Problem:
Score : 700 points

Problem Statement

Snuke is buying a lamp.
The light of the lamp can be adjusted to m levels of brightness, represented by integers from 1 through m, by the two buttons on the remote control.

The first button is a "forward" button. When this button is pressed, the brightness level is increased by 1, except when the brightness level is m, in which case the brightness level becomes 1.

The second button is a "favorite" button. When this button is pressed, the brightness level becomes the favorite brightness level x, which is set when the lamp is purchased.

Snuke is thinking of setting the favorite brightness level x so that he can efficiently adjust the brightness.
He is planning to change the brightness n-1 times. In the i-th change, the brightness level is changed from a_i to a_{i+1}. The initial brightness level is a_1.
Find the number of times Snuke needs to press the buttons when x is set to minimize this number.

Constraints

2 \leq n,m \leq 10^5

1 \leq a_i\leq m

a_i \neq a_{i+1}

n, m and a_i are integers.

Input

Input is given from Standard Input in the following format:

n m
a_1 a_2 … a_n

Output

Print the minimum number of times Snuke needs to press the buttons.

Sample Input 1

4 6
1 5 1 4

Sample Output 1

5

When the favorite brightness level is set to 1, 2, 3, 4, 5 and 6, Snuke needs to press the buttons 8, 9, 7, 5, 6 and 9 times, respectively.
Thus, Snuke should set the favorite brightness level to 4.
In this case, the brightness is adjusted as follows:

In the first change, press the favorite button once, then press the forward button once.

In the second change, press the forward button twice.

In the third change, press the favorite button once.

Sample Input 2

10 10
10 9 8 7 6 5 4 3 2 1

Sample Output 2

45

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

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Runtime.CompilerServices;
using System.Text;
using static Template;
using static System.Console;
using static System.Convert;
using static System.Math;
using Pi = Pair<int, int>;
using Number = System.Int64;

class Solver
{
    Scanner sc = new Scanner();
    //

    public void Solve()
    {
        int n, m;
        sc.Make(out n, out m);
        var ar = new int[n];
        for (var i = 0; i < n; i++)
            ar[i] = sc.Next<int>() - 1;
        var seg = new SegmentTree<int>(m, 0, (a, b) => a + b, (a, b) => a + b);
        var res = 0L;
        for(var i = 0; i < n-1; i++)
        {
            var d = (ar[i + 1] - ar[i] + m) % m - 1;
            if (d <= 0) continue;
            if (ar[i + 1] < (ar[i] + 2) % m)
            {
                seg.Update(ar[i] + 2, m, -1);
                seg.Update(0, ar[i + 1] + 1, -1);
            }
            else seg.Update((ar[i] + 2) % m, ar[i + 1] + 1, -1);
            if (ar[i + 1] != m - 1)
                seg.Update(ar[i + 1] + 1, ar[i + 1] + 2, d);
        }
        for (var i = 0; i < n - 1; i++)
            res += Min((ar[i + 1] - ar[i] + m) % m, 1 + ar[i + 1]);
        var t = res;
        for(var i = 1; i < m; i++)
        {
            t += seg.Query(i);
            chmin(ref res, t);
        }
        WriteLine(res);
    }
}

public class SegmentTree<T>
{
    protected readonly T[] item;
    protected readonly int num;
    protected readonly Func<T, T, T> func;
    protected readonly Func<T, T, T> updateFunc;
    protected readonly T minT;

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    protected int Parent(int index)
        => (index - 1) >> 1;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    protected int Left(int index)
        => (index << 1) + 1;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    protected int Right(int index)
        => (index + 1) << 1;
    public T this[int i]
    {
        get { return item[i + num - 1]; }
        set { item[i + num - 1] = value; }
    }

    public SegmentTree(int num, T minT, Func<T, T, T> func, Func<T, T, T> updateFunc = null)
    {
        this.func = func;
        this.num = 1;
        this.minT = minT;
        this.updateFunc = updateFunc ?? ((T val1, T val2) => val2);
        while (this.num <= num)
            this.num <<= 1;
        item = new T[2 * this.num - 1];
        for (var i = 0; i < 2 * this.num - 1; i++)
            item[i] = minT;
    }

    public void Update(int index, T value)
    {
        index += num - 1;
        item[index] = updateFunc(item[index], value);
        while (index > 0)
        {
            index = Parent(index);
            item[index] = func(item[Left(index)], item[Right(index)]);
        }
    }

    public virtual void Update(int left, int right, T value)
        => Update(left, right, 0, 0, num, value);
    protected virtual void Update(int left, int right, int k, int l, int r, T value)
    {
        if (r <= left || right <= l) return;
        if (left <= l && r <= right) item[k] = updateFunc(item[k], value);
        else
        {
            Update(left, right, Left(k), l, (l + r) >> 1, value);
            Update(left, right, Right(k), (l + r) >> 1, r, value);
        }
    }

    public void All_Update()
    {
        for (int i = num - 2; i >= 0; i--)
            item[i] = func(item[Left(i)], item[Right(i)]);
    }

    public T Query(int index)
    {
        index += num - 1;
        var value = func(minT, item[index]);
        while (index > 0)
        {
            index = Parent(index);
            value = func(value, item[index]);
        }
        return value;
    }

    public virtual T Query(int left, int right)
        => Query(left, right, 0, 0, num);
    protected virtual T Query(int left, int right, int k, int l, int r)
    {
        if (r <= left || right <= l) return minT;
        if (left <= l && r <= right) return item[k];
        else
            return func(Query(left, right, Left(k), l, (l + r) >> 1), Query(left, right, Right(k), (l + r) >> 1, r));
    }

    /// <summary>
    /// check(func(item[st]...item[i]))がtrueとなる最小のi
    /// </summary>
    public int Find(int st, Func<T, bool> check)
    {
        var x = minT;
        return Find(st, check, ref x, 0, 0, num);
    }
    private int Find(int st, Func<T, bool> check, ref T x, int k, int l, int r)
    {
        if (l + 1 == r)
        {
            x = func(x, item[k]);
            return check(x) ? k - num + 1 : -1;
        }
        var m = (l + r) >> 1;
        if (m <= st) return Find(st, check, ref x, Right(k), m, r);
        if (st <= l && !check(func(x, item[k])))
        { x = func(x, item[k]); return -1; }
        var xl = Find(st, check, ref x, Left(k), l, m);
        if (xl >= 0) return xl;
        return Find(st, check, ref x, Right(k), m, r);
    }
}
#region Template
public class Template
{
    static void Main(string[] args)
    {
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        new Solver().Solve();
        Console.Out.Flush();
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmin<T>(ref T num, T val) where T : IComparable<T>
    { if (num.CompareTo(val) == 1) { num = val; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmax<T>(ref T num, T val) where T : IComparable<T>
    { if (num.CompareTo(val) == -1) { num = val; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(ref T v1, ref T v2)
    { var t = v2; v2 = v1; v1 = t; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static T[] Create<T>(int n, Func<T> f)
    {
        var rt = new T[n];
        for (var i = 0; i < rt.Length; ++i)
            rt[i] = f();
        return rt;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static T[] Create<T>(int n, Func<int, T> f)
    {
        var rt = new T[n];
        for (var i = 0; i < rt.Length; ++i)
            rt[i] = f(i);
        return rt;
    }
    public static void Fail<T>(T s) { Console.WriteLine(s); Console.Out.Close(); Environment.Exit(0); }
}

public class Scanner
{
    public string Str => ReadLine().Trim();
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public int[] ArrInt => Str.Split(' ').Select(int.Parse).ToArray();
    public long[] ArrLong => Str.Split(' ').Select(long.Parse).ToArray();
    public char[][] Grid(int n) => Create(n, () => Str.ToCharArray());
    public int[] ArrInt1D(int n) => Create(n, () => Int);
    public long[] ArrLong1D(int n) => Create(n, () => Long);
    public int[][] ArrInt2D(int n) => Create(n, () => ArrInt);
    public long[][] ArrLong2D(int n) => Create(n, () => ArrLong);
    public Pair<T1, T2> PairMake<T1, T2>() => new Pair<T1, T2>(Next<T1>(), Next<T2>());
    public Pair<T1, T2, T3> PairMake<T1, T2, T3>() => new Pair<T1, T2, T3>(Next<T1>(), Next<T2>(), Next<T3>());
    private Queue<string> q = new Queue<string>();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public T Next<T>() { if (q.Count == 0) foreach (var item in Str.Split(' ')) q.Enqueue(item); return (T)Convert.ChangeType(q.Dequeue(), typeof(T)); }
    public void Make<T1>(out T1 v1) => v1 = Next<T1>();
    public void Make<T1, T2>(out T1 v1, out T2 v2) { v1 = Next<T1>(); v2 = Next<T2>(); }
    public void Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3) { Make(out v1, out v2); v3 = Next<T3>(); }
    public void Make<T1, T2, T3, T4>(out T1 v1, out T2 v2, out T3 v3, out T4 v4) { Make(out v1, out v2, out v3); v4 = Next<T4>(); }
    public void Make<T1, T2, T3, T4, T5>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5) { Make(out v1, out v2, out v3, out v4); v5 = Next<T5>(); }
    public void Make<T1, T2, T3, T4, T5, T6>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6) { Make(out v1, out v2, out v3, out v4, out v5); v6 = Next<T6>(); }
}
public class Pair<T1, T2> : IComparable<Pair<T1, T2>>
{
    public T1 v1;
    public T2 v2;
    public Pair() { }
    public Pair(T1 v1, T2 v2)
    { this.v1 = v1; this.v2 = v2; }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int CompareTo(Pair<T1, T2> p)
    {
        var c = Comparer<T1>.Default.Compare(v1, p.v1);
        if (c == 0)
            c = Comparer<T2>.Default.Compare(v2, p.v2);
        return c;
    }
    public override string ToString()
        => $"{v1.ToString()} {v2.ToString()}";
    public void Tie(out T1 a, out T2 b) { a = v1; b = v2; }
}

public class Pair<T1, T2, T3> : Pair<T1, T2>, IComparable<Pair<T1, T2, T3>>
{
    public T3 v3;
    public Pair() : base() { }
    public Pair(T1 v1, T2 v2, T3 v3) : base(v1, v2)
    { this.v3 = v3; }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int CompareTo(Pair<T1, T2, T3> p)
    {
        var c = base.CompareTo(p);
        if (c == 0)
            c = Comparer<T3>.Default.Compare(v3, p.v3);
        return c;
    }
    public override string ToString()
        => $"{base.ToString()} {v3.ToString()}";
    public void Tie(out T1 a, out T2 b, out T3 c) { Tie(out a, out b); c = v3; }
}
#endregion