#include <bits/stdc++.h>
using namespace std;
const int N = 4e5 + 10;
long long gi() {
  long long x = 0, o = 1;
  char ch = getchar();
  while ((ch < '0' || ch > '9') && ch != '-') ch = getchar();
  if (ch == '-') o = -1, ch = getchar();
  while (ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar();
  return x * o;
}
int n, tt;
long long m, k, d[N];
pair<long long, long long> p[N];
int main() {
  int T = gi();
  while (T--) {
    m = gi();
    n = gi();
    k = gi();
    for (int i = 1; i <= n; i++) d[i] = gi();
    d[++n] = m;
    for (int i = n; i; i--) d[i] -= d[i - 1];
    if (!k) {
      cout << *max_element(d + 1, d + n + 1) - *min_element(d + 1, d + n + 1)
           << '\n';
      continue;
    }
    long long l = 1, r = 1e15;
    while (l < r) {
      long long mid = (l + r + 1) >> 1, sum = 0;
      for (int i = 1; i <= n; i++) {
        sum += d[i] / mid - 1;
        if (sum >= k) break;
      }
      if (sum >= k)
        l = mid;
      else
        r = mid - 1;
    }
    long long mx = l;
    l = 1, r = 1e15;
    while (l < r) {
      long long mid = (l + r) >> 1, sum = 0;
      for (int i = 1; i <= n; i++) {
        sum += (d[i] + mid - 1) / mid - 1;
        if (sum > k) break;
      }
      if (sum <= k)
        r = mid;
      else
        l = mid + 1;
    }
    long long mn = l;
    tt = 0;
    for (int i = 1; i <= n; i++) {
      if ((d[i] + mn - 1) / mn > d[i] / mx) {
        long long t = d[i] / mx;
        p[++tt].first = d[i] / (t + 1);
        t = (d[i] + mn - 1) / mn;
        if (t == 1)
          p[tt].second = 1e18;
        else
          p[tt].second = (d[i] + t - 2) / (t - 1);
      }
    }
    sort(p + 1, p + tt + 1);
    long long low = mn, ans = 1e18;
    for (int i = 1, j; i <= tt; i = j + 1) {
      j = i;
      while (j < tt && p[j + 1].first == p[i].first) ++j;
      ans = min(ans, low - p[i].first);
      for (int k = i; k <= j; k++) low = max(low, p[k].second);
    }
    ans = min(ans, low - mx);
    cout << ans << '\n';
  }
  return 0;
}
