#include <algorithm>
#include <cmath>
#include <cstdio>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#define ll long long
#define fr(i, k, N) for (decltype(N + k) i = k; i < N; i++)
#define rep(i, N) for (decltype(N) i = 0; i < N; i++)
#define ALL(v) v.begin(), v.end()
using namespace std;
template <class X>
void pr(X test) {
  cout << test << endl;
}
template <class X>
void prr(X test) {
  for (auto it : test) cout << it << " ";
  cout << endl;
}
template <class X>
void prrr(X test) {
  int f = 0;
  for (auto it : test) cout << (f++ != 0 ? " " : "") << it;
  cout << endl;
}
template <typename X>
istream &operator>>(istream &i, vector<X> &v) {
  for (X &x : v) i >> x;
  return i;
}

class UF {  // union find from https://github.com/kartikkukreja/blog-codes (MIT)
            // [usage]
            // auto uf = new UF(n);
            // uf->merge(l, r); // 0 <= l, r <= n-1
            // ...
 public:
  int *id;  // inner id
  int cnt;  // number of all vartices
  int *sz;  // sz[i] means size of i's set
  UF(int N) {
    cnt = N;
    id = new int[N];
    sz = new int[N];
    for (int i = 0; i < N; i++) {
      id[i] = i;
      sz[i] = 1;
    }
  }
  ~UF() {
    delete[] id;
    delete[] sz;
  }
  int find(int p) {
    int root = p;
    while (root != id[root]) root = id[root];
    while (p != root) {
      int newp = id[p];
      id[p] = root;
      p = newp;
    }
    return root;
  }
  void merge(int x, int y) {
    int i = find(x);
    int j = find(y);
    if (i == j) return;

    if (sz[i] < sz[j]) {
      id[i] = j;
      sz[j] += sz[i];
    } else {
      id[j] = i;
      sz[i] += sz[j];
    }
    cnt--;
  }
  bool connected(int x, int y) { return find(x) == find(y); }
  int count() { return cnt; }
};

// return 約数unordered_set 1 <= x <= n
auto divv = [](auto n) {
  unordered_set<decltype(n)> v;
  for (decltype(n) i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      v.insert(i);
      if (i * i != n) v.insert(n / i);
    }
  }
  return v;
};

// primediv n == sum (first ^ second)
auto primediv = [](auto n) {
  unordered_map<decltype(n), decltype(n)> m;
  fr(i, 1, n + 1) {
    if (!isPrime(i)) continue;
    while (n % i == 0) {
      m[i]++;
      n /= i;
    }
  }
  return m;
};

// check prime (and n>=2) or not
auto isPrime = [](auto n) {
  if (n <= 1) return false;
  for (decltype(n) i = 2; i <= sqrt(n); ++i) {
    if (n % i == 0) {
      return false;
    }
  }
  return true;
};

// 最小公倍数
auto lcm_ = [](auto a, auto b) {
  if (a < b) swap(a, b);
  auto r = a % b;
  auto x = a * b;
  while (r != 0) {
    a = b;
    b = r;
    r = a % b;
  }
  return x / b;
};

unordered_map<ll, unordered_map<ll, ll>> u;
// 最大公約数
auto gcd_ = [](auto a, auto b) {
  if (a > b) swap(a, b);
  if (u[a][b] == 0) {
    u[a][b] = (a * b) / lcm(a, b);
  }
  return u[a][b];
};

// factorial n mod prm
ll factmod(ll a, ll prm) {
  return a == 0 ? 1 : (a * factmod(a - 1, prm)) % prm;
};

// 1/x mod prm
auto invmod = [](auto x, auto prm) {
  decltype(x) r = 1;
  if (x == 1) return r;
  for (auto ex = prm - 2; ex; ex >>= 1) {
    if (ex & 1) r = (r * x) % prm;
    x = (x * x) % prm;
  }
  return r;
};

int main() {
  ll k, n;
  cin >> k >> n;
  vector<ll> a(n);
  cin >> a;

  const ll sum = k;
  ll ans = sum;
  rep(i, n - 1) {
    ll diff = a[i + 1] - a[i];
    ans = min(ans, sum - diff);
  }
  ans = min(ans, sum - (k - a[n - 1] + a[0]));
  pr(ans);
}


Measured memory_bytes: 1920