/*
* じょえチャンネル
* 高評価・チャンネル登録よろしくおねがいします！
* https://www.youtube.com/channel/UCRXsI3FL_kvaVL9zoolBfbQ
*/

#include <bits/stdc++.h>


#define f(i,n) for(int i=0;i<(n);i++)


#define inf (int)(3e18)
#define int long long
#define mod (int)(1000000007)

#define intt long long
#define itn long long
#define P pair<int,int>

#define rep(i,n) for(int i=0;i<n;i++)
#define REP(i,n) for(int i=1;i<=n;i++)

#define ALL(v) v.begin(),v.end()

using namespace std;

//Library
//モッドパウ
int modpow(int x, int y, int m = mod) {
    int res = 1;
    while (y) {
        if (y % 2) {
            res *= x;
            res %= m;
        }
        x = x * x % m;
        y /= 2;
    }
    return res;
}

int mypow(int x, int y) {
    int res = 1;
    while (y) {
        if (y % 2) {
            res *= x;
        }
        x = x * x;
        y /= 2;
    }
    return res;
}
//is the number (x) a prime number?
bool prime(int x) {
    for (int i = 2; i * i <= x; i++) {
        if (!(x % i)) {
            return false;
        }
    }
    return true;
}


//saidai-kouyakusuu
inline int gcd(int x, int y) {
    if (!y) {
        return x;
    }
    return gcd(y, x % y);
}


//number of keta
int keta(int x) {
    int ans = 0;
    while (x) {
        x /= 10;
        ans++;
    }
    return ans;
}

//sum of keta
int ketasum(int x) {
    int ans = 0;
    while (x) {
        ans += x % 10;
        x /= 10;
    }
    return ans;
}

inline int lcm(int x, int y) {
    int ans = x / gcd(x, y) * y;
    return ans;
}
int twobeki(int x) {
    int ans = 0;
    while (1) {
        if (!(x & 1)) {
            ans++;
            x /= 2;
        }
        else {
            break;
        }
    }
    return ans;
}


template <class T, class U>
inline bool chmax(T& lhs, const U& rhs) {
    if (lhs < rhs) {
        lhs = rhs;
        return 1;
    }
    return 0;
}
template <class T, class U>
inline bool chmin(T& lhs, const U& rhs) {
    if (lhs > rhs) {
        lhs = rhs;
        return 1;
    }
    return 0;
}
void Yes(){
    cout<<"Yes"<<endl;
}
void No(){
    cout<<"No"<<endl;
}
void YES(){
    cout<<"YES"<<endl;
}
void NO(){
    cout<<"NO"<<endl;
}


#define fin(i) scanf("%lld",&i)
#define fout(i) printf("%lld",i)
#define fendl printf("\n")
//Library-End

class modInt {
    int value, modulo;
public:
    modInt() : value(0), modulo(mod) { value = 0; }
    template<typename T>
    modInt(T value = 0, int modulo = mod) : value(value), modulo(modulo) {
        if (value < 0) {
            value = -value;
            value %= modulo;
            value = -value;
            value += modulo;
        }
        this->value = value % modulo;
    }
    inline operator int()const { return value; }
    inline modInt& operator+=(modInt x) {
        value += x.value;
        if (value >= modulo)value -= modulo;
        return *this;
    }
    inline modInt& operator++() {
        if (value == modulo - 1)value = 0;
        else value++;
        return *this;
    }
    inline modInt& operator-()const {
        return modInt(0) -= *this;
    }
    inline modInt& operator-=(modInt x) {
        value -= x.value;
        if (value < 0)value += modulo;
        return *this;
    }
    inline modInt& operator--() {
        if (value == 0)value = modulo - 1;
        else value--;
        return *this;
    }
    inline modInt& operator*=(modInt x) {
        value = value * x.value % modulo;
        return *this;
    }
    inline modInt& operator/=(modInt x) {
        return operator*=(x.inv());
    }
    inline modInt inv() {
        return modpow(*this, modulo - 2);
    }
    template<typename T> modInt operator+(T x) { return modInt(*this) += x; }
    template<typename T> modInt& operator+=(T x) { return operator+=(modInt(x, modulo)); }
    template<typename T> modInt operator-(T x) { return modInt(*this) -= x; }
    template<typename T> modInt& operator-=(T x) { return operator-=(modInt(x, modulo)); }
    template<typename T> modInt operator*(T x) { return modInt(*this) *= x; }
    template<typename T> modInt& operator*=(T x) { return operator*=(modInt(x, modulo)); }
    template<typename T> modInt operator/(T x) { return modInt(*this) /= x; }
    template<typename T> modInt& operator/=(T x) { return operator/=(modInt(x, modulo)); }
};
istream& operator>>(istream& ist, modInt& x) {
    int a;
    ist >> a;
    x = a;
    return ist;
}
#define vecin(v) for(int i=0;i<v.size();i++)scanf("%lld",&v[i]);
#define vecout(v) {printf("%lld",v[0]);for(int i=1;i<v.size();i++)printf(" %lld",v[i]);printf("\n");}

int k,n,a[200004],ans,s;

signed main(){
    cin>>k>>n;
    ;
    rep(i,n){
        fin(a[i]);
        if(i)ans+=a[i]-a[i-1];
        chmax(s, a[i]-a[i-1]);
    }
    ans+=k-a[n-1]+a[0];
    chmax(s, k-a[n-1]+a[0]);
    cout<<ans-s<<endl;
}






Measured memory_bytes: 1792