/// __Macro's__
#include <bits/stdc++.h>
using namespace std;
#define ll                   long long
#define II                   pair<int,int>
#define III                  pair<int, II>
#define VI                   vector<int>
#define VII                  vector<II>
#define VIII                 vector<III>
#define VVI                  vector<vector<int> >
#define VVII                 vector<vector<II> >
#define fr                   first
#define sc                   second
#define mkpr                 make_pair
#define PQ                   priority_queue
#define pb                   push_back
#define eb                   emplace_back
#define all(v)               v.begin(), v.end()
#define LINE                 putc('\n', stdout)
#define SPACE                putc(' ' , stdout)
#define TAB                  putc('\t', stdout)
#define fillarr(arr, val)    fill((int*)arr, (int*)arr+(sizeof(arr)/sizeof(int)), val)
#define Log2(x)              (31^__builtin_clz(x))
#define inf64                ((ll)1e17)
#define inf                  1000000007
// #define MOD                  1000000007 
#define getint ReadInt()
const char IO_MODE = 3; // in-->00<--out (MSB-->LSB) | 0: Norm, 1: Fast 
inline ll ReadInt(){ll x=0,s=1;char c=getchar();while(c<'0'||c>'9'){if(c=='-')s=-1;c=getchar();}while(c>='0'&&c<='9'){x=x*10+c-'0';
c=getchar();}return s*x;}inline void WriteInt(ll x){char c[20];if(!x){putchar('0');return;}if(x<0)putchar('-'),x=-x;int i=0;while(x>0)
c[++i]=x%10,x/=10;while(i)putchar(c[i--]+48);}template <typename T>inline void out(T x){if(IO_MODE&1)WriteInt(x);else if(typeid(x)==typeid(int))
printf("%i", x);else printf("%lld", (ll)x);}template<typename T, typename... Args>inline void out(T x,Args...args){out(x);SPACE;out(args...);}
template <typename T>inline void in(T &x){if(IO_MODE&2) x=ReadInt();else if(typeid(x)==typeid(int))scanf("%i",&x);else if(typeid(x)==typeid(ll))
scanf("%lld",&x);}template<typename T, typename... Args>inline void in(T &x,Args&...args){in(x);in(args...);}
int aa,bb,cc,dd,ee,ff,gg,hh,ii,jj,kk,mm,nn,oo,pp,qq,rr,ss,tt,uu,vv,ww,xx,yy,zz;
int tc;
///
/// ---------------------------------------------- (Debug) -----------------------------------------------
#define dbg debug()
#define sim template < class c
#define ris return * this
#define dor > debug & operator <<
#define eni(x) sim > typename enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge { c b, e; }; sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c* x) -> decltype(cerr << *x, 0); sim > char dud(...);
struct debug {
#ifdef LOCAL
~debug() { cerr << endl; }
eni(!=) cerr << boolalpha << i; ris; }
eni(==) ris << range(begin(i), end(i));}
sim, class b dor(pair < b, c > d) {ris << "(" << d.first << ", " << d.second << ")";}
sim dor(rge<c> d) {*this << "["; for (auto it = d.b; it != d.e; ++it) *this << ", " + 2 * (it == d.b) << *it; ris << "]";}
#else
sim dor(const c&) { ris; }
#endif
};
#define var(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
/// ------------------------------------------------------------------------------------------------------

#ifdef LOCAL
  #define nax 10000
  #define qax 1000
#else
  #define nax 200100
  #define qax 300100
#endif


int n,k;
int A[nax];
int32_t main()
{
  in(n, k);
  for(int i=0 ; i<k ; i++) in(A[i]);
  int pre = k-1;
  int ans = A[k-1] - A[0];
  int last = ans;
  for(int i=1 ; i<k ; i++)
  {
    int res = last - abs(A[i] - A[i-1]);
    if(pre == k-1) res += n - A[pre] + A[0];
    else res += A[pre+1] - A[pre];

    pre = (pre+1)%k;
    last = res;
    // cout << res << endl;
    ans = min(ans, res);
  }
  cout << ans << endl;
}

Measured memory_bytes: 1024