#include<bits/stdc++.h>
using namespace std;
//#define int long long
using ll = long long;
//using f80 = __float80;
#define rep(i,n) repi(i,0,n)
#define repi(i,a,b) for(int i=int(a);i<int(b);++i)
#define rrep(i,n) rrepi(i,n-1,0-1)
#define rrepi(i,a,b) for(int i=int(a);i>int(b);--i)
#define SORT(obj) sort((obj).begin(), (obj).end())
#define RSORT(obj) sort((obj).begin(), (obj).end(), greater<>())
#define ALL(obj) (obj).begin(),(obj).end()
#define UNIQUE(v) SORT(v); v.erase( unique(v.begin(), v.end()), v.end() );
#define show(v) rep(i,v.size()){cout<<v[i]<<" ";}cout<<endl;
#define MAX(x) *max_element(ALL(x))
#define MIN(x) *min_element(ALL(x))

//#define MOD 1000000007
#define EPS (1e-7)
#define INF (1e9)
#define PI (acos(-1))
#define SZ(x) ((int)(x).size())
#define SUM(v,i) accumulate(ALL(v),i)
#define nSUM(n) ((n)+1)*(n)/2　//1〜nまでの総和を求める式
//#define debug(a) cout<<a<<endl;
#define debug(a) cout<<a<<" ";
#define deg_to_rad(deg) (((deg)/360)*2*PI);
#define PB push_back
#define MP make_pair
#define rad_to_deg(rad) (((rad)/2/PI)*360);
using vi = vector<int>;
int dx[ 4 ] = { 1,0,-1,0 };
int dy[ 4 ] = { 0,1,0,-1 };
template<class T>bool chmax( T &a , const T &b ) { if ( a < b ) { a = b; return 1; } return 0; }
template<class T>bool chmin( T &a , const T &b ) { if ( b < a ) { a = b; return 1; } return 0; }
template<class T> inline void Yes( T condition ) { if ( condition ) cout << "Yes" << endl; else cout << "No" << endl; }
template<class T> void print( const T &value ) { cout << value << '\n'; }
struct aaa { aaa( ) { cin.tie( nullptr ); ios::sync_with_stdio( false ); cout << fixed << setprecision( 20 ); }; }aaa;
//template <typename... Args>void IN(Args& ... args) {cin >>args;IN(args...);return;} //まとめて入力　IN(a,b,c,d...)

int gcd( int a , int b ) { return b ? gcd( b , a % b ) : a; }//最大公約数
int lcm( int a , int b ) { return a * b / gcd( a , b ); }	//最小公倍数

bool IsPrime( int num ) {
	if ( num < 2 ) return false;
	else if ( num == 2 ) return true;
	else if ( num % 2 == 0 ) return false; // 偶数はあらかじめ除く

	double sqrtNum = sqrt( num );
	for ( int i = 3; i <= sqrtNum; i += 2 ) {
		if ( num % i == 0 ) {
			// 素数ではない
			return false;
		}
	}

	// 素数である
	return true;
}

// n個の数字の最小公倍数
int nlcm( vector<int> numbers ) {
	int res;
	res = numbers[ 0 ];
	for ( int i = 1; i < numbers.size( ); i++ ) {
		res = lcm( res , numbers[ i ] );
	}
	return res;
}

 // n個の数字の最大公約数
int ngcd( vector<int> a ) {
	int res;
	res = a[ 0 ];
	for ( int i = 1; i < a.size( ) && res != 1; i++ ) {
		res = gcd( a[ i ] , res );
	}
	return res;
}

int digsum( int n ) {
	int res = 0;
	while ( n > 0 ) {
		res += n % 10; //桁和
		// res++;       桁数
		n /= 10;
	}
	return res;
}

const int mod = 1000000007;
struct mint {
	ll x;
	mint( ll x = 0 ) :x( x %mod ) {}
	mint &operator+=( const mint a ) {
		if ( ( x += a.x ) >= mod ) x -= mod;
		return *this;
	}
	mint &operator-=( const mint a ) {
		if ( ( x += mod - a.x ) >= mod ) x -= mod;
		return *this;
	}
	mint &operator*=( const mint a ) {
		( x *= a.x ) %= mod;
		return *this;
	}
	mint operator+( const mint a ) const {
		mint res( *this );
		return res += a;
	}
	mint operator-( const mint a ) const {
		mint res( *this );
		return res -= a;
	}
	mint operator*( const mint a ) const {
		mint res( *this );
		return res *= a;
	}
	mint pow( ll t ) const {
		if ( !t ) return 1;
		mint a = pow( t >> 1 );
		//debug(a.x);

		a *= a;
		if ( t & 1 ) a *= *this;
		return a;
	}

	// for prime mod
	mint inv( ) const {
		return pow( mod - 2 );
	}
	mint &operator/=( const mint a ) {
		return ( *this ) *= a.inv( );
	}
	mint operator/( const mint a ) const {
		mint res( *this );
		return res /= a;
	}
};

mint ncr( ll n , ll a ) {
	mint x = 1 , y = 1;
	//rep(i, a) {
	for ( int i = 0; i < a; ++i ) {
		x *= n - i;
		y *= i + 1;
	}
	return x / y;
}

// a^n mod を計算する
long long modpow( long long a , long long n , long long Mod ) {
	long long res = 1;
	while ( n > 0 ) {
		if ( n & 1 ) res = res * a % Mod;
		a = a * a % Mod;
		n >>= 1;
	}
	return res;
}

//素因数分解
map<ll , ll> GetPrimeFactors( ll n ) {
	map<ll , ll> mp;
  // dived by 2, 3, 5, ...
	while ( n % 2 == 0 ) {
		++mp[ 2 ];
		n /= 2;
	}
	for ( int i = 3; i * i <= n; i += 2 ) {
		while ( n % i == 0 ) {
			++mp[ i ];
			n /= i;
		}
	}
	if ( n != 1 ) ++mp[ n ];
	return mp;
}

//約数全列挙
vector<int> enum_div( int n ) {
	vector<int> ret;
	for ( int i = 1; i * i <= n; ++i ) {
		if ( n % i == 0 ) {
			ret.push_back( i );
			if ( i != 1 && i * i != n ) {
				ret.push_back( n / i );
			}
		}
	}
	return ret;
}

//約数全列挙 set ver
set<ll> listDivisors( ll n ) {   // set版
	set<ll> divs;
	repi( i , 1 , ( ll )( sqrt( n ) + 1 ) ) {
	//FOR( i , 1 , ( ll )( sqrt( n ) + 1 ) ) {   // {1, n} を除く場合は2番目の引数を 2 にする
		if ( n % i == 0 ) {
			divs.insert( i );
			divs.insert( n / i );
		}
	}
	return divs;
}

//文字列中に存在する特定の文字の個数カウント
int stringcount( string s , char c ) { return count( s.cbegin( ) , s.cend( ) , c ); }

//int Factorial( int n ) {
//	int ans = 1;
//	while ( n > 1 ) {
//		ans *= n;
//		--n;
//	}
//	return ans;
//}
//
//int npr( int n , int r ) {
//	return Factorial( n ) / Factorial( n - r );
//}
//
//int ncr( int n , int r ) {
//	return npr( n , r ) / Factorial( r );
//}

/*#include <bits/stdc++.h>
using namespace std;
using ll=long long;
using ld=long double;
using ull=unsigned long long;
using uint=unsigned int;
using pcc=pair<char,char>;
using pii=pair<int,int>;
using pll=pair<ll,ll>;
using pdd=pair<double,double>;
using tuplis=pair<ll,pll>;
using tuplis2=pair<pll,ll>;
template<class T> using pq=priority_queue<T,vector<T>,greater<T>>;
const ll LINF=0x1fffffffffffffff;
const ll MINF=0x7fffffffffff;
const int INF=0x3fffffff;
const ll MOD=1000000007;
const ll MODD=998244353;
const ld DINF=numeric_limits<ld>::infinity();
const ld EPS=1e-9;
const ld PI=3.141592653589793238462643383279;
const vector<ll>four{0,1,0,-1,0};
#define _overload4(_1,_2,_3,_4,name,...) name
#define _overload3(_1,_2,_3,name,...) name
#define _rep1(n) for(ll i=0;i<n;++i)
#define _rep2(i,n) for(ll i=0;i<n;++i)
#define _rep3(i,a,b) for(ll i=a;i<b;++i)
#define _rep4(i,a,b,c) for(ll i=a;i<b;i+=c)
#define rep(...) _overload4(__VA_ARGS__,_rep4,_rep3,_rep2,_rep1)(__VA_ARGS__)
#define _rrep1(n) for(ll i=(n)-1;i>=0;i--)
#define _rrep2(i,n) for(ll i=(n)-1;i>=0;i--)
#define _rrep3(i,a,b) for(ll i=(b)-1;i>=(a);i--)
#define _rrep4(i,a,b,c) for(ll i=a+(b-a-1)/c*c;i>=a;i-=c)
#define rrep(...) _overload4(__VA_ARGS__,_rrep4,_rrep3,_rrep2,_rrep1)(__VA_ARGS__)
#define each(i,a) for(auto &i:a)
#define sum(...) accumulate(range(__VA_ARGS__),0LL)
#define dsum(...) accumulate(range(__VA_ARGS__),double(0))
#define _range(i) (i).begin(),(i).end()
#define _range2(i,k) (i).begin(),(i).begin()+k
#define _range3(i,a,b) (i).begin()+a,(i).begin()+b
#define range(...) _overload3(__VA_ARGS__,_range3,_range2,_range)(__VA_ARGS__)
#define _rrange(i) (i).rbegin(),(i).rend()
#define _rrange2(i,k) (i).rbegin(),(i).rbegin()+k
#define _rrange3(i,a,b) (i).rbegin()+a,(i).rbegin()+b
#define rrange(...) _overload3(__VA_ARGS__,_rrange3,_rrange2,_rrange)(__VA_ARGS__)
#define elif else if
#define unless(a) if(!(a))
#define mp make_pair
#define mt make_tuple
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)
#define vec(type,name,...) vector<type> name(__VA_ARGS__)
#define VEC(type,name,size) vector<type> name(size);in(name)
#define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define VV(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__));in(name)
#define vvv(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__)))
inline ll gcd(ll a, ll b){ while(b){ ll c = b; b = a % b; a = c; } return a; }
inline ll lcm(ll a, ll b){ if(!a || !b) return 0; return a * b / gcd(a, b); }
template<class T> inline T min(const vector<T> &v){ return *min_element(range(v)); }
inline char min(const string &v){ return *min_element(range(v)); }
template<class T> inline T max(const vector<T> &v){ return *max_element(range(v)); }
inline char max(const string &v){ return *max_element(range(v)); }
inline ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; }
inline ll modpow(ll a, ll b, ll p){ ll ans = 1; while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }
template<class T> inline bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } return 0; }
template<class T> inline bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } return 0; }
map<ll, ll> factor(ull x){ map<ll, ll> ans; for(ll i = 2; i * i <= x; i++) while(x % i == 0){ ans[i]++; x /= i; } if(x != 1) ans[x]++; return ans; }
set<ll> divisor(ull x){ set<ll> ans; for(ll i = 1; i * i <= x; i++) if(x % i == 0){ ans.insert(i); ans.insert(x / i); } return ans; }
template<class T> unordered_map<T, ll> press(vector<T> &a){ auto b = a; sort(range(b)); b.erase(unique(range(b)), b.end()); unordered_map<T,ll> ans; rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; }
template<class T> map<T, ll> press_map(vector<T> &a){ auto b = a; sort(range(b)); b.erase(unique(range(b)), b.end()); map<T,ll> ans; rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; }
inline int scan(){ return getchar(); }
inline void scan(int &a){ scanf("%d", &a); }
inline void scan(unsigned &a){ scanf("%u", &a); }
inline void scan(long &a){ scanf("%ld", &a); }
inline void scan(long long &a){ scanf("%lld", &a); }
inline void scan(unsigned long long &a){ scanf("%llu", &a); }
inline void scan(char &a){ cin >> a; }
inline void scan(float &a){ scanf("%f", &a); }
inline void scan(double &a){ scanf("%lf", &a); }
inline void scan(long double &a){ scanf("%Lf", &a); }
inline void scan(vector<bool> &vec){ for(unsigned i = 0; i < vec.size(); i++) { int a; scan(a); vec[i] = a; } }
inline void scan(char a[]){ scanf("%s", a); }
inline void scan(string &a){ cin >> a; }
template<class T> inline void scan(vector<T> &vec);
template<class T, size_t size> inline void scan(array<T, size> &vec);
template<class T, class L> inline void scan(pair<T, L> &p);
template<class T, size_t size> inline void scan(T (&vec)[size]);
template<class T> inline void scan(vector<T> &vec){ for(auto &i : vec) scan(i); }
template<class T> inline void scan(deque<T> &vec){ for(auto &i : vec) scan(i); }
template<class T, size_t size> inline void scan(array<T, size> &vec){ for(auto &i : vec) scan(i); }
template<class T, class L> inline void scan(pair<T, L> &p){ scan(p.first); scan(p.second); }
template<class T, size_t size> inline void scan(T (&vec)[size]){ for(auto &i : vec) scan(i); }
template<class T> inline void scan(T &a){ cin >> a; }
inline void in(){}
template <class Head, class... Tail> inline void in(Head &head, Tail&... tail){ scan(head); in(tail...); }
inline void print(){ putchar(' '); }
inline void print(const bool &a){ printf("%d", a); }
inline void print(const int &a){ printf("%d", a); }
inline void print(const unsigned &a){ printf("%u", a); }
inline void print(const long &a){ printf("%ld", a); }
inline void print(const long long &a){ printf("%lld", a); }
inline void print(const unsigned long long &a){ printf("%llu", a); }
inline void print(const char &a){ printf("%c", a); }
inline void print(const char a[]){ printf("%s", a); }
inline void print(const float &a){ printf("%.15f", a); }
inline void print(const double &a){ printf("%.15f", a); }
inline void print(const long double &a){ printf("%.15Lf", a); }
inline void print(const string &a){ for(auto&& i : a) print(i); }
template<class T> inline void print(const vector<T> &vec);
template<class T, size_t size> inline void print(const array<T, size> &vec);
template<class T, class L> inline void print(const pair<T, L> &p);
template<class T, size_t size> inline void print(const T (&vec)[size]);
template<class T> inline void print(const vector<T> &vec){ if(vec.empty()) return; print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } }
template<class T> inline void print(const deque<T> &vec){ if(vec.empty()) return; print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } }
template<class T, size_t size> inline void print(const array<T, size> &vec){ print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } }
template<class T, class L> inline void print(const pair<T, L> &p){ print(p.first); putchar(' '); print(p.second); }
template<class T, size_t size> inline void print(const T (&vec)[size]){ print(vec[0]); for(auto i = vec; ++i != end(vec); ){ putchar(' '); print(*i); } }
template<class T> inline void print(const T &a){ cout << a; }
inline int out(){ putchar('\n'); return 0; }
template<class T> inline int out(const T &t){ print(t); putchar('\n'); return 0; }
template<class Head, class... Tail> inline int out(const Head &head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; }
#ifdef DEBUG
inline void err(){ putchar('\n'); }
template<class T> inline void err(const T &t){ print(t); putchar('\n'); }
template<class Head, class... Tail> inline void err(const Head &head, const Tail&... tail){ print(head); putchar(' '); out(tail...); }
#else
template<class... T> inline void err(const T&...){}
#endif
inline int first(bool i = true){ return out(i?"first":"second"); }
inline int yes(bool i = true){ return out(i?"yes":"no"); }
inline int Yes(bool i = true){ return out(i?"Yes":"No"); }
inline int No(){ return out("No"); }
inline int YES(bool i = true){ return out(i?"YES":"NO"); }
inline int NO(){ return out("NO"); }
inline int Yay(bool i = true){ return out(i?"Yay!":":("); }
inline int possible(bool i = true){ return out(i?"possible":"impossible"); }
inline int Possible(bool i = true){ return out(i?"Possible":"Impossible"); }
inline int POSSIBLE(bool i = true){ return out(i?"POSSIBLE":"IMPOSSIBLE"); }
inline void Case(ll i){ printf("Case #%lld: ", i); }
 */

ll n , m , x , y , k , w , h , a , b , c;
string s , line;

void solve( ) {
	cin >> k >> n;
	vi v( n );
	x = 0;
	rep( i , n ) {
		cin >> y;
		v[ i ] = abs(x - y);
		x = y;
	}
	v.push_back( k-x + v[ 0 ] );
	//SORT( v );
	cout << k - MAX( v );
	//show( v );
}


signed main( ) {
	solve( );
	return 0;
}


Measured memory_bytes: 1792