Problem:
Score : 300 points

Problem Statement

There is a circular pond with a perimeter of K meters, and N houses around them.

The i-th house is built at a distance of A_i meters from the northmost point of the pond, measured clockwise around the pond.

When traveling between these houses, you can only go around the pond.

Find the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.

Constraints

2 \leq K \leq 10^6

2 \leq N \leq 2 \times 10^5

0 \leq A_1 < ... < A_N < K

All values in input are integers.

Input

Input is given from Standard Input in the following format:

K N
A_1 A_2 ... A_N

Output

Print the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.

Sample Input 1

20 3
5 10 15

Sample Output 1

10

If you start at the 1-st house and go to the 2-nd and 3-rd houses in this order, the total distance traveled will be 10.

Sample Input 2

20 3
0 5 15

Sample Output 2

10

If you start at the 2-nd house and go to the 1-st and 3-rd houses in this order, the total distance traveled will be 10.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

#define NDEBUG
#include <cassert>


typedef long long ll;
typedef long double Double;
typedef unsigned long long ull;
typedef pair<int,int> ii;
typedef pair<ll,ll> llll;
typedef pair<double,double> dd;

typedef vector<int> vi;
typedef vector<vector<int>> vvi;
typedef vector<ii> vii;
typedef vector<vector<ii>> vvii;
typedef vector<ll> vll;
typedef vector<vector<ll>> vvll;
typedef vector<llll> vllll;
typedef vector<bool> vb;
typedef vector<string> vs;
typedef vector<double> vd;
typedef vector<long double> vD;

#define sz(a)  int((a).size())
#define pb  push_back
#define eb  emplace_back
#define FOR(var,from,to) for(int var=(from);var<=(to);++var)
#define rep(var,n)  for(int var=0;var<(n);++var)
#define rep1(var,n)  for(int var=1;var<=(n);++var)
#define repC2(vari,varj,n)  for(int vari=0;vari<(n)-1;++vari)for(int varj=vari+1;varj<(n);++varj)
#define repC3(vari,varj,vark,n)  for(int vari=0;vari<(n)-2;++vari)for(int varj=vari+1;varj<(n)-1;++varj)for(int vark=varj+1;vark<(n);++vark)
#define ALL(c)  (c).begin(),(c).end()
#define RALL(c)  (c).rbegin(),(c).rend()
#define tr(i,c)  for(auto i=(c).begin(); i!=(c).end(); ++i)
#define found(s,e)  ((s).find(e)!=(s).end())
#define mset(arr,val)  memset(arr,val,sizeof(arr))
#define mid(x,y) ((x)+((y)-(x))/2)
#define IN(x,a,b) ((a)<=(x)&&(x)<=(b))
#define cons make_pair
#define clamp(v,lo,hi) min(max(v,lo),hi)
#define ABS(x) max((x),-(x))

template<typename T1, typename T2> inline void amin(T1 & a, T2 const & b) { if (a>b) a=b; }
template<typename T1, typename T2> inline void amax(T1 & a, T2 const & b) { if (a<b) a=b; }
template<typename X, typename T> auto vectors(X x, T a) { return vector<T>(x, a); }
template<typename X, typename Y, typename Z, typename... Zs> auto vectors(X x, Y y, Z z, Zs... zs) { auto cont = vectors(y, z, zs...); return vector<decltype(cont)>(x, cont); }

inline ll square(ll x) { return x * x; }
inline ll gcd(ll a, ll b) { while(a) swap(a, b%=a); return b; }
inline ll lcm(ll a, ll b) { return a/gcd(a,b)*b; }
template <typename T>
inline T mod(T a, T b) { return ((a % b) + b) % b; }

template <typename T>
int find_left(vector<T>& v, T elem) {
    return (int)(upper_bound(v.begin(), v.end(), elem) - v.begin()) - 1;
}
template <typename T>
int find_right(vector<T>& v, T elem) {
    return (int)(lower_bound(v.begin(), v.end(), elem) - v.begin());
}

const ll MOD=1000000007LL;

inline ll ADD(ll x, ll y) { return (x+y) % MOD; }
inline ll SUB(ll x, ll y) { return (x-y+MOD) % MOD; }
inline ll MUL(ll x, ll y) { return x*y % MOD; }
inline ll POW(ll x, ll e) { ll v=1; for(; e; x=MUL(x,x), e>>=1) if (e&1) v = MUL(v,x); return v; }
inline ll INV(ll y) { /*assert(y%MOD!=0);*/ return POW(y, MOD-2); }
inline ll DIV(ll x, ll y) { return MUL(x, INV(y)); }

#define INTSPACE 12
char _buf[INTSPACE*1000000 + 3];

int loadint() {
    if (fgets(_buf, INTSPACE+3, stdin)==NULL) return 0;
    return atoi(_buf);
}

int loadvec(vector<int>& v, int N=-1) {
    if (N == 0) {
        v.clear();
        return 0;
    }
    if (N == -1) {
        N = loadint();
        if (N==0) return 0;
    }
    int bufsize = INTSPACE*N + 3;
    if (fgets(_buf, bufsize, stdin)==NULL) return 0;
    v.resize(N);

    int i=0;
    bool last = false;
    for (char *p=&_buf[0]; ;) {
        char *q = p;
        while (*q > ' ') ++q;
        if (*q == 0x0D || *q == 0x0A) last = true;
        *q = 0;
        v[i++] = atoi(p);
        if (last || i == N) break;
        p = q+1;
    }
    return i;
}
void read_cr() {
    fgets(_buf, 256, stdin);
}

void horizontal(vector<int>& v) {
    int L = v.size();
    for (int i=0; i<L; ++i) {
        printf("%d%c", v[i], (i==L-1)?'\n':' ');
    }
}
void horizontall(vector<long long>& v) {
    int L = v.size();
    for (int i=0; i<L; ++i) {
        printf("%lld%c", v[i], (i==L-1)?'\n':' ');
    }
}

int solve(int N, int K, vi& a) {
    vi a2(N*2);
    rep(i,N) {
        a2[i] = a[i];
        a2[N+i] = K + a[i];
    }
    int best = K;
    rep(i,N){
        amin(best, a2[i+N-1] - a2[i]);
    }
    return best;
}

int main() {
    int N, K; scanf("%d %d%*c", &K, &N);
    vi a(N); loadvec(a,N);
    cout << solve(N,K,a) << endl;
    return 0;
}