#include <bits/stdc++.h>
using namespace std;
template <class T>
inline void read(T &x) {
  x = 0;
  char c = getchar();
  int f = 1;
  while (!isdigit(c)) {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (isdigit(c)) {
    x = x * 10 + c - '0';
    c = getchar();
  }
  x *= f;
}
template <class T>
inline void umin(T &x, T y) {
  x = x < y ? x : y;
}
template <class T>
inline void umax(T &x, T y) {
  x = x > y ? x : y;
}
inline unsigned int R() {
  static unsigned int seed = 416;
  return seed ^= seed >> 5, seed ^= seed << 17, seed ^= seed >> 13;
}
const int N = 266666, inf = 0x3f3f3f3f;
int m, n, a[N], b[N], f[N];
inline int solve(int l, int st) {
  for (register int i = (st); i <= (n - 1); i++) {
    if (f[i] + 1 < b[i + 1]) {
      if (b[i + 1] - l <= f[i] + 1) umax(f[i + 1], b[i + 1]);
      if (b[i + 2] - l <= f[i] + 1) umax(f[i + 2], b[i + 1] + l);
    } else {
      umax(f[i + 1], b[i + 1] + l);
    }
  }
  return f[n];
}
bool ck(int l) {
  if (m - b[n] <= l) return 1;
  memset(f, 0, sizeof(f));
  if (solve(l, 1) >= m - l) return 1;
  memset(f, 0, sizeof(f));
  if (b[2] <= l) {
    f[2] = l;
    if (solve(l, 2) >= m - (l - b[2])) return 1;
  }
  return 0;
}
int main() {
  read(m);
  read(n);
  for (register int i = (1); i <= (n); i++) read(a[i]);
  for (register int i = (1); i <= (n); i++) a[n + i] = a[i] + m;
  int p = 2;
  for (register int i = (3); i <= (n + 1); i++)
    if (a[p] - a[p - 1] < a[i] - a[i - 1]) p = i;
  for (register int i = (p); i <= (p + n - 1); i++) b[i - p + 1] = a[i] - a[p];
  m--;
  int L = 0, R = m;
  while (L < R) {
    int mid = (L + R) >> 1;
    if (ck(mid))
      R = mid;
    else
      L = mid + 1;
  }
  cout << L;
  return 0;
}
