#define DEBUG 1
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <cstring>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <utility>
#include <vector>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using vll = vector<ll>;
using vvll = vector<vll>;
using pll = pair<ll, ll>;
using vpll = vector<pll>;
using vvpll = vector<vpll>;
using tll = tuple<ll, ll, ll>;
using vtll = vector<tll>;
using vvtll = vector<vtll>;
#define all(v) (v).begin(), (v).end()
#define for1(i, n) for (ll i = 0; i < (n); i++)
#define for2(i, m, n) for (ll i = (m); i < (n); i++)
#define for3(i, m, n, d) for (ll i = (m); i < (n); i += (d))
#define rfor2(i, m, n) for (ll i = (m); i > (n); i--)
#define rfor3(i, m, n, d) for (ll i = (m); i > (n); i += (d))
#define PI 3.1415926535897932384626433832795028841971693993751L
#define INF 1111111111111111111LL
#define print(...) print_1(__VA_ARGS__)
#define in(...) in_1(__VA_ARGS__)
#if DEBUG
#define dump(...) dump_1(#__VA_ARGS__, __VA_ARGS__)
#define dumpa(...) dumpa_1(#__VA_ARGS__, __VA_ARGS__)
#else
#define dump(...)
#define dumpa(...)
#endif
template <typename Head>
void dump_1(const char* str, Head&& h)
{
    cerr << str << ": " << h << '\n';
}
template <typename Head, typename... Tail>
void dump_1(const char* str, Head&& h, Tail&&... t)
{
    while (*str != ',') {
        cerr << *str++;
    }
    cerr << ": " << h << ' ';
    dump_1(str + 1, t...);
}
template <typename T>
void dumpa_1(const char* str, const T v[], const ll size)
{
    while (*str != ',') {
        cerr << *str++;
    }
    cerr << ": ";
    for1 (i, size) {
        if (i != 0) {
            cerr << ' ';
        }
        cerr << v[i];
    }
    cerr << '\n';
}
template <typename T1, typename T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& v)
{
    os << v.first << ' ' << v.second;
    return os;
}
template <typename T1, typename T2, typename T3>
ostream& operator<<(ostream& os, const tuple<T1, T2, T3>& v)
{
    os << get<0>(v) << ' ' << get<1>(v) << ' ' << get<2>(v);
    return os;
}
template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v)
{
    for (auto 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)
{
    for (auto it = v.begin(); it != v.end(); it++) {
        if (it != v.begin()) {
            os << ' ';
        }
        os << *it;
    }
    return os;
}
template <typename T>
ostream& operator<<(ostream& os, const multiset<T>& v)
{
    for (auto it = v.begin(); it != v.end(); it++) {
        if (it != v.begin()) {
            os << ' ';
        }
        os << *it;
    }
    return os;
}
template <typename T1, typename T2>
ostream& operator<<(ostream& os, const map<T1, T2>& v)
{
    os << '{';
    for (auto it = v.begin(); it != v.end(); it++) {
        if (it != v.begin()) {
            os << ", ";
        }
        os << it->first << ':' << it->second;
    }
    os << '}';
    return os;
}
ll divup(ll nume, ll deno)
{
    assert(nume >= 0);
    assert(deno > 0);
    return (nume + deno - 1) / deno;
}
void Yes(void) { cout << "Yes\n"; }
void No(void) { cout << "No\n"; }
void YES(void) { cout << "YES\n"; }
void NO(void) { cout << "NO\n"; }
template <typename T>
bool chmax(T& a, const T& b)
{
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
template <typename T>
bool chmin(T& a, const T& b)
{
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <typename T>
void vin(vector<T>& v, ll len)
{
    for1 (i, len) {
        cin >> v[i];
    }
}
template <typename Head>
void in_1(Head& h)
{
    cin >> h;
}
template <typename Head, typename... Tail>
void in_1(Head& h, Tail&... t)
{
    cin >> h;
    in_1(t...);
}
template <typename Head>
void print_1(Head&& h)
{
    cout << h << '\n';
}
template <typename Head, typename... Tail>
void print_1(Head&& h, Tail&&... t)
{
    cout << h << ' ';
    print_1(t...);
}
//---------------------------------------------------------
void solve()
{
    ll K, N;
    in(K, N);
    ll ans = INF;
    vll A(N);
    vin(A, N);
    for1 (i, N - 1) {
        chmin(ans, K - (A[i + 1] - A[i]));
    }
    chmin(ans, K - (K - A[N - 1] + A[0]));
    print(ans);
}
//---------------------------------------------------------
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(16);
    cerr << fixed << setprecision(16);
    solve();
}


Measured memory_bytes: 1792