#include <bits/stdc++.h>
using namespace std;
template <typename T, typename U>
inline void smin(T &a, const U &b) {
  if (a > b) a = b;
}
template <typename T, typename U>
inline void smax(T &a, const U &b) {
  if (a < b) a = b;
}
template <class T>
inline void gn(T &first) {
  char c, sg = 0;
  while (c = getchar(), (c > '9' || c < '0') && c != '-')
    ;
  for ((c == '-' ? sg = 1, c = getchar() : 0), first = 0; c >= '0' && c <= '9';
       c = getchar())
    first = (first << 1) + (first << 3) + c - '0';
  if (sg) first = -first;
}
template <class T1, class T2>
inline void gn(T1 &x1, T2 &x2) {
  gn(x1), gn(x2);
}
int power(int a, int b, int m, int ans = 1) {
  for (; b; b >>= 1, a = 1LL * a * a % m)
    if (b & 1) ans = 1LL * ans * a % m;
  return ans;
}
long long a[200200];
long long dp[200200];
int main() {
  int m, n;
  cin >> m >> n;
  if (n == 1) {
    printf("%d\n", m - 1);
    return 0;
  }
  for (int i = 0; i < n; i++) gn(a[i]);
  for (int i = 0; i <= n; i++) a[i + n] = a[i] + m;
  pair<int, int> mx = pair<int, int>(-1, 0);
  for (int i = 0; i < n; i++) smax(mx, pair<int, int>(a[i + 1] - a[i] - 1, i));
  int L = mx.second + 1, R = mx.second + n;
  int st = mx.first - 1 >> 1;
  int ed = m;
  while (ed - st > 1) {
    int r = st + ed >> 1;
    dp[L] = a[L];
    for (int i = L + 1; i <= R; i++) {
      dp[i] = dp[i - 1];
      if (dp[i - 1] >= a[i] - 1) smax(dp[i], a[i] + r);
      if (dp[i - 1] + 1 >= a[i] - r) smax(dp[i], a[i]);
      if (i > L + 1 && dp[i - 2] + 1 >= a[i] - r) smax(dp[i], a[i - 1] + r);
    }
    if (dp[R] + 1 >= a[R + 1] - r) {
      ed = r;
      continue;
    }
    dp[R] = a[R];
    for (int i = R - 1; i >= L; i--) {
      dp[i] = dp[i + 1];
      if (dp[i + 1] <= a[i] + 1) smin(dp[i], a[i] - r);
      if (dp[i + 1] - 1 <= a[i] + r) smin(dp[i], a[i]);
      if (i < R - 1 && dp[i + 2] - 1 <= a[i] + r) smin(dp[i], a[i + 1] - r);
    }
    if (dp[L] - 1 <= a[L - 1] + r) {
      ed = r;
      continue;
    }
    if (a[L + 1] - r + m <= a[R - 1] + r + 1) {
      dp[L - 1] = 1LL << 40;
      dp[L] = dp[L + 1] = a[L] + r;
      for (int i = L + 2; i < R - 1; i++) {
        dp[i] = dp[i - 1];
        if (dp[i - 1] >= a[i] - 1) smax(dp[i], a[i] + r);
        if (dp[i - 1] + 1 >= a[i] - r) smax(dp[i], a[i]);
        if (i > L + 1 && dp[i - 2] + 1 >= a[i] - r) smax(dp[i], a[i - 1] + r);
      }
      if (dp[R - 2] + 1 >= a[R] - r)
        ed = r;
      else
        st = r;
    } else
      st = r;
  }
  printf("%d\n", min(mx.first, ed));
  return 0;
}
