/*      ###########################
        #  Author : Pranay Garg   #
        #  College : SGSITS       #
        ###########################
*/      
# include   <bits/stdc++.h>
# define    ll                  long long int
# define    ironman             ios_base::sync_with_stdio(false);cin.tie(NULL);
# define    MOD                 1000000007 
# define    endl                '\n'
# define    INF                 0x7fffffff
# define    PI                  3.14159265358979323846
# define    mp                  make_pair
# define    fi                  first
# define    se                  second
# define    all(a)              a.begin(), a.end()
# define    allr(a)             a.rbegin(), a.rend()
# define    alla(a,n)           a,a+n
# define    debug1(x)           cout<<#x<<" "<<x<<endl;
# define    debug2(x,y)         cout<<#x<<" "<<x<<" "<<#y<<" "<<y<<endl;
# define    debug3(x,y,z)       cout<<#x<<" "<<x<<" "<<#y<<" "<<y<<" "<<#z<<" "<<z<<endl;
# define    debug4(x,y,z,w)     cout<<#x<<" "<<x<<" "<<#y<<" "<<y<<" "<<#z<<" "<<z<<" "<<#w <<" "<<w<<endl;
# define    debug5(x,y,z,w,v)   cout<<#x<<" "<<x<<" "<<#y<<" "<<y<<" "<<#z<<" "<<z<<" "<<#w <<" "<<w<<" "<<#v <<" "<<v<<endl;
# define    debug6(x,y,z,w,a,b) cout<<#x<<" "<<x<<" "<<#y<<" "<<y<<" "<<#z<<" "<<z<<" "<<#w <<" "<<w<<" "<<#a<<" "<<a<<" "<<#b<<b<<endl;
# define    pb                  push_back

using namespace std;

template<class T> T max(T a, T b, T c) {
    return max(a, max(b, c));
}
template<class T> T min(T a, T b, T c) {
    return min(a, min(b, c));
}

void fastio()
{
    ironman
    #ifndef ONLINE_JUDGE
        freopen("input.txt", "r", stdin);
        freopen("output.txt", "w", stdout);
        freopen("error.txt","w",stderr);
    #endif
}

bool prime[10000005];
void SieveOfEratosthenes(ll n)//O(nloglogn) 
{  
    memset(prime, true, sizeof(prime)); 
  
    for (ll p=2; p*p<=n; p++) 
    { 
        if (prime[p] == true) 
        { 
            for (ll i=p*p; i<=n; i += p) 
                prime[i] = false; 
        } 
    } 
}  
bool isPrime(ll n)//O(sqrt(n))
{
    if(n<2)
        return false;
    for(ll i=2;i*i<=n;i++)
        if(n%i==0)
            return false;
    return true;
}
std::vector<ll> generatePrimeFactors(ll n)
{
    std::vector<ll> prime;
    for(ll i=2;i*i<=n;i++)
    {
        if(n%i==0)
        {
            prime.pb(i);
            while(n%i==0)
                n=n/i;
        }   
    }
    if(n!=1)
        prime.pb(n);
    return prime;
}
std::vector<ll> generateFactors(ll n)
{
    std::vector<ll> fact;
    for(ll i=2;i*i<=n;i++)
    {
        if(n%i==0)
        {
            fact.pb(i);
            if(n/i!=i)
                fact.pb(n/i);
            //24 - 1,2,3,4,6,8,12
        }
    }
    fact.pb(1);
    if(n!=1)
        fact.pb(n);
    sort(fact.begin(),fact.end());
    return fact;
}

ll extendedGCD(ll a,ll b,ll &x,ll &y)
{
    //produces correct results for negative integers as well
    if(a==0)
    {
        x=0;
        y=1;
        return b;
    }
    ll x1,y1,d;
    d = extendedGCD(b%a,a,x1,y1);
    x = y1-(b/a)*x1;
    y=x1;
    return d;
}
ll gcd(ll a,ll b)//O(log min(a,b))
{
    /*
    recursive implementation below
    if(!b) return a;
    return gcd(b,a%b);
    */

    //non-recursive implementation below
    while(b)
    {
        a%=b;
        swap(a,b);
    }
    return a;
}

ll multiply(ll a,ll b,ll m);
ll singlemod(ll a,ll m);
ll modpow(ll x,ll n,ll m)//O(logn)// used for calculating (x^n)%m
{
    if(n==0)
        return 1;
    ll res = 1;
    while(n)
    {
        if(n%2)
            res = multiply(res,x,m);
        x = multiply(x,x,m);
        n = n>>1;
    }
    return singlemod(res,m);
}
ll modinverse(ll x,ll m)//O(logn)
{
    return modpow(x,m-2,m);
}
ll add(ll a,ll b,ll m)
{
    return (((a%m)+(b%m))%m);
}
ll substract(ll a,ll b,ll m)
{
    if(a<b)
        swap(a,b);
    return (((a%m)-(b%m)+m)%m);
}
ll multiply(ll a,ll b,ll m)
{
    return (((a%m)*(b%m))%m);
}
ll divide(ll a,ll b,ll m)
{
    ll temp = modinverse(b,m);
    return multiply(a,temp,m);
}
ll singlemod(ll a,ll m)
{
    return (a%m);
}
ll eulerstotientfunction(ll n)//O(sqrt(n))
{
    ll ans = n;
    for(ll i=2;i*i<=n;i++)
    {
        if(n%i==0)
        {
            while(n%i==0)
                n = n/i;
            ans -= ans/i;
        }
    }
    if(n>1)
        ans -= ans/n;
    return ans;
}

ll ncr(ll n,ll k,ll m)
{
    if(k>n) return 0;
    ll res = 1;
    k = min(k,n-k);
    for(ll i=1;i<=k;i++)
    {
        res = multiply(res,n-i+1,m);
        res = divide(res,i,m);
        // res *= (n-i+1);
        // res/=i;
    }
    return singlemod(res,m);
}
ll kadaneAlgo(const std::vector<ll> &arr)
{
    ll size = arr.size();
    ll currmax=arr[0],maxsofar=arr[0];
    for(ll i=1;i<size;i++)
    {
        //debug2(currmax,maxsofar);
        currmax = max(arr[i],currmax+arr[i]);
        maxsofar = max(maxsofar,currmax);
    }
    return maxsofar;
}
ll getDigitSum(ll n)
{
    ll co = 0;
    while(n>0)
    {
        co+=n%10;
        n = n/10;
    }
    return co;
}

template<class T>
void printVector(const std::vector<T> arr)
{
    for(auto i:arr)
        cout << i << " ";
    cout << endl;
}
template<class T>
void printArray(T arr[],ll n)
{
    for(ll i=0;i<n;i++)
        cout << arr[i] << " ";
    cout << endl;
}

//---------------TEMPLATE ABOVE--------------//
int main()
{
    //fastio();
    ll t=1;
    //cin >> t;
    // ll cases = t;
    while(t--)
    {  
        ll k,n;
        cin >> k >> n;
        std::vector<ll> arr(n);
        for(ll i=0;i<n;i++)
            cin >> arr[i];
        ll ans = INF;
        for(ll i=0;i<n;i++)
        {
            if(i==0)
            {
                ans = min(ans,arr[n-1]-arr[i],k-arr[i]);
            }
            else
            {
                ans = min(ans,arr[i-1]+k-arr[i]);
                if(i+1<n)
                {
                    ans = min(ans,arr[i]+k-arr[i+1]);
                }
                else
                    ans = min(ans,arr[i]-arr[0]);
            }
        }
        cout << ans << endl;

        // cout << "Case " << cases-t << ": " << endl;
    }
}

Measured memory_bytes: 1792