#include <bits/stdc++.h> // ver2.5.0
//#include <complex.h> // FFT用
//#include <boost/math/tools/minima.hpp>
//#include <boost/multiprecision/cpp_int.hpp>
//using boost::math::tools::brent_find_minima;//fmin(f,L,R,100)で最小値をmp(x,min)で取得
//using boost::multiprecision::cpp_int;//cpp_int (任意の長さのint)
#define fmin brent_find_minima
#define int long long
#define endl "\n"
#define ALL(v) (v).begin(),(v).end()
#define Vi vector<int>
#define VVi vector<Vi>
#define VVVi vector<VVi>
#define Vm vector<mint>
#define Vs vector<string>
#define Vd vector<double>
#define Pii pair<int,int>
#define Pdd pair<double,double>
#define VPii vector<Pii>
#define Tiii tuple<int,int,int>
#define VTiii vector<Tiii>
#define PQi priority_queue<int>
#define PQir priority_queue<int,vector<int>,greater<int>>
#define pb push_back
#define mp make_pair
#define mt make_tuple
#define itos to_string
#define stoi stoll
#define FI first
#define SE second
#define cYES cout<<"YES"<<endl
#define cNO cout<<"NO"<<endl
#define cYes cout<<"Yes"<<endl
#define cNo cout<<"No"<<endl
#define cyes cout<<"yes"<<endl
#define cno cout<<"no"<<endl
#define sortr(v) sort(v,greater<>())
#define rep(i,a,b) for(int i=a;i<b;i++)
#define repeq(i,a,b) for(int i=a;i<=b;i++)
#define repreq(i,a,b) for(int i=a;i>=b;i--)
#define dem(a,b) ((a+b-1)/(b))
#define Vin(a) rep(iI,0,a.size())cin>>a[iI]
#define INF 3000000000000000000  //  3.0*10^18(MAXの1/3くらい)
#define MAX LLONG_MAX
#define PI 3.141592653589793238462
#define MOD 1000000007  //  10^9 + 7
const double EPS = 1e-10;
//int MOD = 998244353; // 変更したいときはこちら
struct mint {int x;mint(int x=0):x((x%MOD+MOD)%MOD){}
mint& operator+=(const mint a){if((x+=a.x)>=MOD)x-=MOD;return *this;}
mint& operator-=(const mint a){if((x+=MOD-a.x)>=MOD)x-=MOD;return *this;}
mint& operator*=(const mint a){(x*= a.x)%=MOD;return *this;}
mint operator+(const mint a)const{mint res(*this);return res+=a;}
mint operator-(const mint a)const{mint res(*this);return res-=a;}
mint operator*(const mint a)const{mint res(*this);return res*=a;}
mint pow(int t)const {if(!t)return 1;mint a=pow(t>>1);a*=a;if(t&1)a*= *this;return a;}
mint inv()const{return pow(MOD-2);}
mint& operator/=(const mint a){return (*this)*=a.inv();}
mint operator/(const mint a)const{mint res(*this);return res/=a;}};

using namespace std;

/* デバッグ用 */
void Vout(auto a){if(a.size()==0) cout<<"."<<endl;
else{rep(i,0,a.size()-1)cout<<a[i]<<' ';if(a.size()>0)cout<<a.back()<<endl;}return;}
void Verr(auto a){if(a.size()==0) cerr<<"."<<endl;
else{rep(i,0,a.size()-1)cerr<<a[i]<<' ';if(a.size()>0)cerr<<a.back()<<endl;}return;}
void VVout(auto a){if(a.size()==0)cout<<"."<<endl;
else{rep(i,0,a.size())Vout(a[i]);}return;}
void VVerr(auto a){if(a.size()==0)cerr<<"."<<endl;
else{rep(i,0,a.size())Verr(a[i]);}return;}
void VPout(auto a){if(a.size()==0)cout<<"."<<endl;
else{rep(i,0,a.size())cout<<a[i].FI<<' '<<a[i].SE<<endl;}return;}
void VPerr(auto a){if(a.size()==0)cerr<<"."<<endl;
else{rep(i,0,a.size())cerr<<a[i].FI<<' '<<a[i].SE<<endl;}return;}

/* 便利関数 */
int gcd(int a,int b){return b?gcd(b,a%b):a;} // 最大公約数gcd
int lcm(int a,int b){return a/gcd(a,b)*b;} // 最小公倍数lcm
int mypow(int x, int n, int m){ // 累乗x^n(mod m) O(log(n))
if(n==0)return 1;if(n%2==0)return mypow(x*x%m,n/2,m);else return x*mypow(x,n-1,m)%m;}
int scomb(int n, int r){if(r<0||r>n)return 0;if((n-r)<r)r=n-r; // nCr
int a=1;for(int i=n;i>n-r;--i){a=a*i;}for(int i=1;i<r+1;++i){a=a/i;}return a;}
Vi vis(Vi &v){Vi S(v.size()+1);rep(i,1,S.size())S[i]+=v[i-1]+S[i-1];return S;} // 累積和
int digit(int k,int i){string s = itos(k);return s[s.size()-i]-'0';} // i桁目の数字
void press(auto &v){v.erase(unique(ALL(v)),v.end());} // 圧縮
Vi zip(Vi b){int Z=b.size(); // 座標圧縮
Pii p[Z+10];int a=b.size();Vi l(a);for(int i=0;i<a;i++)
p[i]=mp(b[i],i);sort(p,p+a);int w=0;for(int i=0;i<a;i++)
{if(i&&p[i].first!=p[i-1].first)w++;l[p[i].second]=w;}return l;}
Vi beki2V(){Vi a(63);int q = 1;rep(i,0,63){a[i]=q;q*=2;}return a;}
Vi beki2 = beki2V(); // 2^n配列
int modiv(int a,int b){return a*mypow(b,MOD-2,MOD)%MOD;} // a÷b(MOD環境)
int SMALLER(Vi &a,int x){return lower_bound(a.begin(),a.end(),x)-a.begin();}
int orSMALLER(Vi &a,int x){return upper_bound(a.begin(),a.end(),x)-a.begin();}
int BIGGER(Vi &a,int x){return a.size()-orSMALLER(a,x);}
int orBIGGER(Vi &a,int x){return a.size()-SMALLER(a,x);}
int COUNT(Vi &a,int x) {return upper_bound(ALL(a),x)-lower_bound(ALL(a),x);}
int maxind(Vi &a){return max_element(ALL(a))-a.begin();}
int minind(Vi &a){return min_element(ALL(a))-a.begin();}
Vi stpowV(){Vi a(100005);
a[0]=1;repeq(i,1,100004)a[i]=a[i-1]*i%MOD;return a;}
//Vi stpow = stpowV(); // 階乗配列(%MOD)

/****************************** START ******************************/

signed main() {
  cin.tie(0);cout.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(12);
  int k,n;
  cin >> k >> n;
  Vi a(n);
  Vin(a);
  int ans = INF;
  
  int sa1,sa2;
  sa1 = a[0];
  sa2 = k-a.back();
  ans = k-sa1-sa2;
  cerr << ans << endl;
  
  rep(i,0,n-1){
    int sa = a[i+1]-a[i];
    ans = min(ans,k-sa);
  }
  
  cout << ans << endl;
  return 0;
}

Measured memory_bytes: 1792