#include<bits/stdc++.h>
#pragma GCC optimize("Ofast")
using namespace std;
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
typedef long long ll;
const ll MOD = 1e9+7;
#define rep(i,n) for(int i=0, i##_len=(n); i<i##_len; ++i)
#define REP(i,num,n) for(int i=num, i##_len=(n); i<i##_len; ++i)
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
template<class T> inline void add(T &a, T b){a = ((a+b) % MOD + MOD) % MOD;};
#define print(x) (cout << (x) << endl)
#define pb push_back
#define mp make_pair
#define sz(x) int(x.size())
template<class T> inline void Yes(T condition){ if(condition) cout << "Yes" << endl; else cout << "No" << endl; }
template<class itr> void cins(itr first, itr last){ for(auto i = first; i != last; i++){ cin >> (*i); } }
template<class itr> void array_output(itr start, itr goal){ string ans; for(auto i = start; i != goal; i++) ans += to_string(*i) + " "; if(!ans.empty()) ans.pop_back(); cout << ans << endl; }
#define fs first
#define sc second


const int INF = 1e9;
const ll LLINF = 1e16;

template<typename T>
vector<T> make_v(size_t a){return vector<T>(a);}
 
template<typename T,typename... Ts>
auto make_v(size_t a,Ts... ts){
  return vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...));
}
 
template<typename T,typename U,typename... V>
typename enable_if<is_same<T, U>::value!=0>::type
fill_v(U &u,const V... v){u=U(v...);}
 
template<typename T,typename U,typename... V>
typename enable_if<is_same<T, U>::value==0>::type
fill_v(U &u,const V... v){
  for(auto &e:u) fill_v<T>(e,v...);
}
 
template<typename T>
T gcd(T a,T b){return b?gcd(b,a%b):a;}

template<typename T>
T ngcd(vector<T> a){
    T res;
    res = a[0];
    for(int i = 1; i < a.size() && res != 1; i++) {
        res = gcd(a[i], res);
    }
    return res;
}
 
template<typename T>
T lcm(T a, T b) {
    return a / gcd(a, b) * b;
}

template<typename T>
T nlcm(vector<T> numbers) {
    T res;
    res = numbers[0];
    for (int i = 1; i < numbers.size(); i++) {
        res = lcm(res, numbers[i]);
    }
    return res;
}


// 素数判定
template<typename T>
bool isPrime(T x){
    T i;
    if(x < 2)return 0;
    else if(x == 2) return 1;
    if(x%2 == 0) return 0;
    for(i = 3; i*i <= x; i += 2) if(x%i == 0) return 0;
    return 1;
}

// 桁和
template<typename T>
T digsum(T n) {
    T res = 0;
    while(n > 0) {
        res += n%10;
        n /= 10;
    }
    return res;
}

// 回文判定
bool kai (string s) {
    string t{s};
    reverse(begin(t), end(t));
    return s == t;
};

// 指定した文字cが文字列に何文字入ってるか
ll stringcount(string s, char c) {
    return count(s.cbegin(), s.cend(), c);
}



// 割り算の切り上げ処理
template<typename T>
T rp(T a, T b) {
  return (a + b - 1) / b;
}


using pint = pair<int, int>;
using pll = pair<ll, ll>;


int main(void)
{
    cout.tie(0);
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    ll k,n;
    cin >> k >> n;
    vector<ll> a(n);
    vector<ll> ky;
    rep(i,n) cin >> a[i];
    rep(i, n){
        if(i != n - 1){
            ky.pb(a[i + 1] - a[i]);
        } else {
            ll tmp = k - a[i];
            tmp += a[0];
            ky.pb(tmp);
        }
    }
    sort(all(ky));
    ll ans = 0;
    rep(i, sz(ky) - 1){
        ans += ky[i];
    }
    print(ans);


}

//int n;
//cin >> n;
//vector<int> test(n);
//cins(all(test));
//array_output(all(test));
// Yes(true);

Measured memory_bytes: 3956