#pragma GCC target ("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#define _USE_MATH_DEFINES
#include<iostream>
#include<string>
#include<queue>
#include<cmath>
#include<map>
#include<set>
#include<list>
#include<iomanip>
#include<vector>
#include<random>
#include<functional>
#include<algorithm>
#include<stack>
#include<cstdio>
#include<cstring>
#include<bitset>
#include<unordered_map>
#include<climits>
#include<fstream>
#include<complex>
#include<time.h>
#include<cassert>
#include<functional>
#include<numeric>
#include<tuple>

using namespace std;
using ll = int_fast64_t;
using ld = long double;
#define int ll
#define all(a) (a).begin(),(a).end()
#define fs first
#define sc second
#define xx first
#define yy second.first
#define zz second.second
#define H pair<int, int>
#define P pair<int, pair<int, int>>
#define Q(i,j,k) mkp(i,mkp(j,k))
#define R pair<pair<int, int>, pair<int, int>>
#define S(i,j,k,l) mkp(mkp(i,j),mkp(k,l))
#define rep(i,n) for(int (i) = 0 ; (i) < (n) ; (i)++)
#define rng(i,s,n) for(int (i) = (s) ; (i) < (n) ; (i)++)
#define req(n,i) for(int (i) = (n) - 1 ; (i) >= 0 ; (i)--)
#define range(i,v) for(auto& (i) : v)
#define mkp make_pair
#define mem(x,k) memset(x,k,sizeof(x))
#define vec vector
#define pb emplace_back
#define lb lower_bound
#define ub upper_bound
#define crdcomp(b) sort(all((b)));(b).erase(unique(all((b))),(b).end())
#define getidx(b,i) lower_bound(all(b),(i))-b.begin()
#define ssp(i,n) (i==n-1?"\n":" ")
#define ctoi(c) (int)(c-'0')
#define itoc(c) (char)(c+'0')
#define itn int
#define pri_que priority_queue
#define pp(x,y) pb(H{x,y})
#define ppp(x,y,z) pb(Q(x,y,z))
#define pppp(x,y,z,w) pb(S(x,y,z,w))
#define cyes cout<<"Yes\n"
#define cno cout<<"No\n"
//#define endl "\n"
constexpr int mod = 1e9 + 7;
constexpr int Mod = 998244353;
constexpr int MXN = 500000 + 100;
constexpr ld EPS = 1e-10;
constexpr ll inf = 3 * 1e18;
constexpr int Inf = 15 * 1e8;
const vec<int>dx{ -1,1,0,0 }, dy{ 0,0,-1,1 };
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; }
ll read() { ll u, k = scanf("%lld", &u); return u; }
string reads() { string s; cin >> s; return s; }
H readh(bool g = 0) { H u; ll k = scanf("%lld %lld", &u.fs, &u.sc); if (g) u.fs--, u.sc--; return u; }
void printh(H t) { printf("%lld %lld\n", t.fs, t.sc); }
bool inarea(H t, int h, int w) { return 0 <= t.fs && t.fs < h && 0 <= t.sc && t.sc < w; }
ll gcd(ll i, ll j) { return j ? gcd(j, i % j) : i; }
ll mod_pow(ll x, ll n, ll p = mod) {
	ll res = 1;
	while (n > 0) {
		if (n & 1) res = res * x % p;
		x = x * x % p;
		n >>= 1;
	}
	return res;
}//x^n%p
ll bitcount(ll x) {
	int sum = 0; for (int i = 0; i < 60; i++)if ((1ll << i) & x) sum++;
	return sum;
}
/*constexpr int fn_ = 1000005;
ll fact_[fn_], comp_[fn_];
ll comb(ll x, ll y, ll Mod = mod) {
	if (!fact_[0]) {
		fact_[0] = 1; comp_[0] = 1;
		for (int i = 1; i < fn_; i++)
			fact_[i] = fact_[i - 1] * i % Mod;
		comp_[fn_ - 1] = mod_pow(fact_[fn_ - 1], Mod - 2, Mod);
		for (int i = fn_ - 2; i > 0; i--)
			comp_[i] = comp_[i + 1] * (i + 1) % Mod;
	}
	if (x < y) return 0;
	return fact_[x] * comp_[x - y] % Mod * comp_[y] % Mod;
}*/
//--------------------------------------------------------------
class FFT {
	struct Comp {
		ld real, img;
		Comp(ld a, ld b) :real(a), img(b) {}
		Comp operator+(Comp b) {
			return Comp(real + b.real, img + b.img);
		}
		Comp operator-(Comp b) {
			return Comp(real - b.real, img - b.img);
		}
		Comp operator*(Comp b) {
			return Comp(real * b.real - img * b.img, real * b.img + img * b.real);
		}
		void operator+=(Comp b) {
			real += b.real, img += b.img;
		}
		void operator-=(Comp b) {
			real -= b.real, img -= b.img;
		}
		void operator*=(Comp b) {
			Comp c = Comp(real * b.real - img * b.img, real * b.img + img * b.real);
			real = c.real; img = c.img;
		}
	};
	const ld PI = acos(-1);
	vec<Comp>dft(vec<Comp>A, int n, int sgn = 1) {
		if (n == 1) return A;
		vec<Comp>f0, f1;
		for (int i = 0; i < (n / 2); i++) {
			f0.push_back(A[i * 2 + 0]);
			f1.push_back(A[i * 2 + 1]);
		}
		f0 = dft(f0, n / 2, sgn), f1 = dft(f1, n / 2, sgn);
		Comp zeta = Comp(cos(2.0 * PI / n), sin(2.0 * PI / n) * sgn);
		Comp pow_zeta(1, 0);
		for (int i = 0; i < n; i++) {
			A[i] = f0[i % (n / 2)] + pow_zeta * f1[i % (n / 2)];
			pow_zeta *= zeta;
		}
		return A;
	}
	vec<Comp>inv_dft(vec<Comp>A, int n) {

	}
};
signed main() {
	int k, n;
	vec<int>a;
	cin >> k >> n;
	rep(i, n) a.pb(read());
	int mx = a[0] + k - a[n - 1];
	rep(i, n-1) {
		chmax(mx, a[i + 1] - a[i]);
	}
	cout << k - mx << endl;
}


Measured memory_bytes: 2420