#include <bits/stdc++.h>
using namespace std;
#ifndef LOCAL
#include "gap.h"
#else
static void my_assert(int k){ if (!k) exit(1); }

static int subtask_num, N;
static long long A[100001];
static long long call_count;

long long findGap(int t, int n);

void MinMax(long long s, long long t, long long *mn, long long *mx)
{
	int lo = 1, hi = N, left = N+1, right = 0;
	my_assert(s <= t && mn != NULL && mx != NULL);
	while (lo <= hi){
		int mid = (lo+hi)>>1;
		if (A[mid] >= s) hi = mid - 1, left = mid;
		else lo = mid + 1;
	}
	lo = 1, hi = N;
	while (lo <= hi){
		int mid = (lo+hi)>>1;
		if (A[mid] <= t) lo = mid + 1, right = mid;
		else hi = mid - 1;
	}
	if (left > right) *mn = *mx = -1;
	else{
		*mn = A[left];
		*mx = A[right];
	}
	if (subtask_num == 1) call_count++;
	else if (subtask_num == 2) call_count += right-left+2;
}

int main()
{    
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
	FILE *in = stdin, *out = stdout;
	my_assert(2 == fscanf(in, "%d%d", &subtask_num, &N));
	my_assert(1 <= subtask_num && subtask_num <= 2);
	my_assert(2 <= N && N <= 100000);
	for (int i=1;i<=N;i++) my_assert(1 == fscanf(in, "%lld", A+i));
	for (int i=1;i<N;i++) my_assert(A[i] < A[i+1]);
	fprintf(out, "%lld\n", findGap(subtask_num, N));
	fprintf(out, "%lld\n", call_count);
}
#endif

using ll = long long;

random_device rd;
mt19937_64 rnd(rd());

ll rand(ll n) {
	return rnd() % n;
}

ll rand(ll l, ll r) {
	return l + rand(r - l + 1);
}

ll findGap(int t, int n) {
	if (t == 1) {
		set<ll> Q;
		auto rec = [&](auto &&rec, ll l, ll r) -> void {
			if (l > r || Q.size() == n) {
				return;
			}
			
			MinMax(l, r, &l, &r);
			
			if (l == -1) {
				return;
			} else {
				Q.insert(l);
				Q.insert(r);
				l++;
				r--;
				if (t == 2) {
					if (l >= r) {
						rec(rec, l, r);
					} else {
						ll m = rand(l, r - 1);
						rec(rec, l, m);
						rec(rec, m + 1, r);
					}
				} else {
					rec(rec, l, r);
				}
			}
		};
		rec(rec, 0, ((ll)1e9) * ((ll)1e9));
		vector<ll> F(Q.begin(), Q.end());
		ll res = 0;
		for (int i = 0; i + 1 < n; i++) {
			res = max(res, F[i + 1] - F[i]);
		}
	} else {
		ll mn, mx;
		MinMax(1, 1e18, &mn, &mx);
		ll step = (mx - mn + N - 2) / (N - 1);
		ll ans = step, x, y, l = mn, i;
		for (i = mn; i + step < mx; i += step + 1) {
			MinMax(i, i + step, &x, &y);
			if (x != -1) {
				ans = max(ans, x - l);
				l = y;
			}
		}
		MinMax(i, mx, &x, &y);
		if (x != -1) ans = max(ans, x - l);
		return ans;
	}
}

answer.code: In function ‘ll findGap(int, int)’:
answer.code:105:38: error: ‘N’ was not declared in this scope
  105 |                 ll step = (mx - mn + N - 2) / (N - 1);
      |                                      ^
answer.code:118:1: warning: control reaches end of non-void function [-Wreturn-type]
  118 | }
      | ^