#include <bits/stdc++.h>
// #include <iostream>
// #include <cstdio>
// #include <cstdlib>
// #include <algorithm>
// #include <cmath>
// #include <vector>
// #include <set>
// #include <map>
// #include <queue>
// #include <ctime>
// #include <cassert>
// #include <complex>
// #include <string>
// #include <cstring>
// #include <queue>
// #include <bitset>

using namespace std;

// #pragma GCC optimize("Ofast,no-stack-protector")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
// #pragma GCC optimize("unroll-loops")


#define ll              long long int
#define vi              vector< int >
#define vll             vector< ll >
#define pii             pair< int, int >
#define vpii            vector< pii >

#define sc              scanf
#define pf              printf
#define cspf(i)         pf("Case %d: ", i)
#define spc             pf(" ")
#define line            pf("\n")

#define ff              first
#define ss              second
#define mp              make_pair
#define pb              push_back
#define tp(v,j)         get<j>(v)
#define Log(b,x)        (log(x)/log(b))

#define FOR(i,x,y)      for(int i = int(x); i < int(y); i++)
#define ROF(i,x,y)      for(int i = int(x)-1; i >= int(y); i--)
#define clr(arr,x)      memset(arr, x, sizeof arr)
#define vout(v,sz)      for(int w=0;w<sz;w++){if(w) spc; cout<<v[w];}
#define all(v)          v.begin(), v.end()
#define rall(v)         v.rbegin(), v.rend()
#define unq(v)          sort(all(v)),(v).resize(unique(all(v))-v.begin())
#define fastIO          ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr)

#define sc1(x)          sc("%d",&x);
#define sc2(x,y)        sc("%d %d", &x, &y)
#define sc3(x,y,z)      sc("%d %d %d", &x, &y, &z)
#define scl1(x)         sc("%lld",&x);
#define scl2(x,y)       sc("%lld %lld", &x, &y)
#define scf1(x)         sc("%lf",&x);
#define scf2(x,y)       sc("%lf %lf", &x, &y)

#define pf1(x)          pf("%d",x);
#define pf2(x,y)        pf("%d %d", x, y)
#define pfl1(x)         pf("%lld",x);
#define pfl2(x,y)       pf("%lld %lld", x, y)
 
#define MOD             (int)(998244353)
#define MaxN            100005
#define inf             0x3f3f3f3f
#define PI              acos(-1.0)  // 3.1415926535897932
#define eps             1e-9

template <class T> inline T bigMod(T p,T e,T M){T ret=1; for(;e>0;e>>=1){ if(e&1) ret=(ret*p)%M; p=(p*p)%M;} return (T)ret;}
template <class T> inline T modInverse(T a,T M){return bigMod(a,M-2,M);}
template <class T> inline T gcd(T a,T b){if(b==0)return a;return gcd(b,a%b);}
template <class T> inline T lcm(T a,T b) {a=abs(a);b=abs(b); return (a/gcd(a,b))*b;}


int main()
{
    // #ifndef ONLINE_JUDGE
    //     clock_t tStart = clock();
    //     freopen("input.txt", "r", stdin);
    //     freopen("output.txt", "w", stdout);
    // #endif

    ll k; scl1(k);
    int n; sc1(n);
    ll a[n];
    FOR(i,0,n) scl1(a[i]);
    ll mn = min(k-((k-a[n-1]) + a[0]), k - (a[1]-a[0]));
    FOR(i,1,n-1){
        mn = min({mn, k - a[i] + a[i-1], k - a[i+1] + a[i]});
    }
    pfl1(mn); line;


    // #ifndef ONLINE_JUDGE
    //     fprintf(stderr, "\n>> Runtime: %.10fs\n", (double) (clock() - tStart) / CLOCKS_PER_SEC);
    // #endif
 
    return 0;
}

Measured memory_bytes: 1792