// Problem : C - Traveling Salesman around Lake
// Contest : AtCoder Beginner Contest 160
// URL : https://atcoder.jp/contests/abc160/tasks/abc160_c
// Memory Limit : 1024 MB
// Time Limit : 2000 ms
// Powered by CP Editor (https://github.com/cpeditor/cp-editor)

#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize ("Ofast")
#define fio ios::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL)
#define ull unsigned long long
#define ll long long
#define inf INT_MAX
#define mninf INT_MIN
#define infl 1e18+5
#define mninfl -1e18-5
#define Mod 1000000007
#define newmod  998244353
int ah=911382323;
int bh=972663749;
#define endl "\n"
#define cp(x) cout<<(x)<<" "
#define cl(x) cout<<(x)<<endl
#define ct(x,y) cout<<(x)<<" "<<(y)<<endl;
#define nl   cout<<endl
//const long double pi=acos(-1);
//looping
#define int long long
#define For(i,a,b) for(int i=a;i<b;i++)
#define test(t)  int (t); cin>>(t); while((t)--)
#define array(a,n) int (n); cin>>(n); int a[n]; for(int i=0;i<(n);i++) cin>>a[i];
#define max3(a,b,c) max(a,max(b,c))
#define min3(a,b,c) min(a,min(b,c))
#define pa(a,n) for(int i = 0 ; i < n ; i++) cout<<a[i]<<' ';  cout<<endl
#define pv(v)  for(int i=0;i<(v).size();i++) cout<<v[i]<<" ";  cout<<endl
template < typename F, typename S >
ostream& operator << ( ostream& os, const pair< F, S > & p ) {
    return os << "(" << p.first << ", " << p.second << ")";
}
template < typename T >
ostream &operator << ( ostream & os, const vector< T > &v ) {
    os << "{";
    typename vector< T > :: const_iterator it;
    for( it = v.begin(); it != v.end(); it++ ) {
        if( it != v.begin() ) os << ", ";
        os << *it;
    }
    return os << "}";
}
template < typename T >
ostream &operator << ( ostream & os, const set< T > &v ) {
    os << "[";
    typename set< T > :: const_iterator it;
    for ( it = v.begin(); it != v.end(); it++ ) {
        if( it != v.begin() ) os << ", ";
        os << *it;
    }
    return os << "]";
}
template < typename F, typename S >
ostream &operator << ( ostream & os, const map< F, S > &v ) {
    os << "[";
    typename map< F , S >::const_iterator it;
    for( it = v.begin(); it != v.end(); it++ ) {
        if( it != v.begin() ) os << ", ";
        os << it -> first << " = " << it -> second ;
    }
    return os << "]";
}
#define deb(x) cerr << #x << " = " << x << endl;
#define deb2(x,y)  cerr << #x << " = " << x <<"   "<< #y << " = " << y << endl;
//containers
#define F first
#define S second
#define pb emplace_back
#define pf push_front
#define pob pop_back
#define pof pop_front
#define mkp make_pair
#define all(v) (v).begin(),(v).end()
int dx[8]={1,-1,0,0,1,1,-1,-1};
int dy[8]={0,0,1,-1,1,-1,1,-1};
typedef vector<int> vi;
typedef vector< vector< int > > vvi;
typedef vector < pair <int, int> > vpii;
/*/----------------------------Code begins----------------------------------/*/
int32_t main(){
fio;
int k,n;
cin>>k>>n;
vi a(n);
For(i,0,n)
cin>>a[i];
a.pb(a[0]);
int mx=mninf;
for(int i=0;i<n-1;i++){
	if((a[i+1]<=k/2)){
		mx=max(mx,a[i+1]-a[i]);
	}
	else if(a[i+1]>k/2){
		if(a[i]<=k/2){
			mx=max(mx,min((a[i+1]-a[i]),(a[i]+k-a[i+1])));
		}
		else mx=max(mx,a[i+1]-a[i]);
	}
}
mx=max(mx,min((a[n-1]-a[n]),(a[n]+k-a[n-1])));
cl(k-mx);
}




























Measured memory_bytes: 4864