#include <bits/stdc++.h>
using namespace std;
const int mod = 998244353, N = 410000;
int t, m;
long long n, p[N], k;
vector<long long> a;
vector<pair<long long, long long> > b;
multiset<long long> s;
inline int addMod(int a, int b) { return (a += b) >= mod ? a - mod : a; }
inline long long quickpow(long long base, long long pw) {
  long long ret = 1;
  while (pw) {
    if (pw & 1) ret = ret * base % mod;
    base = base * base % mod, pw >>= 1;
  }
  return ret;
}
template <class T>
inline void read(T &x) {
  x = 0;
  char ch = getchar(), w = 0;
  while (!isdigit(ch)) w = (ch == '-'), ch = getchar();
  while (isdigit(ch)) x = (x << 1) + (x << 3) + (ch ^ 48), ch = getchar();
  x = w ? -x : x;
  return;
}
inline int chkMax(long long mid) {
  long long ret = 0;
  for (auto &v : a) ret += (v + mid - 1) / mid;
  return ret <= k;
}
inline int chkMin(long long mid) {
  long long ret = 0;
  for (auto &v : a) {
    if (v < mid) return 0;
    ret += v / mid;
  }
  return ret >= k;
}
int main() {
  read(t);
  while (t--) {
    read(n), read(m), read(k);
    p[m + 1] = n, a.clear(), k += m + 1;
    for (register int i = 1; i <= m; ++i) read(p[i]);
    sort(p + 1, p + 1 + m);
    for (register int i = 1; i <= m + 1; ++i) a.push_back(p[i] - p[i - 1]);
    long long l = 1, r = n, mid, lt, rt;
    while (l != r) mid = (l + r) >> 1, chkMax(mid) ? r = mid : l = mid + 1;
    rt = l, l = 1, r = rt;
    while (l != r) mid = (l + r + 1) >> 1, chkMin(mid) ? l = mid : r = mid - 1;
    lt = l, b.clear();
    for (auto &v : a) {
      l = v / lt, r = (v + rt - 1) / rt;
      if (l >= r) continue;
      assert(l == r - 1);
      b.push_back(make_pair((v + l - 1) / l, v / r));
    }
    sort(b.begin(), b.end(), greater<pair<long long, long long> >());
    s.clear(), s.insert(rt), s.insert(lt);
    for (auto &v : b) s.insert(v.first);
    long long ans = *s.rbegin() - *s.begin();
    for (auto &v : b) {
      s.erase(s.find(v.first));
      s.insert(v.second);
      ans = min(ans, *s.rbegin() - *s.begin());
    }
    printf("%lld\n", ans);
  }
  return 0;
}
