#include <bits/stdc++.h>
using namespace std;
namespace mine {
const int INF = 0x3f3f3f3f;
const long long LLINF = 0x3f3f3f3f3f3f3f3fll;
long long qread() {
  long long ans = 0;
  char c = getchar();
  int f = 1;
  while (c < '0' or c > '9') {
    if (c == '-') f = -1;
    c = getchar();
  }
  while ('0' <= c and c <= '9') ans = ans * 10 + c - '0', c = getchar();
  return ans * f;
}
void write(long long num) {
  if (num < 0) {
    num = -num;
    putchar('-');
  }
  if (num > 9) write(num / 10);
  putchar('0' + num % 10);
}
void write1(long long num) {
  write(num);
  putchar(' ');
}
void write2(long long num) {
  write(num);
  puts("");
}
void chmax(int &x, const int y) { x = x > y ? x : y; }
void chmin(int &x, const int y) { x = x < y ? x : y; }
const int MAX_N = 1e6 + 10;
const long long MOD = 1e9 + 7;
void add(int &x, int y) {
  x += y;
  if (x >= MOD) x -= MOD;
  if (x < 0) x += MOD;
}
long long qpower(long long x, long long e) {
  long long ans = 1;
  while (e) {
    if (e & 1) ans = ans * x % MOD;
    x = x * x % MOD;
    e >>= 1;
  }
  return ans;
}
long long inv(long long x) { return qpower(x, MOD - 2); }
int m, n, st;
pair<int, int> mx;
int f[MAX_N][2], a[MAX_N];
void dp(int T, int op) {
  for (int i = st + 1 + op; i <= st + n - 1; i++) {
    if (f[i - 1][0] >= a[i] - T) chmax(f[i][0], a[i] + 1);
    if (f[i - 1][1] >= a[i] - T)
      chmax(f[i][0], max(a[i - 1] + T + 1, a[i] + 1));
    int tmp = max(f[i - 1][0], f[i - 1][1]);
    if (tmp >= a[i]) chmax(f[i][1], a[i] + T + 1);
    chmax(f[i][0], tmp);
    chmax(f[i][1], tmp);
  }
}
bool check(int T) {
  int st = mx.second;
  {
    memset(f, -0x3f, sizeof f);
    f[st][0] = a[st] + 1;
    dp(T, 0);
    if (max(f[st + n - 1][0], f[st + n - 1][1]) >= a[st] + m - T) return 1;
  }
  if (a[st] + T + 1 >= a[st + 1]) {
    memset(f, -0x3f, sizeof f);
    f[st + 1][0] = max(a[st] + T + 1, a[st + 1] + 1);
    dp(T, 1);
    if (max(f[st + n - 1][0], f[st + n - 1][1]) >= a[st + 1] + m - T) return 1;
  }
  return 0;
}
void main() {
  m = qread(), n = qread();
  for (int i = 1; i <= n; i++) a[i] = qread();
  mx = make_pair(a[1] - 1 + m - a[n] + 1, 1);
  for (int i = 2; i <= n; i++) mx = max(mx, make_pair(a[i] - a[i - 1], i));
  st = mx.second;
  for (int i = 1; i <= n; i++) a[n + i] = a[i] + m;
  int l = 0, r = mx.first - 1, ans = mx.first;
  while (l <= r) {
    int mid = (l + r) >> 1;
    if (check(mid))
      ans = mid, r = mid - 1;
    else
      l = mid + 1;
  }
  write(ans);
}
};  // namespace mine
signed main() {
  srand(time(0));
  mine::main();
}
