#pragma region template
// clang-format off
#ifdef ONLINE_JUDGE
  #pragma GCC target("avx2")
  #pragma GCC optimize("tree-vectorize")
  #pragma GCC diagnostic ignored "-Wunused-result"
  #define here
  #define com(msg)
  #define obs(...)
  #define see(vec)
  #define local(x)
  #define alter(x,y) y
#else
  #define here cerr<<__func__<<"/"<<__LINE__<<": reached\n"
  #define com(msg) cerr<<"{ "<<msg<< " }\n"
  #define obs(...) observe(#__VA_ARGS__, __VA_ARGS__)
  #define see(vec) do{cerr<<#vec<<": ";printv(vec);}while(0)
  #define local(x) x
  #define alter(x,y) x
#endif

#include <bits/stdc++.h>

#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define rep(i,n) for(int i=0,i##_len=(n);i<i##_len;i++)
#define brep(i,a,b) for(int i=(a),i##_len=(b);i<=i##_len;i++)
#define rrep(i,n) for(int i=(n)-1,now=0;i>=0;i--,now++)
#define rbrep(i,a,b) for(int i=(a),i##_len=(b),now=0;i>=i##_len;i--,now++)
#define xrep(i,n) for(int i=1,i##_len=(n);i<=i##_len;i++)
#define yes(n) cout<<((n)?YES:NO)<<"\n"
#define cco(...) prints(__VA_ARGS__)
#define Sort(v) sort((v).begin(),(v).end())
#define rSort(v) sort((v).rbegin(),(v).rend())
#define Rev(v) reverse((v).begin(),(v).end())
#define Unique(v) (v).erase(unique((v).begin(),(v).end()),(v).end())
#define in_range(x,a,b) ((a)<=(x)&&(x)<(b))
#define in_area(x,y,a,b) (0<=(x)&&0<=(y)&&(x)<(a)&&(y)<(b))

using namespace std;
using ll    = long long;
using ld    = long double;
using pt    = pair<int, int>;
using ull   = unsigned long long;
using str   = string;
using vbl   = vector<bool>;
using dqbl  = deque<bool>;
using vint  = vector<int>;
using vll   = vector<long long>;
using vdb   = vector<double>;
using vld   = vector<long double>;
using vpt   = vector<pair<int, int>>;
using vstr  = vector<string>;
using vvdb  = vector<vector<double>>;
using vvbl  = vector<vector<bool>>;
using vdqbl = vector<deque<bool>>;
using vvint = vector<vector<int>>;
using vvll  = vector<vector<long long>>;

constexpr int       INF   = 1e9;
constexpr long long LINF  = 1e18;
constexpr double    EPS   = 1e-9;
constexpr int       dy[]  = {1,0,-1,0,1,1,-1,-1};
constexpr int       dx[]  = {0,1,0,-1,-1,1,1,-1};

// --- functions which take 1 argument --- //
template<class T> int sgn(const T &x){return (x>0)-(x<0);}
template<class S,class T=int> int digit(S x,const T &b=10){int r=1;while((x/=b)>=1)r++;return r;}
template<class T> double degToRad(const T &a){return a/180.0*M_PI;}
template<class T> double radToDeg(const T &a){return a/M_PI*180.0;}
template<class T> long long factorial(const T &n) {if(n==0)return 1;long long r=1;for(int i=2;i<=n;i++)r*=i;return r;}
template<class T> bool isPrime(const T &n){if(n<=1)return false;T i=2;while(i*i<=n){if(n%i==0&&n!=i)return false;i++;}return true;}
template<class T> map<T,T> factorize(T n){map<T,T>r;for(T i=2;i*i<=n;i++){while(n%i==0){r[i]++;n/=i;}}if(n!=1)r[n]=1;return r;}
template<class T> vector<T> divisor(const T &n){vector<T>r;for(T i=1;i*i<=n;i++){if(!(n%i)){r.emplace_back(i);if(i*i!=n)r.emplace_back(n/i);}}return r;}

// --- functions which take more than 1 argument --- //
template<class S,class T> [[maybe_unused]] bool chmax(S &a,const T &b){if(a<b){a=b;return true;}return false;}
template<class S,class T> [[maybe_unused]] bool chmin(S &a,const T &b){if(a>b){a=b;return true;}return false;}
template<class S,class T> bool near(const S &a, const T &b){return abs(a-b)<EPS;}
template<class S,class T> long long bpow(S m,T n){long long r=1;while(n>0){if(n&1)r*=m;m*=m;n/=2;}return r;}
template<class S,class T> typename common_type<S,T>::type min(const S &m,const T &n){return min((typename common_type<S,T>::type)m,(typename common_type<S,T>::type)n);}
template<class S,class T> typename common_type<S,T>::type max(const S &m,const T &n){return max((typename common_type<S,T>::type)m,(typename common_type<S,T>::type)n);}
template<class S,class T> long long nPr(const S &n,const T &k){if(n<k||n<0||k<0)return 0;long long r=1;for(int i=n-k+1;i<=n;i++)r*=i;return r;}
template<class S,class T> long long nCr(const S &n,T k){if(n<k||n<0||k<0)return 0;long long r=1;k=min(k,n-k);for(int i=n-k+1;i<=n;i++)r*=i;return r/factorial(k);}
template<class T>            void prints(const T &v){cout<<v<<"\n";}
template<class S,class... T> void prints(const S &v,const T&... w){cout<<v<<" ";prints(w...);}

// --- functions which take vector/deque as argument --- //
template<class T> void printd(const vector<T> &v,string d){for(int i=0,i_len=(int)v.size()-1;i<i_len;i++)cout<<v[i]<<d;cout<<*v.rbegin()<<'\n';}
template<class T> void printd(const vector<vector<T>> &v,string d){for(const auto &x:v)printD(x,d);}
template<class T> bool in(const T &k,const vector<T> &v)          {return find(v.begin(),v.end(),k)!=v.end();}
                  bool in(const int &k,const vector<long long> &v){return find(v.begin(),v.end(),k)!=v.end();}
                  bool in(const long long &k,const vector<int> &v){return find(v.begin(),v.end(),k)!=v.end();}
                  bool in(const char &k,const string &v)          {return find(v.begin(),v.end(),k)!=v.end();}
                  bool in(const char* k,const vector<string> &v)  {return find(v.begin(),v.end(),k)!=v.end();}
template<class T> double veclen(const vector<T> &v){return sqrt(reduce(v.begin(),v.end(),0.0,[](T s,T v){return s+=v*v;}));}
template<class T> T min(const vector<T> &v){return *min_element(v.begin(),v.end());}
template<class T> T max(const vector<T> &v){return *max_element(v.begin(),v.end());}
template<class T> T sum(const vector<T> &v){return reduce(v.begin(),v.end(),(T)0);}
template<class T> T gcd(const vector<T> &v){T r=v[0];for(int i=1,i_len=v.size();i<i_len;i++)r=gcd(r,v[i]);return r;}
template<class T> T lcm(const vector<T> &v){T r=v[0];for(int i=1,i_len=v.size();i<i_len;i++)r=lcm(r,v[i]);return r;}
template<class T> T vectorAdd(const T &u,const T &v)     {T r(u.size());for(int i=0,i_len=u.size();i<i_len;i++)r[i]=u[i]+v[i];return r;}
template<class T> T vectorSubtract(const T &u,const T &v){T r(u.size());for(int i=0,i_len=u.size();i<i_len;i++)r[i]=u[i]-v[i];return r;}
template<class T> T vectorMultiply(const T &u,const T &v){T r(u.size());for(int i=0,i_len=u.size();i<i_len;i++)r[i]=u[i]*v[i];return r;}
template<class T> T vectorDivide(const T &u,const T &v)  {T r(u.size());for(int i=0,i_len=u.size();i<i_len;i++)r[i]=u[i]/v[i];return r;}
template<class T> T dotProduct(const deque<bool> &u,const vector<T> &v){T r=0;for(int i=0,i_len=u.size();i<i_len;i++)if(u[i])r+=v[i];return r;}
template<class S,class T> typename common_type<S,T>::type dotProduct(const vector<S> &u,const vector<T> &v){typename common_type<S,T>::type r=0;for(int i=0,i_len=u.size();i<i_len;i++)r+=u[i]*v[i];return r;}
template<class S,class T> void sortBySecond(vector<pair<S,T>> &v){sort(v.begin(),v.end(),[](auto &L,auto &R){if(L.second==R.second)return L.first<R.first;return L.second<R.second;});}

// --- functions which take set/map as argument --- //
template<class T> T min(const set<T> &v){return *min_element(v.begin(),v.end());}
template<class T> T max(const set<T> &v){return *max_element(v.begin(),v.end());}
template<class T> T sum(const set<T> &v){return reduce(v.begin(),v.end(),(T)0);}
template<class T> T gcd(const set<T> &v){T r=0;for(const T &x:v)r=(r==0)?x:gcd(r,x);return r;}
template<class T> T lcm(const set<T> &v){T r=0;for(const T &x:v)r=(r==0)?x:lcm(r,x);return r;}
template<class T> bool in(const T &k,const set<T> &v){return find(v.begin(),v.end(),k)!=v.end();}
template<class S,class T> pair<S,T> min(const map<S,T> &m){pair<S,T> r=*m.begin();for(const pair<S,T> &p:m)if(r.second>p.second)r=p;return r;}
template<class S,class T> pair<S,T> max(const map<S,T> &m){pair<S,T> r=*m.begin();for(const pair<S,T> &p:m)if(r.second<p.second)r=p;return r;}

// --- operators --- //
template<class T>         istream& operator>>(istream &i,vector<T> &v){for(T &x:v)i>>x;return i;}
template<class T>         ostream& operator<<(ostream &o,vector<T> &v){for(T &x:v)o<<x<<"\n";return o;}
template<class S,class T> istream& operator>>(istream &i,pair<S,T> &p){i>>p.first>>p.second;return i;}
template<class S,class T> ostream& operator<<(ostream &o,pair<S,T> &p){o<<p.first<<" "<<p.second<<"\n";return o;}
template<class S,class T> pair<S,T> operator+(const pair<S,T> &p,const pair<S,T> &q){return pair<S,T>{p.first+q.first,p.second+q.second};}
template<class S,class T> pair<S,T> operator-(const pair<S,T> &p,const pair<S,T> &q){return pair<S,T>{p.first-q.first,p.second-q.second};}
template<class S,class T> pair<S,T> operator*(const pair<S,T> &p,const pair<S,T> &q){return pair<S,T>{p.first*q.first,p.second*q.second};}
template<class S,class T> pair<S,T> operator/(const pair<S,T> &p,const pair<S,T> &q){return pair<S,T>{p.first/q.first,p.second/q.second};}
template<class S,class T> [[maybe_unused]] pair<S,T> operator--(pair<S,T> &p){return pair<S,T>{--p.first,--p.second};}
template<class S,class T> [[maybe_unused]] pair<S,T> operator++(pair<S,T> &p){return pair<S,T>{++p.first,++p.second};}
template<class S,class T> [[maybe_unused]] pair<S,T> operator+=(pair<S,T> &p,const pair<S,T> &q){return p=p+q;}
template<class S,class T> [[maybe_unused]] pair<S,T> operator-=(pair<S,T> &p,const pair<S,T> &q){return p=p-q;}
template<class S,class T> [[maybe_unused]] pair<S,T> operator*=(pair<S,T> &p,const pair<S,T> &q){return p=p*q;}
template<class S,class T> [[maybe_unused]] pair<S,T> operator/=(pair<S,T> &p,const pair<S,T> &q){return p=p/q;}

// --- functions for debugging --- //
template<class T>            void observe(const char* n,T &&v)         {cerr<<n<<": "<<v<<"\n";}
template<class S,class... T> void observe(const char* n,S &&v,T&&... w){const char* c=strchr(n+1,',');cerr.write(n,c-n)<<": "<<v<<" |";observe(c+1,w...);}
template<class T> void printv(const vector<T> &v)        {cerr<<"[ ";for(const T &x:v)cerr<<x<<" ";cerr<<"]\n";}
template<class T> void printv(const deque<T> &v)         {cerr<<"[ ";for(const T &x:v)cerr<<x<<" ";cerr<<"]\n";}
template<class T> void printv(const set<T> &v)           {cerr<<"[ ";for(const T &x:v)cerr<<x<<" ";cerr<<"]\n";}
template<class P> void printv(const P &p)                {cerr<<"{ "<<p.first<<" "<<p.second<<" } ";}
template<class T> void printv(const vector<vector<T>> &v){for(const vector<T> &x:v)printv<T>(x);}
template<class T> void printv(const vector<deque<T>> &v) {for(const deque<T> &x:v) printv<T>(x);}
template<class S,class T> void printv(const map<S,T> &m) {cerr<<"[ ";for(const pair<S,T> &p:m)cerr<<"{ "<<p.first<<", "<<p.second<<" } ";cerr<<"]\n";}
template<class S,class T> void printv(const vector<pair<S,T>> &v){cerr<<"[ ";for(const pair<S,T> &p:v)printv<pair<S,T>>(p);cerr<<"]\n";}
// clang-format on
#pragma endregion

void solve(int K, int N, vector<int> A) {
  int res = 0, tmp;
  rep(i, N) {
    tmp = A[(i + 1) % N] - A[i];
    if (tmp < 0) tmp += K;
    chmax(res, tmp);
  }
  cout << K - res << "\n";
}

int main() {
  int K;
  scanf("%d", &K);
  int N;
  scanf("%d", &N);
  vector<int> A(N);
  for (int i = 0; i < N; i++) {
    scanf("%d", &A[i]);
  }
  solve(K, N, move(A));
  exit(EXIT_SUCCESS);
}


Measured memory_bytes: 4052