/*
Author - Bohot harami
Motive - Candidate Master banunga ek din
*/
#include<bits/stdc++.h>

#include <ext/pb_ds/assoc_container.hpp> // Policy_based_Data_Structure 
#include <ext/pb_ds/tree_policy.hpp> 
using namespace __gnu_pbds;

/*#include <boost/multiprecision/cpp_int.hpp>
using namespace boost::multiprecision;*/
 
#define ll long long int
#define ld long double
#define bigint int64_t
#define vll vector<ll>
#define vpll vector<pair<ll,ll>>
#define mp make_pair
#define pb push_back
#define MOD 1000000007
#define flash ios_base::sync_with_stdio(false);cin.tie(NULL);
#define test ll t;read(t);while(t--)
#define all(v) v.begin(),v.end()
#define pll pair<ll,ll>
#define INF (ll)(1e15)
#define vvll vector<vector<ll>>
#define R_0 return 0
#define db1(x) cout<<#x<<"="<<x<<'\n'
#define db2(x,y) cout<<#x<<"="<<x<<","<<#y<<"="<<y<<'\n'
#define db3(x,y,z) cout<<#x<<"="<<x<<","<<#y<<"="<<y<<","<<#z<<"="<<z<<'\n'

 
#define forn(i,n) for(ll (i) = 0 ; (i) < (n) ; ++(i))
#define for1(i,n) for(ll (i) = 1 ; (i) <= (n) ; ++(i))
#define forr(i,n) for(ll (i) = (n)-1 ; (i)>=0 ; --(i))
#define forab(i,a,b,c) for(ll (i) = a ; (i) <= (b) ; (i)+=(c))
 
using namespace std;
template <typename T>
void read(T &x){
    cin >> x;
}
template <typename T , typename T0>
void read(T &x,T0 &y){
    cin >> x >> y;
}
 
template <typename T , typename T0 , typename T1>
void read(T &x,T0 &y,T1 &z){
    cin >> x >> y >> z;
}
 
template <typename T , typename T0 , typename T1 , typename T2>
void read(T &x,T0 &y,T1 &z,T2 &w){
    cin >> x >> y >> z >> w;
}
 
template <typename T , typename T0>
void read(pair< T , T0 > &p){
    cin >> p.fst >>p.scd;
}
 
template <typename T>
void read(vector< T > &oneD,ll n){
    forn(i,n)
    {
        ll x;
        read(x);
        oneD.push_back(x);
    }
}
 
template <typename T>
void read(T oneD[] , ll n){
    for(ll i=0;i<n;i++){
        read(oneD[i]);
    }
}
 
template <typename T>
void write(T &x){
    
    cout << x << " ";
}
 
template <typename T , typename T0>
void write(T &x,T0 &y){
    cout << x << " " << y << "\n";
}
 
template <typename T , typename T0 , typename T1>
void write(T &x,T0 &y,T1 &z){
    cout << x << " " << y << " " << z << "\n";
}
 
template <typename T , typename T0 , typename T1 , typename T2>
void write(T &x,T0 &y,T1 &z,T2 &w){
    cout << x << " " << y << " " << z << " " << w << "\n";
}
 
template <typename T , typename T0>
void write(pair< T , T0 > &p){
    write(p.fst);
    write(p.scd);
    cout << endl;
}
 
template <typename T>
void write(vector< T > &oneD,ll n){
    for(ll i=0;i<n;i++){
        cout<<oneD[i]<<" ";
    }
    cout << endl;
}
 
template <typename T>
void write(T oneD[] ,int n){
    for(ll i=0;i<n;i++){
        write(oneD[i]);
    }
    cout << endl;
}
 
template <typename T , typename T0>
void write(map< T , T0 > &mpp){
    for(auto it : mpp){
        write(it.fst);
        cout << ": ";
        write(it.scd);
        cout << "\n";
    }
    cout<<endl;
}
 
vll seive;
void Seive(){
    const ll maxn = 1e6+5;
    seive.resize(maxn);
    forn(i,maxn) seive[i] = i;
    forab(i,2,maxn,2)
    seive[i]=2;
    seive[1] = -1;
    seive[0] = -1;
    for(ll i=3;i<=maxn;i+=2) if(i == seive[i]) for(ll j = i*i ; j < maxn ; j+=i) if(seive[j] == j) seive[j] = i;
}
 
ll extended_GCD(ll a , ll b , ll &x , ll &y){
    if(a == 0){
        x = 0;
        y = 1;
        return b;
    }
    ll x1 , y1;
    ll gcd = extended_GCD(b%a , a , x1 , y1);
    x = y1 - (b/a)*x1; 
    y = x1;
    return gcd;
}
 
ll modinv(ll a , ll mod = MOD){
    ll x , y;
    extended_GCD(a , mod , x , y);
    if(x < 0) x += mod;
    return x;
}
 
//Chinese Remainder Theoram
ll find_x_CRT(ll num[],ll rem[],ll n)
{
    ll pro=1;
    forn(i,n)
    pro*=num[i];
    ll res=0;
    forn(i,n)
    {
        ll pp = pro/num[i];
        res+=(rem[i]*modinv(pp,num[i])*pp);
    }
    res%=pro;
    return res;
}
 
ll power(ll a, ll b, ll m = MOD) {
    a%=m;
    ll res = 1;
    while (b > 0) {
        if (b & 1)
            res = res * a %m;
        a = a * a %m;
        b >>= 1;
    }
    return res;
}
 
ll powe(ll a, ll b, ll m = MOD) {
    ll res = 1;
    while (b > 0) {
        if (b & 1)
            res = res * a;
        a = a * a;
        b >>= 1;
    }
    return res;
}
 
ll gcd(ll a, ll b)
{
    if (a == 0)
        return b;
    return gcd(b % a, a);
}
 
string getString(char x) 
{ 
    string s(1, x); 
    return s;    
} 

void update(vll &BIT,ll index,ll inc)
{
    while(index<=(ll)(BIT.size()))
    {
        BIT[index]+=inc;
        index+=(index&(-index));
    }
}

ll query(vll &BIT,ll index)
{
    ll sum=0;
    while(index>0)
    {
        sum+=BIT[index];
        index-=(index&(-index));
    }
    return sum;
}

typedef tree<ll, null_type, less<ll>, rb_tree_tag, tree_order_statistics_node_update> index_set; 
//typedef tree<ll, null_type, less_equal<ll>, rb_tree_tag, tree_order_statistics_node_update> indexed_multiset;
void make_set(ll v,vll &parent,vll &siz)
{
    parent[v]=v;
    siz[v]=1;
}

ll find_set(ll x,vll &parent)
{
    if(x==parent[x])
    return x;
    else
    {
        return parent[x]=find_set(parent[x],parent);
    }
}

void union_set(ll a,ll b,vll &siz,vll &parent)
{
    a = find_set(a,parent);
    b = find_set(b,parent);
    if(a!=b)
    {
        if(siz[a]<siz[b])
        swap(a,b);
        parent[b]=a;
        siz[a]+=siz[b];
        siz[b]=0;
    }
}

void precompute_NCR(vll &fact)
{
    const ll N = 1e6+5;
    fact[0] = 1;
    forab(i,1,(N-1),1)
    {
        ll y = (i%MOD*fact[i-1]%MOD)%MOD;
        fact[i] = y;
    }
}

ll NCR(vll &fact,ll N,ll R,ll mod=MOD)
{
    ll n = fact[N];
    ll r = fact[R];
    ll n_r = fact[N-R];
    ll y = (r%mod*n_r%mod)%mod;
    ll z = modinv(y,mod);
    ll ans = (n%mod*z%mod)%mod;
    return ans;
}

void shuru_karte_hai_bina_kise_bakchodi_ke()
{
    flash;
    #ifndef ONLINE_JUDGE
        freopen("input.txt","r",stdin);
        freopen("output.txt","w",stdout);
    #endif
}

int main()
{
    //shuru_karte_hai_bina_kise_bakchodi_ke();
    ll k,n;
    read(k,n);
    ll a[n];
    read(a,n);
    ll pre[n]={};
    pre[0]=a[0];
    forab(i,1,(n-1),1)
    {
        pre[i]=pre[i-1]+(a[i]-a[i-1]);
    }
    ll suf[n]={};
    suf[n-1] = (k-a[n-1]);
    for(ll i=(n-2);i>=0;i--)
    {
        suf[i] = suf[i+1]+(a[i+1]-a[i]);
    }
    ll ans = INF;
    forn(i,n)
    {
        ll y = pre[i];
        if((i+1)<n)
            y+=suf[i+1];
        ans = min(ans,y);
    }
    ans = min(ans,(pre[n-1]-a[0]));
    ans = min(ans,suf[0]);
    write(ans);
    return 0;
}

Measured memory_bytes: 4992