#ifndef LOCAL
#include "gap.h"
#endif
#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
long long t, n;
vector<long long> vcL;
void MinMax(long long a, long long b, long long &mn, long long &mx) {
cout << "MinMax(" << a << ", " << b << "): ";
bool MN = false, MX = false;
for (int i = 0; i < n; ++i) {
if (!MN and vcL[i] >= a and vcL[i] <= b) {
mn = vcL[i];
MN = true;
}
if (!MX and vcL[n - i - 1] <= b and vcL[n - i - 1] >= a) {
mx = vcL[n - i - 1];
MX = true;
}
if (MN and MX) {
break;
}
}
if (!MN or !MX) {
mn = -1;
mx = -1;
}
cout << "mn = " << mn << ", mx = " << mx << '\n';
return;
}
#endif
const int maxn = 1E5 + 5;
vector<long long> num(maxn, -1);
long long mn, mx, cnt = 0;
long long findGap1(int N) {
mn = -1;
mx = (long long)1E18 + 2;
for (int i = 0; i < (N+1)/2; ++i) {
#ifdef LOCAL
MinMax(mn + 1, mx - 1, mn, mx);
#else
MinMax(mn + 1, mx - 1, &mn, &mx);
#endif
num[i] = mn;
num[N - i - 1] = mx;
if (mn == -1 and mx == -1) assert(false);
else if (mn == mx) break;
}
long long answer = 0;
for (int i = 1; i < N; ++i) {
answer = max(answer, num[i] - num[i - 1]);
}
return answer;
}
/*
void recur(long long lo, long long hi, long long &mn, long long &mx) {
#ifdef LOCAL
MinMax(lo, hi, mn, mx);
#else
MinMax(lo, hi, &mn, &mx);
#endif
if (mx == mn + 1) {
num[cnt++] = mn;
num[cnt++] = mx;
}
else if (mn != mx and mx != -1) {
long long mi = (mn + mx) >> 1;
long long tmpMN = mn, tmpMX = mx;
recur(tmpMN, mi, mn, mx);
recur(mi + 1, tmpMX, mn, mx);
}
else if (mn == mx and mx != -1) {
num[cnt++] = mn;
}
}
*/
long long findGap2(int N) {
// recur(0, (long long)1E18, mn, mx);
#ifdef LOCAL
MinMax(0, (long long)1E18, mn, mx);
#else
MinMax(0, (long long)1E18, &mn, &mx);
#endif
long long LO = mn, HI = mx;
num.assign(1, mn);
long long block[N][2];
block[0][1] = LO;
for (int i = 1; i < N; ++i) {
block[i][0] = block[i - 1][1] + 1;
block[i][1] = block[i][0] + (HI - LO) / (N - 1) - ((HI - LO) % (N - 1) <= i);
#ifdef LOCAL
cout << block[i][0] << ' ' << block[i][1] << '\n';
#endif
}
for (int i = 1; i < N; ++i) {
#ifdef LOCAL
MinMax(block[i][0], block[i][1], mn, mx);
#else
MinMax(block[i][0], block[i][1], &mn, &mx);
#endif
if (mn == mx and mn != -1) {
num.push_back(mn);
}
else if (mn != mx) {
num.push_back(mn);
num.push_back(mx);
}
}
num.push_back(HI);
long long answer = 0;
int sz = num.size();
for (int i = 1; i < sz; ++i) {
answer = max(answer, num[i] - num[i - 1]);
}
return answer;
}
long long findGap(int T, int N) {
if (T == 1) return findGap1(N);
else return findGap2(N);
}
#ifdef LOCAL
int main() {
long long ANSWER = 0;
cin >> t >> n;
vcL.assign(n, 0);
for (int i = 0; i < n; ++i) {
cin >> vcL[i];
if (i) ANSWER = max(ANSWER, vcL[i] - vcL[i - 1]);
}
long long myAns = findGap(t, n);
cout << "Your answer: " << myAns << '\n';
cout << "Real answer: " << ANSWER << '\n';
return 0;
}
#endif
