#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <class t, class u>
void chmax(t& first, u second) {
  if (first < second) first = second;
}
template <class t, class u>
void chmin(t& first, u second) {
  if (second < first) first = second;
}
template <class t>
using vc = vector<t>;
template <class t>
using vvc = vc<vc<t>>;
using pi = pair<ll, ll>;
using vi = vc<ll>;
template <class t, class u>
ostream& operator<<(ostream& os, const pair<t, u>& p) {
  return os << "{" << p.first << "," << p.second << "}";
}
template <class t>
ostream& operator<<(ostream& os, const vc<t>& v) {
  os << "{";
  for (auto e : v) os << e << ",";
  return os << "}";
}
using uint = unsigned;
using ull = unsigned long long;
template <class t, size_t n>
ostream& operator<<(ostream& os, const array<t, n>& first) {
  return os << vc<t>(first.begin(), first.end());
}
template <ll i, class T>
void print_tuple(ostream&, const T&) {}
template <ll i, class T, class H, class... Args>
void print_tuple(ostream& os, const T& t) {
  if (i) os << ",";
  os << get<i>(t);
  print_tuple<i + 1, T, Args...>(os, t);
}
template <class... Args>
ostream& operator<<(ostream& os, const tuple<Args...>& t) {
  os << "{";
  print_tuple<0, tuple<Args...>, Args...>(os, t);
  return os << "}";
}
template <class t>
void print(t x, ll suc = 1) {
  cout << x;
  if (suc == 1) cout << "\n";
  if (suc == 2) cout << " ";
}
ll read() {
  ll i;
  cin >> i;
  return i;
}
vi readvi(ll n, ll off = 0) {
  vi v(n);
  for (ll i = ll(0); i < ll(n); i++) v[i] = read() + off;
  return v;
}
template <class T>
void print(const vector<T>& v, ll suc = 1) {
  for (ll i = ll(0); i < ll(v.size()); i++)
    print(v[i], i == ll(v.size()) - 1 ? suc : 2);
}
string readString() {
  string s;
  cin >> s;
  return s;
}
template <class T>
T sq(const T& t) {
  return t * t;
}
void yes(bool ex = true) {
  cout << "Yes"
       << "\n";
  if (ex) exit(0);
}
void no(bool ex = true) {
  cout << "No"
       << "\n";
  if (ex) exit(0);
}
void possible(bool ex = true) {
  cout << "Possible"
       << "\n";
  if (ex) exit(0);
}
void impossible(bool ex = true) {
  cout << "Impossible"
       << "\n";
  if (ex) exit(0);
}
constexpr ll ten(ll n) { return n == 0 ? 1 : ten(n - 1) * 10; }
const ll infLL = LLONG_MAX / 3;
const ll inf = infLL;
ll topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
ll topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
ll botbit(signed first) { return first == 0 ? 32 : __builtin_ctz(first); }
ll botbit(ll first) { return first == 0 ? 64 : __builtin_ctzll(first); }
ll popcount(signed t) { return __builtin_popcount(t); }
ll popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(ll i) { return i && (i & -i) == i; }
ll mask(ll i) { return (ll(1) << i) - 1; }
bool inc(ll first, ll second, ll c) { return first <= second && second <= c; }
template <class t>
void mkuni(vc<t>& v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
}
ll rand_int(ll l, ll r) {
  static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
  return uniform_int_distribution<ll>(l, r)(gen);
}
template <class t>
void myshuffle(vc<t>& first) {
  for (ll i = ll(0); i < ll(ll(first.size())); i++)
    swap(first[i], first[rand_int(0, i)]);
}
template <class t>
ll lwb(const vc<t>& v, const t& first) {
  return lower_bound(v.begin(), v.end(), first) - v.begin();
}
void sub(const vi& first, ll k) {
  void(0);
  ll n = ll(first.size());
  ll mx = *max_element(first.begin(), first.end());
  auto cost = [&](ll len, ll tar) { return (len + tar - 1) / tar - 1; };
  vi cnt(n);
  {
    ll lw = 0, up = mx;
    while (up - lw > 1) {
      const ll mid = (lw + up) / 2;
      ll sum = 0;
      for (ll i = ll(0); i < ll(n); i++) sum += cost(first[i], mid);
      if (sum <= k)
        up = mid;
      else
        lw = mid;
    }
    mx = up;
  }
  {
    assert(mx > 0);
    for (ll i = ll(0); i < ll(n); i++) cnt[i] = cost(first[i], mx);
    ll sum = accumulate(cnt.begin(), cnt.end(), ll(0));
    ll rem = k - sum;
    assert(rem >= 0);
    for (ll i = ll(0); i < ll(n); i++) {
      ll up = mx == 1 ? first[i] - 1 : cost(first[i], mx - 1);
      if (up > cnt[i]) {
        ll use = min(rem, up - cnt[i]);
        rem -= use;
        cnt[i] += use;
      }
    }
    for (ll i = ll(0); i < ll(n); i++) assert(cnt[i] < first[i]);
    assert(rem == 0);
  }
  ll ans = inf;
  {
    ll mn = inf;
    for (ll i = ll(0); i < ll(n); i++) chmin(mn, first[i] / (cnt[i] + 1));
    chmin(ans, mx - mn);
  }
  void(0);
  if (ans == 0) {
    print(ans);
    return;
  }
  if (mx > 1) {
    ll left = mx - 1;
    ll lw = -1, up = inf;
    while (up - lw > 1) {
      const ll mid = (lw + up) / 2;
      ll p = left + mid;
      ll x = 0, y = 0;
      bool ok = true;
      for (ll i = ll(0); i < ll(n); i++) {
        ll c = first[i] / mid - 1;
        x += c;
        ll d = (first[i] + p - 1) / p - 1;
        if (c < d) {
          ok = false;
          break;
        }
        y += d;
      }
      if (ok && inc(y, k, x))
        up = mid;
      else
        lw = mid;
    }
    chmin(ans, up);
  }
  void(0);
  using T = tuple<ll, ll, ll>;
  priority_queue<T> pq;
  auto add = [&](ll i, ll c) {
    if (first[i] <= c) return;
    pq.emplace(first[i] / (c + 1), i, c);
  };
  for (ll i = ll(0); i < ll(n); i++) add(i, cnt[i] + 1);
  vi lw(n, -inf);
  lw[0] = mx;
  for (ll waf = ll(1); waf < ll(n); waf++) {
    if (pq.empty()) break;
    ll x, i, c;
    tie(x, i, c) = pq.top();
    pq.pop();
    lw[waf] = x;
    add(i, c + 1);
  }
  void(0);
  {
    vi tmp(n);
    for (ll i = ll(0); i < ll(n); i++) {
      tmp[i] = first[i] / (cnt[i] + 1);
    }
    void(0);
  }
  void(0);
  vc<pi> li(n);
  for (ll i = ll(0); i < ll(n); i++) li[i] = pi(first[i] / (cnt[i] + 1), i);
  sort(li.begin(), li.end());
  ll left = mx - 1;
  for (ll i = ll(0); i < ll(n); i++) {
    chmin(ans, mx - min({li[i].first, lw[i], left}));
    ll j = li[i].second;
    if (cnt[j]) {
      chmax(mx, (first[j] + cnt[j] - 1) / cnt[j]);
    } else {
      break;
    }
  }
  print(ans);
}
void slv() {
  ll n, m, k;
  cin >> n >> m >> k;
  vi len(m + 1);
  ll pre = 0;
  for (ll i = ll(0); i < ll(m); i++) {
    ll first = read();
    len[i] = first - pre;
    pre = first;
  }
  len[m] = n - pre;
  sub(len, k);
}
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(20);
  ll t;
  cin >> t;
  for (ll _ = ll(0); _ < ll(t); _++) slv();
}
