i] * t) / (C - b[i]));
    }
    double t3(0), t4(0);
    for (int i = 1; i <= n; i++) if (!vis[i]) {
        if (a[i] < 0) t3 = max(t3, (p + t1 * C - a[i] + b[i] * (t + t1)) / (C - b[i]));
        else t4 = max(t4, (a[i] + b[i] * (t + t2) - p + t2 * C) / (C - b[i]));
    }
    rs = min(rs, t + min(t1 + t3, t2 + t4));
    return t + max(t1, t2) >= rs;
}
bool end() {
    for (int i = 1; i <= n; i++) if (!vis[i]) return 0;
    return 1;
}
void dfs(double p, double t) {
    if (clock() * 1.0 / CLOCKS_PER_SEC > 1.6) return;
    if (check(p, t)) return;
    if (end()) return rs = t, void();
    int mx1(0), mx2(0), id1(0), id2(0);
    for (int i = 1; i <= n; i++) if (!vis[i]) {
        if (a[i] > 0) {
            if (b[i] > mx1) mx1 = b[i], id1 = i;
        } else {
            if (b[i] > mx2) mx2 = b[i], id2 = i;
        }
    }
    if (id1) {
        double tt = (a[id1] + b[id1] * 1.0 * t - p) / (C - b[id1]);
        vector<int> dl;
        for (int i = 1; i <= n; i++) if (!vis[i] && a[i] > 0) {
            if ((a[i] + b[i] * 1.0 * t - p) / (C - b[i]) <= tt) dl.push_back(i), vis[i] = 1;
        }
        dfs(p + tt * C, t + tt);
        for (int i : dl) vis[i] = 0;
    }
    if (id2) {
        double tt = (-a[id2] + b[id2] * 1.0 * t + p) / (C - b[id2]);
        vector<int> dl;
        for (int i = 1; i <= n; i++) if (!vis[i] && a[i] < 0) {
            if ((-a[i] + b[i] * 1.0 * t + p) / (C - b[i]) <= tt) dl.push_back(i), vis[i] = 1;
        }
        dfs(p - tt * C, t + tt);
        for (int i : dl) vis[i] = 0;
    }
}

int TT;

void solve() {
    cin >> C >> n;
    for (int i = 1; i <= n; i++) cin >> a[i];
    for (int i = 1; i <= n; i++) cin >> b[i];
    rs = 1e18;
    double t1(0), t2(0);
    for (int i = 1; i <= n; i++) if (a[i] > 0) t1 = max(t1, a[i] * 1.0 / (C - b[i]));
    for (int i = 1; i <= n; i++) if (a[i] < 0) t2 = max(t2, (b[i] * t1 + C * t1 - a[i]) / (C - b[i]));
    rs = t1 + t2;
    t1 = t2 = 0;
    for (int i = 1; i <= n; i++) if (a[i] < 0) t1 = max(t1, a[i] * -1.0 / (C - b[i]));
    for (int i = 1; i <= n; i++) if (a[i] > 0) t2 = max(t2, (b[i] * t1 + C * t1 + a[i]) / (C - b[i]));
    rs = min(rs, t1 + t2);
    dfs(0, 0);
    cout << "Case #" << ++TT << ": " << fixed << setprecision(7) << rs << '\n';
}

signed main() {
#ifdef LARRIX
    freopen("sample.in", "r", stdin);
    freopen("sample.out", "w", stdout);
#endif
    ios::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);
    int T; cin >> T;
    while (T--) solve();
    return 0;
}
/*
*/