// #pragma comment(linker, "/stack:200000000")
// #pragma GCC optimize("Ofast")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
// #pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
// using namespace __gnu_pbds;
// typedef tree< int   ,     // change type 
//               null_type, 
//               less_equal  < int >  ,  // change type ..    
//               rb_tree_tag,
//               tree_order_statistics_node_update> o_set;
// less for set and  less_equal  for multiset  
// order_of_key (k) : Number of items strictly smaller than k 
// find_by_order(k) : K-th element in a set (counting from zero) returns iterator 
// debuging ...

/////max size of a global array = 499105527

using namespace std;
 
#define     inf               LONG_LONG_MIN
#define     INF               LONG_LONG_MAX

#define     forn(i,ii,n)         for(int i=ii; i<=n; ++i)
#define     ford(i,n,ii)         for(int i=n; i>=ii; --i)
#define     repit(i, c)         for( auto i = (c).begin(); i != (c).end();++i )
 
#define     pb                  push_back
#define     eb                  emplace_back
#define     sz(xx)              (int) xx.size()
#define     mk                  make_pair
#define     mem(x,v)            memset(x,v,sizeof x)
#define		clr(xx)				xx.clear()
#define		ff 					first
#define		ss 					second
#define		all(x)				x.begin(),x.end()
#define		nl 					cout << endl
#define     kase(x)             cout << "Case " << x <<": "
#define     fastt               ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define     dbg(args...)        do {   cerr << #args << ' ' ;  print(args); } while(0); cerr<< endl ;
 
///Geometry
#define		distance(x1,y1,x2,y2) 		sqrt((x1-x2)*(x1-x2))+((y1-y2)*(y1-y2))
#define 	triangleArea(a,b,c,s) 		sqrt(s*(s-a)*(s-b)*(s-c))
#define 	triAngle(a,b,c) 			cosi((b*b+c*c-a*a)/(2*b*c))
 
///Trigonmetry
#define PI acos(-1.0)
#define sinD(degree) sin((degree * PI) / 180.0)
#define cosD(degree) cos((degree * PI) / 180.0)
#define tanD(degree) tan((degree * PI) / 180.0)
#define cotD(degree) (1.0 / tanD(degree))
#define secD(degree) (1.0 / cosD(degree))
#define cosecD(degree) (1.0 / sinD(degree))
#define asinD(value) (asin(value) * 180.0) / PI
#define acosD(value) (acos(value) * 180.0) / PI
#define atanD(value) (atan(value) * 180.0) / PI

#define gray    1		//discoverd
#define black  -1		//finished
#define white   0		//undiscoverd

template< typename T > void print(const T& v) {    cerr << v << ' ' ;}
template< typename T1, typename... T2 > void print( const T1& first, const T2&... rest ){ print(first); print(rest...) ;}
 
/*typedef*/
typedef long long ll;
typedef unsigned long long ull;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vi> vvi;
typedef vector<vl> vvl;
typedef vector<ull> vul;
typedef pair<int,int> pii;
typedef pair<int,ull> piul;
typedef pair<int,double> pid;
typedef vector<pii> vii;
typedef vector<pid> vid;
typedef vector<piul> viul;
typedef map<int,int> mii;
typedef map<string,int> msi;
typedef set<int> si;
typedef priority_queue <pii, vector<pii>, greater<pii> > pq;	///for djkstra
/*typedef ends*/
 
 
int setbit(int N,int pos){return N=N | (1<<pos);}
int resetbit(int N,int pos){return N= N & ~(1<<pos);}
bool checkbit(int N,int pos){return (bool)(N & (1<<pos));}
int nextN(int N) {return N + ( N & (-N));}
int parentN(int N) {return N - ( N & (-N));}

/*functions*/
template<typename T> T extGcd(T a, T b, T& x, T& y) { if(a==0) { x=0,y=1; return b; } T x1,y1,gcd = extGcd(b%a,a,&x1,&y1); x= y1-(b/a)*x1, y = x1; return gcd;}
template<typename T> T bigMod(T a, T p, T m) { if(p==1) return a; T x = bigMod(a,p/2,m)%m; x = (x*x)%m; return (p&1) ? (x*a)%m : x;}
template<typename T> T modMul(T a, T b, T m) { return ((a%m)*(b%m))%m; }
template<typename T> T modAdd(T a, T b, T m) { return ((a%m)+(b%m))%m; }
template<typename T> T modSub(T a, T b, T m) { return (a-b+m)%m; }
template<typename T> T modInverse(T a , T m) { return bigMod(a,m-2,m); }  ///m must be prime

/*direction array*/
 
/***4 moves***/
/*
int dx[] = { 0,  0, -1, +1 } ;
int dy[] = {-1, +1,  0,  0 };
 */
/***8 moves***/
/*
int dx[] = { 0,  0, -1, -1, -1, +1, +1, +1 } ;
int dy[] = {-1, +1, -1,  0, +1, -1,  0, +1 } ;
*/
 
/*direction array ends*/
 
/**************************************************************************************************/


/*const int maxn = 1e5;
int spf[maxn+1];
vector<int> primes;
void seive()
{
    int sq = sqrt(maxn);
    for (int i=1; i<= maxn; i+=2) spf[i] = i;
    for (int i=2; i<=maxn ; i+=2 ) spf[i]= 2;

    primes.pb(2);
    for (int i=3; i<=maxn ; i+=2 ){
        if(spf[i]==i){
            primes.pb(i);
            if(i<=sq){
                for (int j=i*i; j<=maxn; j+=(2*i)){ if(spf[j]==j) spf[j]=i; }
            }
        }
    }
    // dbg(sz(primes));
}*/

/*
vii primeFactors[maxn+1];
void primeFactorize(int x)
{
    int n=x;
    for(int i=0,d=0; i<sz(primes) && n>1; i++,d=0){
        if(n<maxn){if(spf[n]==n)break;}
        while(n>1 && n%primes[i]==0) d++, n/=primes[i];
        if(d>0) primeFactors[x].pb({primes[i],d});
    }
    if(n>1) primeFactors[x].pb({n,1});
}
*/


/*vii primeFactors[maxn+1];
void primeFactorizeBySpf(int x)
{
    int n= x, prv=spf[x],d=0;   ///prv=previous prime
    while(n>1){
        if(spf[n]==prv) d++;
        else { primeFactors[x].pb({prv,d}); d=1;}
        prv = spf[n]; n/=spf[n];
    }
    primeFactors[x].pb({prv,d});
}*/

/*
///for dijkstra
class node{
public:
	int at,cost;
	node(int a,int b){at=a,cost=b;}
	bool operator <(const node& e)const{return cost<e.cost;}
};
class edge{public: int v,w;};
*/
/*
ll a,b,c,n,m;
ll sum;

ll bsrc(ll l,ll h)
{
    ll ans = 0;
    ll hi=h, lo=l, mid;

    while(hi>=lo){
        mid = (lo+hi)/2;
        if(min(mid,a+c)<=n && min(mid,b+c)<=m) {ans = mid; lo=mid+1;}
        else { hi= mid-1; }
    }

    return ans;
}*/

/*
ll fact[maxn+1];
void factorial(){
    fact[0]=1;
    forn(i,1,maxn) fact[i] = modMul(fact[i-1],(ll)i, mod);
}
ll ncr(int n, int r){
    return modMul(fact[n],modInverse(modMul(fact[r],fact[n-r],mod),mod),mod);
}*/


/*****************************************************************************/

int main()
{
	
     //  freopen("in.txt", "r", stdin);
      //   freopen("out.txt", "w", stdout);
    

    fastt;
    int k,n;
    cin>>k>>n;
    ll a[n];
    forn(i,0,n-1) cin>>a[i];
    ll ans=LONG_LONG_MAX;
    forn(i,0,n-1){
        if(i<n-1)ans = min(ans,a[i]+k-a[i+1]);
        else ans = min(ans,a[i]-a[0]);
        if(i>0) ans = min(ans,a[i-1]+k-a[i]);
        else ans = min(ans,a[n-1]-a[i]);
    }
    cout << ans ;

	return 0;
}

Measured memory_bytes: 1792