#ifndef _GLIBCXX_NO_ASSERT
#include <cassert>
#endif
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
 
#if __cplusplus >= 201103L
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
//#include <cstdalign>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#endif
 
using namespace std;
// C++
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
 
#if __cplusplus >= 201103L
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <tuple>
#include <typeindex>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#endif
 
 
#define ms(s, n) memset(s, n, sizeof(s))
#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define FORd(i, a, b) for (int i = (a) - 1; i >= (b); i--)
#define FORall(it, a) for (__typeof((a).begin()) it = (a).begin(); it != (a).end(); it++)
#define sz(a) int((a).size())
#define all(a) (a).begin(), (a).end()
#define uni(a) (a).erase(unique(all(a)), (a).end())
#define pb push_back
#define pf push_front
#define mp make_pair
#define fi first
#define se second
#define prec(n) fixed<<setprecision(n)
#define bit(n, i) (((n) >> (i)) & 1)
#define bitcount(n) __builtin_popcount(n)
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pi;
typedef vector<int> vi;
typedef vector<pi> vii;
const int MOD = (int) 1e9 + 7;
const int INF = (int) 1e9;
const ll LINF = (ll) 1e18;
const ld PI = acos((ld) -1);
const ld EPS = 1e-9;
ll gcd(ll a, ll b) {ll r; while (b) {r = a % b; a = b; b = r;} return a;}
ll lcm(ll a, ll b) {return a / gcd(a, b) * b;}
ll fpow(ll n, ll k, int p = MOD) {ll r = 1;for (; k; k >>= 1) {if (k & 1) r = r * n % p; n = n * n % p;} return r;}
ll pow(ll n, ll k) {ll r = 1;for (; k; k >>= 1) {if (k & 1) r = r * n ; n = n * n ;} return r;}
 
template<class T> void setmin(T& a, T val) {if (a > val) a = val;}
template<class T> void setmax(T& a, T val) {if (a < val) a = val;}
void addmod(int& a, int val, int p = MOD) {if ((a = (a + val)) >= p) a -= p;}
void submod(int& a, int val, int p = MOD) {if ((a = (a - val)) < 0) a += p;}
int mult(int a, int b, int p = MOD) {return (ll) a * b % p;}
ll inv(int a, int p = MOD) {return fpow(a, p - 2, p);}
 
 
const int N = 200005;
int a[N];

int main()
{
  	ios::sync_with_stdio(false);
  	cout.tie(0);cin.tie(NULL);
 
	// freopen("input.txt", "r", stdin); 
	// freopen("output.txt", "w", stdout); 
	

	int k, n;
	cin >> k >> n;

	for(int i = 1; i <= n; i++)
		cin >> a[i];

	int pos = 0, mn = 0;

	for (int i = 2; i <= n; i++)
	{
		if(a[i] - a[i-1] > mn)
		{
			mn = a[i] - a[i-1];
			pos = i;
		}
	}

	if (k - a[n] + a[1] > mn)
	{
		mn = k - a[n] + a[1];
		pos = 1;
	}


	ll ans = 0; 
	for (int j = pos + 1 ; j <= n; j++)
		ans += (a[j] - a[j-1]);
	
	if(pos != 1)
	{
		ans += k - a[n] + a[1];

		for (int i = 2; i < pos; i++)
			ans += a[i] - a[i-1];
	}
	

	cout << ans <<"\n";


	return 0;
 
}


Measured memory_bytes: 1152