#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>

#define ll long long
#define ull unsigned long long
#define pii pair<int,int>
#define xx first
#define yy second
#define sci(n) scanf("%d",&n)
#define scii(n,m) scanf("%d%d",&n,&m)
#define sciii(n,m,w) scanf("%d%d%d",&n,&m,&w)
#define scl(n) scanf("%lld",&n)
#define scll(n,m) scanf("%lld%lld",&n,&m)
#define sclll(n,m,w) scanf("%lld%lld%lld",&n,&m,&w)
#define pf(a)   printf("%d\n",a)
#define CASE(a) printf("Case %d: ",a)
#define dbg(i) printf("yo %d\n", i)
#define endl '\n'
#define READ  freopen("input.txt","r",stdin)
#define WRITE freopen("output.txt","w",stdout);
#define pi acos(-1)
#define mem(a,b) memset(a,b,sizeof(a))
#define SQR(a) (a)*(a)
#define all(v) v.begin(),v.end()
#define pb push_back
#define pri priority_queue<int>
#define rev_pri priority_queue<int,vector<int>,greater<int> >
#define IOS ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define mod 1000000007
#define inf INT_MAX
#define eps 1e-9

using namespace __gnu_pbds;
using namespace std;

//int dx[] = {0,1,0,-1,1,1,-1,-1};
//int dy[] = {1,0,-1,0,1,-1,-1,1};

//ll ncr(ll n,ll r){if(n==r)return 1;if(r==1)return n;if(dp[n][r]!=-1)return dp[n][r];return dp[n][r]=ncr(n-1,r)+ncr(n-1,r-1);}

// bit manipulations

//bool checkbit(int mask,int bit){return mask & (1<<bit);}
//int setbit(int mask,int bit){ return mask  (1<<bit) ; }
//int clearbit(int mask,int bit){return mask & ~(1<<bit);}
//int togglebit(int mask,int bit){return mask ^ (1<<bit);}

template <typename T> T BigMod (T b,T p,T m){if (p == 0) return 1;if (p%2 == 0){T s = BigMod(b,p/2,m);return ((s%m)*(s%m))%m;}return ((b%m)*(BigMod(b,p-1,m)%m))%m;}
template <typename T> T ModInv (T b,T m){return BigMod(b,m-2,m);}
template <typename T> T in(){char ch;T n = 0;bool ng = false;while (1){ch = getchar();if (ch == '-'){ng = true;ch = getchar();break;}if (ch>='0' && ch<='9')     break;}while (1){n = n*10 + (ch - '0');ch = getchar();if (ch<'0' || ch>'9')   break;}return (ng?-n:n);}
template <typename T> T POW(T B,T P){ if(P==0) return 1; if(P&1) return B*POW(B,P-1);  else return SQR(POW(B,P/2));}
template <typename T> T Bigmod(T b,T p,T m){ if(p==0) return 1; else if (!(p&1)) return SQR(Bigmod(b,p/2,m)) % m;else return ((b % m) * Bigmod(b,p-1,m)) % m;}
template <typename T> T Dis(T x1,T y1,T x2, T y2){return sqrt( SQR(x1-x2) + SQR(y1-y2) );}
template <typename T> T Angle(T x1,T y1,T x2, T y2){ return atan( double(y1-y2) / double(x1-x2));}
template <typename T> T DIFF(T a,T b) { T d = a-b;if(d<0)return -d;else return d;}
template <typename T> T ABS(T a) {if(a<0)return -a;else return a;}
template <typename T> T gcd(T a,T b){if(a<0)return gcd(-a,b);if(b<0)return gcd(a,-b);return (b==0)?a:gcd(b,a%b);}
template <typename T> T lcm(T a,T b) {if(a<0)return lcm(-a,b);if(b<0)return lcm(a,-b);return a*(b/gcd(a,b));}
template <typename T> T euclide(T a,T b,T &x,T &y) {if(a<0){T d=euclide(-a,b,x,y);x=-x;return d;}   if(b<0){T d=euclide(a,-b,x,y);y=-y;return d;}   if(b==0){x=1;y=0;return a;}else{T d=euclide(b,a%b,x,y);T t=x;x=y;y=t-(a/b)*y;return d;}}
template <typename T> void ia (T a[],int n){for (int i=0; i<n; i++) cin >> a[i];}
template <typename T> void pa (T a[],int n){for (int i=0; i<n-1; i++) cout << a[i] << " ";cout << a[n-1] << endl;}
template <typename T> ll isLeft(T a,T b,T c) { return (a.x-b.x)*(b.y-c.y)-(b.x-c.x)*(a.y-b.y);}

template<typename T>
using ordered_set=tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;

///********************************MY CODE STARTS HERE********************************///


#define mxn 100005




int main(){
       //IOS;

      ll k , n;
      cin >> k >> n;
      ll tot = 0;
      ll mn = 0;
      vector<ll> arr(n + 1);
      for(int i = 1;i <= n;i++){
        cin >> arr[i];

      }

      arr[0] = k - arr[n] + arr[1] + arr[1];


      for(int i = 1;i <= n;i++){
        mn = max(mn , abs(arr[i] - arr[i - 1]));
        tot += abs(arr[i] - arr[i - 1]);
      }

      cout << tot - mn << endl;
















return 0;}




Measured memory_bytes: 1792