#ifdef __GNUC__
#include <bits/stdc++.h>
#else
// C++ includes used for precompiling -*- C++ -*-

// Copyright (C) 2003-2013 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.

// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.

// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
// <http://www.gnu.org/licenses/>.

/** @file stdc++.h
 *  This is an implementation file for a precompiled header.
 */

 // 17.4.1.2 Headers

 // C
#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 <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#endif

// 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>
#include <unordered_map>
#include <unordered_set>

#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
#endif
using namespace std;
using ll = long long;

#define REPI(i, a, n)	for(ll (i)=(a);(i)<(n);(i++))
#define REP(i,n) REPI(i,0,n)
#define REP1(i,n) for(ll (i)=1;(i)<=(n);(i++))
#define ALL(x) x.begin(), x.end()
#define MAX(x) *max_element(ALL(x))
#define MIN(x) *min_element(ALL(x))

struct ProconInit {
	static constexpr int IOS_PREC = 15;
	static constexpr bool AUTOFLUSH = false;

	ProconInit() {
		cin.tie(nullptr);
		ios::sync_with_stdio(false);
		cout << fixed << setprecision(IOS_PREC);
		if (AUTOFLUSH)
			cout << unitbuf;
	}
} PROCON_INIT;

int vector_finder(std::vector<int> vec, int number) {
	auto itr = std::find(vec.begin(), vec.end(), number);
	size_t index = std::distance(vec.begin(), itr);
	if (index != vec.size()) { // 発見できたとき
		return 1;
	}
	else { // 発見できなかったとき
		return 0;
	}
}
ll gcd(ll a, ll b) {
	if (a < b)swap(a, b);
	if (a % b == 0)return b;
	return gcd(a % b, b);
}
ll lcm(ll a, ll b) {
	return a / gcd(a, b) * b;
}
ll fact(ll n) {
	ll m;
	if (n == 0) {
		return 1;
	}
	m = fact(n - 1);
	return n * m;
}

ll Combination(unsigned long long n, unsigned long long r) {
	if (r * 2 > n) r = n - r;
	uintmax_t dividend = 1;
	uintmax_t divisor = 1;
	for (unsigned int i = 1; i <= r; ++i) {
		dividend *= (n - i + 1);
		divisor *= i;
	}
	return dividend / divisor;
}

struct vec {
	ll x, y;

	bool operator == (const vec &v) const{
		return x == v.x && y == v.y;
	}

};

namespace std {
	template<>
	class hash<vec> {
	public:
		size_t operator () (const vec& p) const { return p.x%SIZE_MAX; }
	};
}

int main() {
	ll K, N;
	cin >> K >> N;
	vector<ll> A(N), D(N);

	REP(i, N) {
		cin >> A[i];
	}

	REP(i, N) {
		if (i == N - 1) {
			D[i] = abs(K - A[i] + A[0]);
		}
		else {
			D[i] = abs(A[(i + 1) % N] - A[i]);
		}
	}
	D.erase(max_element(ALL(D)));
	cout << accumulate(ALL(D), 0);
	return 0;
}

Measured memory_bytes: 3328