Problem:
Score : 300 points

Problem Statement

We will play a one-player game using a number line and N pieces.

First, we place each of these pieces at some integer coordinate.

Here, multiple pieces can be placed at the same coordinate.

Our objective is to visit all of the M coordinates X_1, X_2, ..., X_M with these pieces, by repeating the following move:

Move: Choose a piece and let x be its coordinate. Put that piece at coordinate x+1 or x-1.

Note that the coordinates where we initially place the pieces are already regarded as visited.

Find the minimum number of moves required to achieve the objective.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq M \leq 10^5

-10^5 \leq X_i \leq 10^5

X_1, X_2, ..., X_M are all different.

Input

Input is given from Standard Input in the following format:

N M
X_1 X_2 ... X_M

Output

Find the minimum number of moves required to achieve the objective.

Sample Input 1

2 5
10 12 1 2 14

Sample Output 1

5

The objective can be achieved in five moves as follows, and this is the minimum number of moves required.

Initially, put the two pieces at coordinates 1 and 10.

Move the piece at coordinate 1 to 2.

Move the piece at coordinate 10 to 11.

Move the piece at coordinate 11 to 12.

Move the piece at coordinate 12 to 13.

Move the piece at coordinate 13 to 14.

Sample Input 2

3 7
-10 -3 0 9 -100 2 17

Sample Output 2

19

Sample Input 3

100 1
-100000

Sample Output 3

0

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            ABC117.C();
        }

        class ABC117
        {
            public static void A()
            {
                Console.WriteLine(1.0 * Read.Int() / Read.Int());
            }
            public static void B()
            {
                var N = Read.Int();
                var L = Read.IntN();
                Console.WriteLine(L.Sum() > L.Max() * 2 ? "Yes" : "No");
            }
            public static void C()
            {
                var N = Read.Int();
                var M = Read.Int();
                var X = Read.LongN();
                X = X.OrderBy(x => x).ToArray();
                if (N >= M) { Console.WriteLine(0); return; }
                var diff = Enumerable.Range(0, M - 1).Select(i => X[i + 1] - X[i]).OrderBy(x => x).ToArray();
                Console.WriteLine(diff.Take(M - N).Sum());
            }
            public static void D()
            {
                var N = Read.Int();
                var K = Read.Long();
                var A = Read.LongN();
                int[] C0 = new int[50];
                int[] C1 = new int[C0.Length];
                for(int i = 0; i < N; ++i)
                {
                    for(int j = 0; j < C0.Length; ++j)
                    {
                        if ((A[i] & (1L << j)) > 0)
                        {
                            C1[j]++;
                        }
                        else
                        {
                            C0[j]++;
                        }
                    }
                }
                var dp = new long[C0.Length, 2];
                for (int j = 0; j < C0.Length - 1; ++j)
                {
                    var is1 = (K & (1L << j)) > 0;
                    dp[j + 1, 0] = is1 ? Math.Max(dp[j, 1] + C1[j] * (1L << j), dp[j, 0] + C0[j] * (1L << j)) : dp[j, 0] + C1[j] * (1L << j);
                    dp[j + 1, 1] = dp[j, 1] + Math.Max(C0[j], C1[j]) * (1L << j);
                }
                Console.WriteLine(dp[C0.Length - 1, 0]);
            }
        }

        class Util
        {
            public class BST<T> where T : IComparable
            {
                public class Node
                {
                    public T V;
                    public Node L, R;
                    public int Count;
                    public Node(T v) { V = v; Count = 1; }
                }
                static Random _rnd = new Random();
                public static int Count(Node t) { return t == null ? 0 : t.Count; }
                static Node Update(Node t) { t.Count = Count(t.L) + Count(t.R) + 1; return t; }
                public static Node Merge(Node l, Node r)
                {
                    if (l == null || r == null) return l == null ? r : l;
                    if ((double)Count(l) / (double)(Count(l) + Count(r)) > _rnd.NextDouble())
                    { l.R = Merge(l.R, r); return Update(l); }
                    else { r.L = Merge(l, r.L); return Update(r); }
                }
                public static Tuple<Node, Node> Split(Node t, int k)
                {
                    if (t == null) return new Tuple<Node, Node>(null, null);
                    if (k <= Count(t.L))
                    {
                        var s = Split(t.L, k);
                        t.L = s.Item2;
                        return new Tuple<Node, Node>(s.Item1, Update(t));
                    }
                    else
                    {
                        var s = Split(t.R, k - Count(t.L) - 1);
                        t.R = s.Item1;
                        return new Tuple<Node, Node>(Update(t), s.Item2);
                    }
                }
                public static Node Remove(Node t, T v)
                {
                    if (Find(t, v) == null) return t;
                    return RemoveAt(t, LowerBound(t, v));
                }
                public static Node RemoveAt(Node t, int k)
                {
                    var s = Split(t, k);
                    var s2 = Split(s.Item2, 1);
                    return Merge(s.Item1, s2.Item2);
                }
                public static bool Contains(Node t, T v) { return Find(t, v) != null; }
                public static Node Find(Node t, T v)
                {
                    while (t != null)
                    {
                        var cmp = t.V.CompareTo(v);
                        if (cmp > 0) t = t.L;
                        else if (cmp < 0) t = t.R;
                        else break;
                    }
                    return t;
                }

                public static Node FindByIndex(Node t, int idx)
                {
                    if (t == null) return null;
                    var currentIdx = Count(t) - Count(t.R) - 1;
                    while (t != null)
                    {
                        if (currentIdx == idx) return t;
                        if (currentIdx > idx)
                        { t = t.L; currentIdx -= (Count(t == null ? null : t.R) + 1); }
                        else { t = t.R; currentIdx += (Count(t == null ? null : t.L) + 1); }
                    }
                    return null;
                }
                public static int UpperBound(Node t, T v)
                {
                    var torg = t;
                    if (t == null) return -1;

                    var ret = Int32.MaxValue;
                    var idx = Count(t) - Count(t.R) - 1;
                    while (t != null)
                    {
                        var cmp = t.V.CompareTo(v);

                        if (cmp > 0)
                        {
                            ret = Math.Min(ret, idx);
                            t = t.L;
                            idx -= (Count(t == null ? null : t.R) + 1);
                        }
                        else if (cmp <= 0)
                        {
                            t = t.R;
                            idx += (Count(t == null ? null : t.L) + 1);
                        }
                    }
                    return ret == Int32.MaxValue ? Count(torg) : ret;
                }
                public static int LowerBound(Node t, T v)
                {
                    var torg = t;
                    if (t == null) return -1;

                    var idx = Count(t) - Count(t.R) - 1;
                    var ret = Int32.MaxValue;
                    while (t != null)
                    {
                        var cmp = t.V.CompareTo(v);
                        if (cmp >= 0)
                        {
                            if (cmp == 0) ret = Math.Min(ret, idx);
                            t = t.L;
                            if (t == null) ret = Math.Min(ret, idx);
                            idx -= t == null ? 0 : (Count(t.R) + 1);
                        }
                        else if (cmp < 0)
                        {
                            t = t.R;
                            idx += (Count(t == null ? null : t.L) + 1);
                            if (t == null) return idx;
                        }
                    }
                    return ret == Int32.MaxValue ? Count(torg) : ret;
                }
                public static Node Insert(Node t, T v)
                {
                    var ub = LowerBound(t, v);
                    return InsertByIdx(t, ub, v);
                }
                static Node InsertByIdx(Node t, int k, T v)
                {
                    var s = Split(t, k);
                    return Merge(Merge(s.Item1, new Node(v)), s.Item2);
                }
                public static IEnumerable<T> Enumerate(Node t)
                {
                    var ret = new List<T>();
                    Enumerate(t, ret);
                    return ret;
                }
                static void Enumerate(Node t, List<T> ret)
                {
                    if (t == null) return;
                    Enumerate(t.L, ret);
                    ret.Add(t.V);
                    Enumerate(t.R, ret);
                }
            }
            public class Set<T> where T : IComparable
            {
                protected BST<T>.Node _root;
                public T this[int idx] { get { return ElementAt(idx); } }
                public int Count() { return BST<T>.Count(_root); }
                public virtual void Insert(T v)
                {
                    if (_root == null) _root = new BST<T>.Node(v);
                    else
                    {
                        if (BST<T>.Find(_root, v) != null) return;
                        _root = BST<T>.Insert(_root, v);
                    }
                }
                public void Clear() { _root = null; }
                public void Remove(T v) { _root = BST<T>.Remove(_root, v); }
                public bool Contains(T v) { return BST<T>.Contains(_root, v); }
                public T ElementAt(int k)
                {
                    var node = BST<T>.FindByIndex(_root, k);
                    if (node == null) throw new IndexOutOfRangeException();
                    return node.V;
                }
                public int Count(T v) { return BST<T>.UpperBound(_root, v) - BST<T>.LowerBound(_root, v); }
                public int LowerBound(T v) { return BST<T>.LowerBound(_root, v); }
                public int UpperBound(T v) { return BST<T>.UpperBound(_root, v); }
                public Tuple<int, int> EqualRange(T v)
                {
                    if (!Contains(v)) return new Tuple<int, int>(-1, -1);
                    return new Tuple<int, int>(BST<T>.LowerBound(_root, v), BST<T>.UpperBound(_root, v) - 1);
                }
                public List<T> ToList() { return new List<T>(BST<T>.Enumerate(_root)); }
            }
            public class MultiSet<T> : Set<T> where T : IComparable { public override void Insert(T v) { if (_root == null) { _root = new BST<T>.Node(v); } else { _root = BST<T>.Insert(_root, v); } } }
        }

        static class Read
        {
            static Queue<string> queue = new Queue<string>();
            static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
            public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
            public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
            public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
            public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
            public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
            public static string[] StrN() { return Console.ReadLine().Split(' '); }
            public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
            public static long[,] LongMatrix(int r, int c)
            {
                var mat = new long[r, c];
                for (int i = 0; i < r; ++i)
                {
                    var x = Read.LongN();
                    for (int j = 0; j < c; ++j)
                    {
                        mat[i, j] = x[j];
                    }
                }
                return mat;
            }
            public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M)
            {
                Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new HashSet<int>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1]);
                    dict[ab[1]].Add(ab[0]);
                }
                return dict;
            }
        }
    }
}