#include <bits/stdc++.h>
using namespace std;
inline char gc() {
  static char buf[100000], *p1 = buf, *p2 = buf;
  return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 100000, stdin), p1 == p2)
             ? EOF
             : *p1++;
}
inline long long read() {
  long long x = 0;
  char ch = getchar();
  bool positive = 1;
  for (; !isdigit(ch); ch = getchar())
    if (ch == '-') positive = 0;
  for (; isdigit(ch); ch = getchar()) x = x * 10 + ch - '0';
  return positive ? x : -x;
}
inline void write(long long a) {
  if (a < 0) {
    a = -a;
    putchar('-');
  }
  if (a >= 10) write(a / 10);
  putchar('0' + a % 10);
}
inline void writeln(long long a) {
  write(a);
  puts("");
}
inline void wri(long long a) {
  write(a);
  putchar(' ');
}
inline unsigned long long rnd() {
  return ((unsigned long long)rand() << 30 ^ rand()) << 4 | rand() % 4;
}
const int N = 400005;
long long n, k, p[N], a[N];
pair<long long, long long> q[N];
int m;
long long checks(long long x) {
  long long sum = 0;
  for (int i = (int)(0); i <= (int)(m); i++) sum += (a[i] + x - 1) / x;
  return sum <= k;
}
long long checkx(long long x) {
  long long sum = 0;
  for (int i = (int)(0); i <= (int)(m); i++) sum += a[i] / x;
  return sum >= k;
}
int main() {
  int T = read();
  while (T--) {
    n = read();
    m = read();
    k = read() + m + 1;
    for (int i = (int)(1); i <= (int)(m); i++) p[i] = read();
    for (int i = (int)(0); i <= (int)(m); i++) a[i] = p[i + 1] - p[i];
    a[m] = n - p[m];
    long long l = 1, r = 1e15;
    while (l < r) {
      long long mid = (l + r) >> 1;
      if (checks(mid))
        r = mid;
      else
        l = mid + 1;
    }
    long long U = l;
    l = 1;
    r = 1e15;
    while (l < r) {
      long long mid = (l + r) >> 1;
      mid++;
      if (checkx(mid))
        l = mid;
      else
        r = mid - 1;
    }
    long long D = l;
    int tot = 0;
    for (int i = (int)(0); i <= (int)(m); i++) {
      long long d = a[i] / D;
      if (d == 0)
        q[++tot] = make_pair(a[i], 1e18);
      else if ((a[i] + d - 1) / d > U) {
        q[++tot] = make_pair(a[i] / (d + 1), (a[i] + d - 1) / d);
      }
    }
    q[++tot] = make_pair(D, 1e18);
    sort(q + 1, q + tot + 1);
    long long dq = U, ans = 1e18;
    for (int i = (int)(1); i <= (int)(tot); i++) {
      ans = min(ans, dq - q[i].first);
      dq = max(dq, q[i].second);
    }
    cout << ans << endl;
  }
}
