#include <bits/stdc++.h>
using namespace std;
template <typename T>
void maxtt(T& t1, T t2) {
  t1 = max(t1, t2);
}
template <typename T>
void mintt(T& t1, T t2) {
  t1 = min(t1, t2);
}
bool debug = 0;
int n, m, k;
string direc = "RDLU";
const long long MOD2 = (long long)998244353 * (long long)998244353;
long long ln, lk, lm;
void etp(bool f = 0) {
  puts(f ? "YES" : "NO");
  exit(0);
}
void addmod(int& x, int y, int mod = 998244353) {
  x += y;
  if (x >= mod) x -= mod;
  if (x < 0) x += mod;
  assert(x >= 0 && x < mod);
}
void et(int x = -1) {
  printf("%d\n", x);
  exit(0);
}
long long fastPow(long long x, long long y, int mod = 998244353) {
  long long ans = 1;
  while (y > 0) {
    if (y & 1) ans = (x * ans) % mod;
    x = x * x % mod;
    y >>= 1;
  }
  return ans;
}
long long gcd1(long long x, long long y) { return y ? gcd1(y, x % y) : x; }
long long p[400135], a[400135];
long long M, K;
long long L, U;
bool bsl(long long mid) {
  if (mid == 0) return 0;
  long long s = 0;
  for (int(i) = 1; (i) <= (int)(M); (i)++) {
    long long td = max(1LL, a[i] / mid);
    while ((a[i] + td - 1) / td > mid) {
      td++;
    }
    s += td;
  }
  return s <= K;
}
bool bsd(long long mid) {
  if (mid == 0) return 1;
  long long s = 0;
  for (int(i) = 1; (i) <= (int)(M); (i)++) {
    long long td = max(1LL, a[i] / mid);
    while (a[i] / (td + 1) >= mid) {
      td++;
    }
    s += td;
  }
  return s >= K;
}
void cal() {
  long long l = 0, r = ln;
  while (l + 1 < r) {
    long long mid = (l + r) / 2;
    if (bsl(mid))
      r = mid;
    else
      l = mid;
  }
  U = r;
  l = 1;
  r = ln;
  for (int(i) = 1; (i) <= (int)(M); (i)++) mintt(r, a[i]);
  r++;
  while (l + 1 < r) {
    long long mid = (l + r) / 2;
    if (bsd(mid))
      l = mid;
    else
      r = mid;
  }
  L = l;
}
void calb() {
  assert(L > 0);
  vector<pair<long long, long long> > vp;
  for (int(i) = 1; (i) <= (int)(M); (i)++) {
    long long z = max(1LL, a[i] / L);
    if ((a[i] + z - 1) / z > U) {
      long long y = (a[i] + z - 1) / z;
      z++;
      long long x = a[i] / z;
      vp.push_back({x, y});
    }
  }
  if (vp.empty()) {
    printf("%lld\n", U - L);
    return;
  }
  multiset<long long> ms;
  ms.insert(L);
  ms.insert(U);
  int N = vp.size();
  sort(vp.begin(), vp.end());
  for (int(i) = 0; (i) < (int)(N); (i)++) ms.insert(vp[i].first);
  long long ans = (*ms.rbegin()) - (*ms.begin());
  for (int(i) = 0; (i) < (int)(N); (i)++) {
    ms.erase(ms.find(vp[i].first));
    ms.insert(vp[i].second);
    mintt(ans, (*ms.rbegin()) - (*ms.begin()));
  }
  printf("%lld\n", ans);
}
void fmain(int tid) {
  scanf("%lld%d%lld", &ln, &m, &lk);
  for (int(i) = 1; (i) <= (int)(m); (i)++) {
    scanf("%lld", p + i);
    a[i] = p[i] - p[i - 1];
  }
  a[m + 1] = ln - p[m];
  M = m + 1;
  K = m + 1 + lk;
  cal();
  calb();
}
int main() {
  int t = 1;
  scanf("%d", &t);
  for (int(i) = 1; (i) <= (int)(t); (i)++) {
    fmain(i);
  }
  return 0;
}
