// 
// じょえチャンネル
// 高評価・チャンネル登録よろしくお願いします！
// https://www.youtube.com/watch?v=gPFr7q7eLL8
//
#include <stdio.h>
#include <cstdio>
#include <iostream>
#include <iomanip>
#include <string>
#include <algorithm>
#include <math.h>
#include <vector>
#include <stack>
#include <queue>
#include <deque>     
#include<map>
#include <set>
using namespace std;
#define int long long
#define ll long long
#define ld long double
#define rep(i,n) for(ll i=0;i<n;++i)
#define Rep(i,n) for(ll i=1;i<=n;++i)
#define loop(i,m,n) for(ll i=m;i<n;++i)
#define rev(i,n) for(ll i=n-1;i>=0;--i)
#define ggr getchar(); getchar();return 0;
#define pie 3.141592653589793238462643383279
#define elif else if
#define P pair<ll,ll>
#define prique priority_queue<ll>
#define all(a)  (a).begin(),(a).end()
const int mod = 1000000007;
const int mod2 = 998244353;
const int inf = 1 << 30;
const int MOD = 1e9 + 7;
long long fac[510000], finv[510000], inv[510000];
long long MAX = 510000;
bool COMinited = false;
long long COM(int n, int k) {
	if (COMinited == false) {
		fac[0] = fac[1] = 1;
		finv[0] = finv[1] = 1;
		inv[1] = 1;
		for (int i = 2; i < MAX; i++) {
			fac[i] = fac[i - 1] * i % MOD;
			inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
			finv[i] = finv[i - 1] * inv[i] % MOD;
		}
		COMinited = true;
	}
	if (n < k) return 0;
	if (n < 0 || k < 0) return 0;
	return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}
struct mint {
	ll x;
	mint(ll x = 0) :x((x% mod + mod) % mod) {}
	mint operator-() const { return mint(-x); }
	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);
		a *= a;
		if (t & 1) a *= *this;
		return a;
	}
	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;
	}
};
int bin(int bina) {
	int ans = 0;
	for (int i = 0; bina > 0; i++)
	{
		ans = ans + (bina % 2) * pow(10, i);
		bina = bina / 2;
	}
	return ans;
}
bool prime(int n) {
	for (ll i = 2; i <= sqrt(n); i++) {
		if (n % i == 0)return false;
	}
	return n != 1;
}
int gcd(int x, int y) {
	if (y == 0)return x;
	return gcd(y, x % y);
}
int lcm(int x, int y) {
	return x * y / gcd(x, y);
}
int kai(int x, int y) {
	int res = 1;
	for (int i = x - y + 1; i <= x; i++) {
		res *= i; res %= mod;
	}
	return res;
}
int mod_pow(int x, int y, int m) {
	int res = 1;
	while (y > 0) {
		if (y & 1) {
			res = res * x % m;
		}
		x = x * x % m;
		y >>= 1;
	}
	return res;
}

int per(int n, int r) {
	r = n - r;
	int sum = 1;
	int i;
	for (i = n; i >= r + 1; i--)sum *= i;
	return sum;
}
struct UnionFind {
	vector<int> par;

	UnionFind(int n) : par(n, -1) { }

	int root(int x) {
		if (par[x] < 0) return x;
		else return par[x] = root(par[x]);
	}

	bool issame(int x, int y) {
		return root(x) == root(y);
	}

	bool merge(int x, int y) {
		x = root(x); y = root(y);
		if (x == y) return false;
		if (par[x] > par[y]) swap(x, y);
		par[x] += par[y];
		par[y] = x;
		return true;
	}

	int size(int x) {
		return -par[root(x)];
	}
};
#define F first
#define S second
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
//cout << fixed << setprecision(10) << num << endl;
int a[200020], b[200020];
signed main() {
	int k, n;
	cin >> k >> n;
	rep(i, n) {
		cin >> a[i];
	}
	loop(i,1,n){
		b[i] = a[i] - a[i - 1];
	}
	b[0] = a[0] + k - a[n - 1];
	sort(b, b + n);
	cout << k - b[n-1] << endl;
}


Measured memory_bytes: 4352