#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <cmath>
#include <queue>
#include <climits>
#include <set>
#include <map>
#include <stack>
#include <iomanip>
#include <tuple>
#include <cstdio>
#define ll long long
#define rep(i,s,n) for(ll i = (ll)(s); i < (ll)(n); i++)
#define all(a) (a).begin(),a.end()
#define mod 1000000007
#define P pair<ll,ll>
#define V vector<ll>
using namespace std;
using graph =vector<vector<ll>>;
const ll MAX = 510000;
const ll MOD = 1000000007;

ll fac[MAX], finv[MAX], inv[MAX];

// テーブルを作る前処理
void cominit() {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (ll i = 2; i < MAX; i++){
        fac[i] = fac[i - 1] * i % MOD;
        inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
        finv[i] = finv[i - 1] * inv[i] % MOD;
    }
}

// 二項係数計算nCk
ll com(ll n, ll k){
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

// 二項係数計算nPk
ll per(ll n, ll k){
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return fac[n] * (finv[n-k] % MOD) % MOD;
}

// mod. m での a の逆元 a^{-1} を計算する
ll modinv(ll a, ll m) {
    ll b = m, u = 1, v = 0;
    while (b) {
        ll t = a / b;
        a -= t * b; swap(a, b);
        u -= t * v; swap(u, v);
    }
    u %= m;
    if (u < 0) u += m;
    return u;
}

/* ユークリッドの互除法 最大公約数*/
ll gcd(ll a, ll b) {
	return b ? gcd(b,a%b) : a;
}



/*最小公倍数*/

ll lcm(ll a,ll b){
	return a/gcd(a,b)*b;
}


/*二点間の距離*/
double dist(pair<double,double> a,pair<double,double> b){
	return sqrt(pow((a.first - b.first) ,2) + pow((a.second - b.second),2));
}

//繰り返し自乗法
double ism(double aa,ll p){
    double ap=aa;
    double ans=1;
    while(p>0){
        //cout<<"p="<<p<<",ap="<<ap<<endl;
        if(p&1){//奇数が真
            ans*=ap;
        }
        p/=2;
        ap=ap*ap;
    }
    return ans;

}
//繰り返し自乗法(アマリトリバージョン)
ll ismm(ll aa,ll p,ll m){
    ll ap=aa;
    ll ans=1;
    while(p>0){
        //cout<<"p="<<p<<",ap="<<ap<<endl;
        if(p&1){//奇数が真
            ans=(ans*ap)%m;    
        }
        p/=2;              
        ap=(ap*ap)%m;
    }
    return ans;

}
/*
ll solve(ll i,ll m,vector<ll>t,ll n){
    if(m==0){
        return 1;
    }
    if(i>=n){
        return 0;
    }
    
    
    cout<<i+1<<" "<<m<<endl;
    cout<<i+1<<" "<<m-t[i]<<endl;
    ll res=solve(i+1,m,t,n)||solve(i+1,m-t[i],t,n);
    return res;
}
*/

struct UnionFind {
    vector<ll> par;
    
    UnionFind(ll n) : par(n, -1) { }

    ll root(ll x) {
        if (par[x] < 0) return x;
        else return par[x] = root(par[x]);
    }
    
    bool issame(ll x, ll y) {
        return root(x) == root(y);
    }
    
    bool merge(ll x, ll y) {
        x = root(x); y = root(y);
        if (x == y) return false;
        if (par[x] > par[y]) swap(x, y); // merge technique
        par[x] += par[y];
        par[y] = x;
        return true;
    }
    ll size(ll x) {
        return -par[root(x)];
    }
};

using pint = pair<ll,ll>;
//小数点12桁
struct all_init
{
    all_init()
    {
        cout << fixed << setprecision(12);
    }
} All_init;


int main()
{
    ll k,n;
    cin>>k>>n;
    vector<ll>a(n);
    rep(i,0,n){
        cin>>a[i];
        a[i]=a[i]%k;
        /*
        if(a[i]==0){
            a[i]=k;
            cout<<a[i]<<endl;
        }
        */
    }
    sort(all(a));
    ll t=LLONG_MIN;
    rep(i,0,n-1){
        //cout<<a[i+1]<<endl;
        t=max(t,abs(a[i]-a[i+1]));
        //cout<<t<<endl;
    }
    /*if(a[0]==0){
        a[0]=k;
            //cout<<a[i]<<endl;
    }
    */
    ll x=abs(a[n-1]-k)+a[0];
    t=max(t,x);
    
    cout<<k-t<<endl;
    

    
    
}


Measured memory_bytes: 1792