#pragma GCC optimize("Ofast,no-stack-protector")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize("fast-math")

#include<bits/stdc++.h>
using namespace std;

typedef long long int      ll;
typedef long double        ld;
typedef unsigned long long ull;
typedef vector<ll>         vl;
typedef vector<vl>         vvl;
typedef pair<ll,ll>        pll;
typedef vector<pll>        vpll;

#define ff          first
#define ss          second
#define pb          push_back
#define mp          make_pair
#define eb          emplace_back
#define tr(x,c)     for(auto &x:c)
#define fr(i,n)     for(ll i = 0; i < n; ++i)
#define frs(i,s,n)  for(ll i = s; i < n; ++i)
#define frb(i,s,e)  for(ll i = s; i <= e; ++i)
#define rfr(i,n)    for(ll i = n-1; i >= 0; i--)
#define frbr(i,e,s) for(ll i = e; i >= s; i--)
#define all(x)      (x).begin(), (x).end()
#define sz(x)       ((ll)(x).size())

inline void __print(int x) {cerr << x;}
inline void __print(long x) {cerr << x;}
inline void __print(long long x) {cerr << x;}
inline void __print(unsigned x) {cerr << x;}
inline void __print(unsigned long x) {cerr << x;}
inline void __print(unsigned long long x) {cerr << x;}
inline void __print(float x) {cerr << x;}
inline void __print(double x) {cerr << x;}
inline void __print(long double x) {cerr << x;}
inline void __print(char x) {cerr << '\'' << x << '\'';}
inline void __print(const char *x) {cerr << '\"' << x << '\"';}
inline void __print(const string &x) {cerr << '\"' << x << '\"';}
inline void __print(bool x) {cerr << (x ? "true" : "false");}

template<typename T, typename V>
inline void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T>
inline void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";}
inline void _print() {cerr << "]\n";}
template <typename T, typename... V>
inline void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}

clock_t startTime;
inline double getCurrentTime() {return ((double)(clock() - startTime)) / CLOCKS_PER_SEC;} 

#ifdef UBC
#define dbg(x...)      cerr << "[" << #x << "] = ["; _print(x)
#define dbg_arr(a,n)   cerr << "[" << #a << "] = [ ";fr(i,n)cerr<<a[i]<<" ";cerr<<"]\n";
#define dbg_mat(m,r,c) cerr<<"[" <<#m<<"]:\n";fr(i,r){cerr<<"[ ";fr(j,c)cerr<<m[i][j]<<" ";cerr<<"]\n";}
#define dbg_time()     cerr<<"Time elapsed: "<<getCurrentTime()<<endl;
#define tle()          {if(getCurrentTime() > 5.0) {dbg_time();cerr<< "[-INF-Exit-]" << endl; exit(1);}}
#else
#define dbg(x...)      {}
#define dbg_arr(a,n)   {}
#define dbg_mat(m,r,c) {}
#define dbg_time(t)    {}
#define tle()          {}
#endif

const ll MOD  = 1e9+7;
const ll SMOD = 998244353;
const ll INF  = 1e18;
const ll SINF = 1e9;
const ll MAX  = 100100;


void pre()
{
  
}

void solve()
{
  ll k,n;
  cin >> k >> n;
  vl v(n);
  // ll p = 0;
  fr(i,n)
  {
    cin >> v[i]; 
  }
  vl v1;
  frs(i,1,n)
  {
    v1.pb(v[i] - v[i-1]);
  }
  v1.pb((k-v[n-1]) + v[0]);
  cout << k - *max_element(all(v1)) << '\n';  
}

signed main()
{  
    startTime = clock();

    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);

    #ifdef UBC
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    #endif

    //cout<<fixed<<setprecision(15);
    //pre();

    ll test = 1;
    // cin>>test;
    fr(ii,test)
    {
      // cout << "Case #" << ii + 1 << ": ";
      solve();
    }

    dbg_time();
    
    return 0;
}    


Measured memory_bytes: 3956