//  [typescript]
import * as fs from 'fs';

// main
function main(input: string[]) {
    // param
    var k: number = 0;
    var n: number = 0;
    var an: number[] = [];
    var ans: number = 0;
    // init
    [k, n] = input.shift().split(" ").map(x => Number(x));
    an = input.shift().split(" ").map(x => Number(x));
    // solve
    var max = 0;
    for (var nx = 0; nx < n; nx++) {
        if (nx < n - 1) {
            max = Math.max(max, an[nx + 1] - an[nx]);
        } else {
            max = Math.max(max, k + an[0] - an[nx]);
        }
    }
    ans = k - max;
    // answer
    console.log(ans);
}

// graph lib
/*
function GRAPH_enumPattern(cur: number[], pat: number[][]): number[][] {
    var arr = [];
    for (var patx = 0; patx < pat.length; patx++) {
        var pos = [cur[0] + pat[patx][0], cur[1] + pat[patx][1]];
        arr.push(pos);
    }
    return arr;
}
*/

// math lib
/*
function Math_max(arr: number[]): number { return arr.reduce((x, y) => Math.max(x, y)); }
function Math_min(arr: number[]): number { return arr.reduce((x, y) => Math.min(x, y)); }
function Math_gcd(): number {
    var ans = arguments[0];
    var f = (a: number, b: number): number => b ? f(b, a % b) : a
    for (var i = 1; i < arguments.length; i++) {
        ans = f(ans, arguments[i]);
    }
    return ans
};
function Math_gcdArray(values: number[]): number {
    var ans = values[0];
    var f = (a: number, b: number): number => b ? f(b, a % b) : a
    for (var i = 1; i < values.length; i++) {
        ans = f(ans, values[i]);
    }
    return ans
};
function Math_lcm(): number {
    var a = arguments
    var g = (n: number, m: number): number => m ? g(m, n % m) : n
    var l = (n: number, m: number): number => n * m / g(n, m)
    var ans = a[0]
    for (var i = 1; i < a.length; i++) {
        ans = l(ans, a[i])
    }
    return ans
}
function Math_lcmArray(values: number[]): number {
    var a = values
    var g = (n: number, m: number): number => m ? g(m, n % m) : n
    var l = (n: number, m: number): number => n * m / g(n, m)
    var ans = a[0]
    for (var i = 1; i < a.length; i++) {
        ans = l(ans, a[i])
    }
    return ans
}
function Math_primeList(value: number): number[] {
    var ans = [];
    var arr = new Array(value).fill(0);
    for (var i = 2; i < value; i++) {
        if (arr[i] == 0) {
            for (var j = i; j < value; j += i) {
                if (arr[j] == 0) arr[j] = i;
            }
        }
    }
    for (var i = 2; i < value; i++) {
        if (arr[i] == i) ans.push(i);
    }
    return ans;
}
function Math_primeFactor(p: number[], value: number): number[][] {
    var ans: number[][] = [];
    var valmax = value / 2;;
    for (var i = 0; i < p.length; i++) {
        var prime = p[i];
        if (valmax < prime) break;
        var count = 0;
        while (value % prime == 0) {
            value /= prime;
            count++;
        }
        if (count != 0) {
            ans.push([prime, count]);
        }
        if (value == 1) break;
    }
    return ans;
}
*/

// union-find lib
/*
var g_uf_root: number[];
var g_uf_count: number[];
function UF_initRoot(num: number) {
    g_uf_root = new Array(num).fill(-1);
    g_uf_count = new Array(num).fill(1);
}
function UF_getRoot(index: number) {
    if (g_uf_root[index] < 0) {
        return index;
    } else {
        var work0: number = UF_getRoot(g_uf_root[index]);
        g_uf_root[index] = work0;
        return work0
    }
}
function UF_mergeRoot(a: number, b: number) {
    var root0: number = UF_getRoot(a);
    var root1: number = UF_getRoot(b);
    if (root0 == root1) return;
    if (root0 > root1) [root0, root1] = [root1, root0];
    g_uf_count[root0] += g_uf_count[root1];
    g_uf_count[root1] = 0;
    g_uf_root[root1] = root0;
}
*/

// entrypoint
function entrypoint() {
    try {
        // linux
        var input = fs.readFileSync("/dev/stdin", "utf8").trim().split("\n");
        console.debug = function () { };
        main(input);
    }
    catch (ex) {
        // windows
        const lines: string[] = [];
        // @ts-ignore
        const reader = require('readline').createInterface({
            // @ts-ignore
            input: process.stdin,
            // @ts-ignore
            output: process.stdout
        });
        reader.on('line', function (line: string) {
            lines.push(line);
        });
        reader.on('close', function () {
            input = lines;
            main(input);
        });
    }
}
entrypoint();