#include <bits/stdc++.h>
using std::cin;
using std::cout;
const int N = 400005;
const unsigned long long inf = 1e18;
int T, m;
struct pr {
  unsigned long long l, r;
};
inline bool operator<(const pr& x, const pr& y) { return x.l < y.l; }
unsigned long long n, k;
unsigned long long p[N];
pr range[N];
inline unsigned long long calc_least(unsigned long long x) {
  unsigned long long sum = 0;
  for (int i = 0; i <= m; ++i) {
    sum += (p[i] + x - 1) / x;
  }
  return sum;
}
inline unsigned long long calc_most(unsigned long long x) {
  unsigned long long sum = 0;
  for (int i = 0; i <= m; ++i) {
    sum += p[i] / x;
  }
  return sum;
}
inline void solve() {
  cin >> n >> m >> k;
  for (int i = 0; i < m; ++i) cin >> p[i];
  p[m] = n;
  for (int i = m; i >= 1; --i) p[i] -= p[i - 1];
  unsigned long long l = 0, r = n + 1;
  unsigned long long c = m + 1 + k;
  for (; l + 1 < r;) {
    unsigned long long mid = (l + r) >> 1;
    if (calc_least(mid) <= c) {
      r = mid;
    } else {
      l = mid;
    }
  }
  unsigned long long max = r;
  l = 0, r = n + 1;
  for (; l + 1 < r;) {
    unsigned long long mid = (l + r) >> 1;
    if (calc_most(mid) >= c) {
      l = mid;
    } else {
      r = mid;
    }
  }
  unsigned long long min = l;
  int cnt = 0;
  for (int i = 0; i <= m; ++i) {
    unsigned long long c0 = (p[i] + max - 1) / max, v0 = p[i] / c0;
    unsigned long long c1 = p[i] / min, v1 = c1 ? (p[i] + c1 - 1) / c1 : inf;
    if (v0 < min && v1 > max) {
      range[cnt++] = (pr){v0, v1};
    }
  }
  unsigned long long ans = inf, R = max;
  if (!cnt)
    ans = max - min;
  else {
    std::sort(range, range + cnt);
    for (int i = 0; i < cnt; ++i)
      ans = std::min(ans, R - range[i].l), R = std::max(range[i].r, R);
    ans = std::min(ans, R - min);
  }
  cout << ans << '\n';
}
int main() {
  std::ios::sync_with_stdio(false), cin.tie(0);
  cin >> T;
  for (int i = 0; i < T; ++i) {
    solve();
  }
}
