#include "bits/stdc++.h"
using namespace std;
using lint = long long;
#define low lower_bound
#define upp upper_bound
#define rep(i, n) for (lint (i) = 0; (i) < (n); ++(i))
#define Rep(i, n) for (lint (i) = (n); (i) >= 0; --(i))
#define all(vec) (vec).begin(), (vec).end()
#define cend printf("\n");
#define prique(T) priority_queue<T, vector<T>, greater<T>>
#define prique2(T) priority_queue<T>

struct edge { lint to; lint cost; };
using P = pair<lint, lint>;
using D = pair<double, double>;
using mll = map<lint, lint>;
//constexpr lint mod = 998244353LL;
constexpr lint mod = 1000000007LL;
constexpr lint inf = 3LL * mod * mod;
const double Pi = acos(-1.0);

template<class T> inline bool chmax(T& a, T b) {
	if (a < b) {
		a = b;
		return true;
	}
	return false;
}
template<class T> inline bool chmin(T& a, T b) {
	if (a > b) {
		a = b;
		return true;
	}
	return false;
}

lint modpow(lint x, lint n, lint m) {
	lint ans = 1;
	while (n > 0) {
		if (n & 1) {
			ans *= x;
			if (m <= ans) ans %= m;
		}
		x *= x;
		if (m <= x) x %= m;
		n >>= 1;
	}
	return ans;
}

lint fact[3000000];
void f_init(lint n) {
	if (3000000 <= n) return;
	fact[0] = fact[1] = 1;
	for (lint i = 2; i <= n; ++i) {
		fact[i] = i * fact[i - 1];
		if (mod <= fact[i]) fact[i] %= mod;
	}
	return;
}

lint comb(lint n, lint r) {
	if (n < r) return 0;
	if (n == r) return 1;
	lint ans = fact[n] * modpow(fact[n - r], mod - 2, mod) % mod * modpow(fact[r], mod - 2, mod) % mod;
	if (ans < 0) return ans + mod;
	return ans;
}

lint nck[1010][1010];
void comb(lint n) {
	rep(i, n + 1) {
		rep(j, i + 1) {
			if (j == 0 || i == j) nck[i][j] = 1;
			else nck[i][j] = nck[i - 1][j - 1] + nck[i - 1][j];
		}
	}
}

lint gcd(lint a, lint b) {
	if (b == 0) return a;
	return gcd(b, a % b);
}

lint lcm(lint a, lint b) { return a / gcd(a, b) * b; }

bool pri(lint p) {
	for (lint i = 2; i * i <= p; i == 2 ? ++i : i += 2) if (p % i == 0) return false;
	return p > 1;
}

mll factring(lint n) {
	mll ans;
	for (lint i = 2; i * i <= n; ++i) {
		while (n % i == 0) {
			n /= i;
			++ans[i];
		}
	}
	if (n != 1) ++ans[n];
	return ans;
}

lint xor128() {
	static lint x = 123456789, y = 362436069, z = 521288629, w = 88675123;
	lint t = (x xor (x << 11));
	x = y; y = z; z = w;
	return (w = (w xor (w >> 19)) xor (t xor (t >> 8)));
}

double dis(D a, D b) {
	double x = a.first - b.first, y = a.second - b.second;
	return sqrt(x * x + y * y);
}

bool kousa(double ax, double ay, double bx, double by, double cx, double cy, double dx, double dy) {
	double  ta = (cx - dx) * (ay - cy) + (cy - dy) * (cx - ax);
	double  tb = (cx - dx) * (by - cy) + (cy - dy) * (cx - bx);
	double  tc = (ax - bx) * (cy - ay) + (ay - by) * (ax - cx);
	double  td = (ax - bx) * (dy - ay) + (ay - by) * (ax - dx);

	return tc * td < -1e-12 && ta * tb < -1e-12;
}

class unionfind {
private:
	int par[2 * 100010], ranks[2 * 100010], sizeth[2 * 100010];
public:
	void init(int n) {
		for (int i = 0; i < n; ++i) {
			par[i] = i;
			ranks[i] = 0;
			sizeth[i] = 1;
		}
	}

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

	int size(int x) {
		return sizeth[x];
	}

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

	void unite(int x, int y) {
		x = root(x);
		y = root(y);
		if (x == y) return;
		if (ranks[x] < ranks[y]) {
			par[x] = y;
			sizeth[y] += sizeth[x];
		}
		else {
			par[y] = x;
			if (ranks[x] == ranks[y]) ++ranks[x];
			sizeth[x] += sizeth[y];
		}
	}
};

class BIT {
private:
	int n;
	int bit[500010];
public:
	void init(int m) {
		n = m;
	}
	void add(int a, int w) {
		for (int x = a; x <= n; x += (x & -x)) bit[x] += w;
	}
	int sum(int a) {
		int ret = 0;
		for (int x = a; x > 0; x -= (x & -x)) ret += bit[x];
		return ret;
	}
};

int k, n, ans = 10000000;
int a[2 * 100010];
int main() {
	cin >> k >> n;
	rep(i, n) cin >> a[i];
	sort(a, a + n);
	a[n] = k + a[0];
	rep(i, n) {
		ans = min(ans, k - (a[i + 1] - a[i]));
	}
	cout << ans << endl;
}

Measured memory_bytes: 1024