#include <bits/stdc++.h>
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
using namespace std;

/***** type *****/
using ll = long long;
using ld = long double;
using ml = boost::multiprecision::cpp_int;
using md = boost::multiprecision::cpp_dec_float_100;
template <class T> using vt = vector<T>;
template <class T> using vvt = vector<vector<T>>;
template <class T> using vvvt = vector<vector<vector<T>>>;
template <class T> using uset = unordered_set<T>;
template <class T1, class T2> using umap = unordered_map<T1, T2>;

/***** define *****/
#define all(c) (c).begin(), (c).end()            // begin to end
#define coutld cout << fixed << setprecision(10) // cout long double
#define rep(i, b, e) for (ll i = b; i < e; i++)  // repeat
#define repr(i, b, e) for (ll i = b; e < i; i--) // repeat reverse
#define pair NyaaPair                            // nyaa pair
#define first f                                  // pair::first
#define second s                                 // pair::second
/***** const value *****/
#define llong_max 9223372036854775807            // 9 * 10^18
#define ldbl_max 1.79769e+308                    // 1.7 * 10^308
#define pi 3.1415926535897932                    // 3.14 ...
#define loop_end 9223372036854775806             // LLONG_MAX-1
/***** for each macro *****/
#define fori(i, ...) if(ll i = -1) for(__VA_ARGS__) if(i++, true)
#define each(i, e, c) fori(i, auto& e: c)
#define forir(i, v, ...) if(ll i=(ll)v.size())for(__VA_ARGS__)if(i--,true)
#define eachr(i, e, c) forir(i, auto e = c.rbegin(); e != c.rend(); ++e)

/***** lambda *****/
auto Count = [] // long long count value
(auto b, auto e, auto x) { return (ll)count(b, e, x); };
auto CtoL = [] // char to number
(auto c) { return (ll)(c - '0'); };
auto CeilD = [] // long double ceiling div
(auto a, auto b) { return ceil((ld)a / (ld)b); };
auto Fix = [] // fix value
(auto b, auto e, auto fix)
{ for (auto it = b; it != e; ++it) *it += fix; };
auto LtoC = [] // number to char
(auto n) { return (char)('0' + n); };
auto Pow = [] // long long pow
(auto a, auto b) { return (ll)pow(a, b); };
auto Pow2 = [] // long long pow2
(auto n) { return (1LL << n); };
auto Pow10 = [] // long long pow10
(auto n) { return (ll)pow(10, n); };
auto Size = []  // long long collection size
(auto& c) { return (ll)(c).size(); };
auto Sum = [] // long long accumulate
(auto b, auto e) { return accumulate(b, e, 0LL); };

/***** template *****/
template <class T> void MakeVVT
(ll ys, ll xs, vvt<T>& v, T fill = T())
{	// vector<vector<T>> resize + fill
	v.resize(ys); rep(y, 0, ys) v[y].resize(xs, fill);
}
template <class T> void MakeVVVT
(ll zs, ll ys, ll xs, vvvt<T>& v, T fill = T())
{	// vector<vector<vector<T>>> resize + fill
	v.resize(zs); rep(z, 0, zs) MakeVVT(ys, xs, v[z], fill);
}
template <class T> void InputVT
(ll xs, vt<T>& v, T fix = T())
{	// input vector<T> (T != struct) + fix
	v.resize(xs); rep(i, 0, xs) { cin >> v[i]; v[i] += fix; }
}
template <class T> void InputVVT
(ll ys, ll xs, vvt<T>& v, T fix = T())
{	// input vector<vector<T>> (T != struct) + fix
	MakeVVT(ys, xs, v, fix);
	rep(y, 0, ys) rep(x, 0, xs) { cin >> v[y][x]; v[y][x] += fix; }
}
template <class T> void InputVVVT
(ll zs, ll ys, ll xs, vvvt<T>& v, T fix = T())
{	// input vector<vector<vector<T>>> (T != struct) + fix
	v.resize(zs); rep(z, 0, zs) InputVVT(ys, xs, v[z], fix);
}
template <class T1, class T2> struct NyaaPair
{	// nyaa pair template
	T1 f; T2 s;
};
template <class T1, class T2> bool
operator < (const NyaaPair<T1, T2>& l, const NyaaPair<T1, T2>& r)
{	// nyaa pair template operator <
	return (l.f != r.f) ? l.f < r.f : l.s < r.s;
}
template <class T1, class T2> bool
operator > (const NyaaPair<T1, T2>& l, const NyaaPair<T1, T2>& r)
{	// nyaa pair template operator >
	return (l.f != r.f) ? l.f > r.f : l.s > r.s;
}

/**************************************/
/********** BEGIN OF NYA LIB **********/
/**************************************/

namespace NyaGadget {}

namespace NyaGadget
{
	/*** 強連結成分分解ライブラリ ***/

	struct StronglyConnectedComponents
	{
		vector<bool> visited;         // DFSするときに訪れた頂点かどうか
		vector<long long> vs;         // トポロジカルに並べ直した頂点集合
		vector<vector<long long>> g;  // グラフ
		vector<vector<long long>> rg; // 辺を逆向きにしたグラフ
		// その他の変数
		// vector<T> vdata;
		// vector<unordered_map<long long, T>> edata;

		/**
		@brief 強連結成分分解の実行
		@param vmax グラフ頂点数
		@param res 強連結成分分解した頂点集合
		**/
		void Run(long long vmax, vector<vector<long long>>& res)
		{
			visited.clear();
			visited.resize((long long)g.size(), false);
			vs.clear();
			vs.resize((long long)g.size());
			rg.clear();
			rg.resize((long long)g.size());
			for (long long from = 0; from < (long long)g.size(); from++)
			{
				for (long long to = 0; to < (long long)g[from].size(); to++)
					rg[g[from][to]].push_back(from);
			}

			for (long long v = 0; v < vmax; v++)
			{
				if (!visited[v]) DFS(-1, v);
			}

			visited.clear();
			visited.resize((long long)g.size(), false);
			for (long long i = (long long)vs.size() - 1; 0 <= i; i--)
			{
				if (!visited[vs[i]])
				{
					res.resize((long long)res.size() + 1);
					RDFS(-1, vs[i], res);
				}
			}
		}

		/**
		@brief DFS処理関数
		@param r 頂点vの根
		@param v 現在の頂点
		**/
		void DFS(long long r, long long v)
		{
			{	// 頂点の更新処理
				visited[v] = true;
			}
			for (auto e : g[v])
			{	// 後戻りしないようにする
				if (e == r) continue;
				if (!visited[e]) DFS(v, e);
			}
			vs.push_back(v);
		}

		/**
		@brief 逆順DFS処理関数
		@param r 頂点vの根
		@param v 現在の頂点
		@param res 強連結成分分解した頂点集合
		**/
		void RDFS(long long r, long long v, vector<vector<long long>>& res)
		{
			{	// 頂点の更新処理
				visited[v] = true;
				res.back().push_back(v);
			}
			for (auto e : rg[v])
			{	// 後戻りしないようにする
				if (e == r) continue;
				if (!visited[e]) RDFS(v, e, res);
			}
		}
	};
}

/**************************************/
/*********** END OF NYA LIB ***********/
/**************************************/

using namespace NyaGadget;
//using mll = ModLL< 1000000007 >;
//using mll = ModLL< 998244353 >;


int main(void)
{
	ll K, N; cin >> K >> N;
	vt<ll> A; InputVT(N, A);

	vt<ll> ans;
	ans.push_back(A[0] + K - A.back());
	rep(i, 1, Size(A)) ans.push_back(A[i] - A[i - 1]);
	sort(all(ans));

	ll sum = 0;
	rep(i, 0, Size(ans) - 1) sum += ans[i];
	cout << sum;
	return 0;
}


Measured memory_bytes: 3956