#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC push_options
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
#include<bits/stdc++.h>
#include <xmmintrin.h>
#include <immintrin.h>
using namespace::std;
__attribute__((constructor))void init(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);}
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/priority_queue.hpp>
#include<ext/pb_ds/tag_and_trait.hpp>
// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// typedef mp::number<mp::cpp_dec_float<0>> cdouble;
// typedef mp::cpp_int cint;
template<typename T>using pbds=__gnu_pbds::tree<T,__gnu_pbds::null_type,less<T>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>;
template<typename T>using pbds_map=__gnu_pbds::tree<T,T,less<T>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>;
template<typename T,typename E>using hash_map=__gnu_pbds::gp_hash_table<T,E>;
template<typename T>using pqueue =__gnu_pbds::priority_queue<T, greater<T>,__gnu_pbds::rc_binomial_heap_tag>;
typedef long long lint;
typedef long long ll;
#define INF (1LL<<60)
#define IINF (1<<30)
#define LINF (9223372036854775807LL)
#define EPS (1e-10)
#define endl ('\n')
#define MOD 1000000007LL
//#define MOD 998244353LL
typedef vector<lint> vec;
typedef vector<vector<lint>> mat;
typedef vector<vector<vector<lint>>> mat3;
typedef vector<string> svec;
typedef vector<vector<string>> smat;
template<typename T>inline void numout(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i<INF/2?i:"INF";f=1;}cout<<endl;}
template<typename T>inline void numout2(T t){for(auto i:t)numout(i);}
template<typename T>inline void output(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i;f=1;}cout<<endl;}
template<typename T>inline void output2(T t){for(auto i:t)output(i);}
template<typename T>inline void _output(T t){bool f=0;for(lint i=0;i<t.size();i++){cout<<f?"":" "<<t[i];f=1;}cout<<endl;}
template<typename T>inline void _output2(T t){for(lint i=0;i<t.size();i++)output(t[i]);}
template<typename T>inline void debug(T t){bool f=0;for(auto i:t){cerr<<(f?" ":"")<<i;f=1;}cerr<<endl;}
#define rep(i,n) for(lint i=0;i<lint(n);++i)
#define repi(i,a,b) for(lint i=lint(a);i<(lint)(b);++i)
#define rrep(i,n) for(lint i=lint(n)-1;i>=0;--i)
#define rrepi(i,a,b) for(lint i=lint(b)-1;i>=lint(a);--i)
#define irep(i) for(lint i=0;;++i)
#define all(n) begin(n),end(n)
#define dist(a,b,c,d) sqrt(pow(a-c,2)+pow(b-d,2))
inline lint gcd(lint A,lint B){return B?gcd(B,A%B):A;}
inline lint lcm(lint A,lint B){return A/gcd(A,B)*B;}
// inline cint cgcd(cint A,cint B){return B?cgcd(B,A%B):A;}
// inline cint clcm(cint A,cint B){return A/cgcd(A,B)*B;}
bool chmin(auto& s,const auto& t){bool res=s>t;s=min(s,t);return res;}
bool chmax(auto& s,const auto& t){bool res=s<t;s=max(s,t);return res;}
const vector<lint> dx={1,0,-1,0,1,1,-1,-1};
const vector<lint> dy={0,1,0,-1,1,-1,1,-1};
#define SUM(v) accumulate(all(v),0LL)
auto call=[](auto f,auto... args){return f(f,args...);};

class Knapsack {
    struct item {
        ll v, w;
    };
 
    vector<item> items;
    ll W, lv;
 
    ll solve_rec(size_t k, ll v, ll w) {
        if (w + items[k].w > W)
            return solve_rec(k + 1, v, w);
        ll cv = v, cw = w;
        for (size_t i = k; i < items.size(); ++i) {
            if (cw + items[i].w <= W) {
                cw += items[i].w;
                cv += items[i].v;
            }
        }
        if (lv < cv)
            lv = cv;
        double fv = v, fw = w;
        for (size_t i = k; i < items.size(); ++i) {
            if (fw + items[i].w <= W) {
                fw += items[i].w;
                fv += items[i].v;
            } else {
                fv += items[i].v * (W - fw) / items[i].w;
                break;
            }
        }
        if (fv - lv < 1 || fv < lv)
            return lv;
        solve_rec(k + 1, v + items[k].v, w + items[k].w);
        return solve_rec(k + 1, v, w);
    }
 
  public:
    // 価値v, 重みwのアイテムを追加
    void add_item(ll v, ll w) { items.push_back({v, w}); }
 
    // 重みの合計がW以下になるようにアイテムを選んだときの価値の和の最大値を返す．
    ll solve(ll W_) {
        if (items.empty())
            return 0;
        // 番兵として価値0、重さ1を追加
        items.push_back({0, 1});
        W = W_;
        sort(items.begin(), items.end(), [](const item &a, const item &b) {
            // 単位重量あたりの価値 v/w を大きい順にする（除算は遅いので乗算）
            return a.v * b.w > a.w * b.v;
        });
        lv = 0;
        return solve_rec(0, 0, 0);
    };
};

int main(){
    lint k,n;
    cin>>k>>n;
    vec a(n);
    rep(i,n)cin>>a[i];
    lint mx=INF;
    rep(i,n-1){
        chmin(mx,k-a[i+1]+a[i]);
    }
    chmin(mx,a.back()-a[0]);
    cout<<mx<<endl;
}


Measured memory_bytes: 1792