#include <bits/stdc++.h>
using namespace std;
const long double pi = acos(-1.0);
const int day[12] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
const int digarr[10] = {6, 2, 5, 5, 4, 5, 6, 3, 7, 6};
const int dx[4] = {0, 1, 0, -1};
const int dy[4] = {1, 0, -1, 0};
const int dxo[8] = {-1, -1, -1, 0, 1, 1, 1, 0};
const int dyo[8] = {-1, 0, 1, 1, 1, 0, -1, -1};
const int alf = 26;
const int dig = 10;
const int two = 2;
const int th = 3;
const long long prost = 239;
const long long btc = 30;
const long double eps = 1e-8;
const long long INF = (long long)(1e18 + 239);
const int BIG = (int)(1e9 + 239);
const int MOD = 1e9 + 7;
mt19937 rnd(239);
const int M = (int)(4e5 + 239);
const int N = (int)(2e3 + 239);
const int L = 20;
const int T = (1 << 18) + 239;
const int B = 500;
const int X = 210;
long long up(long long a, long long b) { return (a + b - 1) / b; }
long long down(long long a, long long b) { return a / b; }
int m;
long long l[M], n, k;
void solve() {
  cin >> n >> m >> k;
  long long pr = 0;
  for (int i = 0; i < m; i++) {
    long long p;
    cin >> p;
    l[i] = p - pr;
    pr = p;
  }
  l[m++] = n - pr;
  long long sum = k + m;
  long long bl = 1;
  long long br = n + 1;
  while (br - bl > 1) {
    long long h = (bl + br) >> 1LL;
    long long cur = 0;
    for (int i = 0; i < m; i++) cur += down(l[i], h);
    if (sum <= cur)
      bl = h;
    else
      br = h;
  }
  long long MIN = bl;
  bl = 0;
  br = n + 1;
  while (br - bl > 1) {
    long long h = (bl + br) >> 1LL;
    long long cur = 0;
    for (int i = 0; i < m; i++) cur += up(l[i], h);
    if (sum >= cur)
      br = h;
    else
      bl = h;
  }
  long long MAX = br;
  vector<pair<long long, long long>> ban;
  for (int i = 0; i < m; i++) {
    if (up(l[i], MAX) <= down(l[i], MIN)) continue;
    long long bl = 0;
    long long br = MIN;
    while (br - bl > 1) {
      long long h = (bl + br) >> 1LL;
      if (down(l[i], h) == down(l[i], MIN))
        br = h;
      else
        bl = h;
    }
    long long first = MIN - br;
    bl = MAX;
    br = INF;
    while (br - bl > 1) {
      long long h = (bl + br) >> 1LL;
      if (up(l[i], MAX) == up(l[i], h))
        bl = h;
      else
        br = h;
    }
    long long second = bl - MAX;
    ban.push_back(make_pair(first, second));
  }
  long long add = MAX - MIN;
  if (ban.empty()) {
    cout << add << "\n";
    return;
  }
  sort(ban.begin(), ban.end());
  vector<pair<long long, long long>> a;
  for (int i = 0; i < (int)ban.size(); i++) {
    while (!a.empty() && a.back().second <= ban[i].second) a.pop_back();
    a.push_back(ban[i]);
  }
  long long ans = INF;
  ans = min(a[0].second + 1, ans);
  ans = min(a.back().first + 1, ans);
  for (int i = 0; i + 1 < (int)a.size(); i++)
    ans = min(ans, a[i].first + a[i + 1].second + 2);
  cout << ans + add << "\n";
}
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t;
  cin >> t;
  while (t--) solve();
  return 0;
}
