import std.stdio, std.string, std.conv, std.range;
import std.algorithm, std.array, std.typecons, std.container;
import std.math, std.numeric, std.random, core.bitop;

enum inf = 1_001_001_001;
enum infl = 1_001_001_001_001_001_001L;


void main() {
    int K, N;
    scan(K, N);
    auto a = readln.split.to!(int[]);

    long ans = infl;

    foreach (i ; 0 .. N) {
        long v;
        if (i < N - 1) {
            v = K - (a[i + 1] - a[i]);
        }
        else {
            v = K - (a[0] - a[N - 1] + K);
        }
        chmin(ans, v);
    }

    writeln(ans);
}



void scan(T...)(ref T args) {
    auto line = readln.split;
    foreach (ref arg; args) {
        arg = line.front.to!(typeof(arg));
        line.popFront;
    }
    assert(line.empty);
}

void fillAll(R, T)(ref R arr, T value) {
    static if (is(typeof(arr[] = value))) {
        arr[] = value;
    }
    else {
        foreach (ref e; arr) {
            fillAll(e, value);
        }
    }
}

bool chmin(T, U...)(ref T x, U args) {
    bool isChanged;
    foreach (arg; args) if (x > arg) {
        x = arg;
        isChanged = true;
    }
    return isChanged;
}

bool chmax(T, U...)(ref T x, U args) {
    bool isChanged;
    foreach (arg; args) if (x < arg) {
        x = arg;
        isChanged = true;
    }
    return isChanged;
}

void yes(bool ok, string y = "Yes", string n = "No") {
    return writeln(ok ? y : n);
}
