Problem:
F: Absum

問題

長さ $N$ の数列 $A$ が与えられる．あなたは高々 $M$ 回まで，数列の $i$ 番目と $j$ 番目（$0 \leq i, j \leq N-1$）の要素を入れ替える操作を行うことができる．

操作を行なってできる数列の $\sum_{i = 0}^{N - 1} abs(A_i - i)$ の最大値を求めよ．

制約

$2 \leq N \leq 10^5$

$0 \leq M \leq N$

$0 \leq A_i \leq 10^5$

入力形式

入力は以下の形式で与えられる.

$N\ M$（15:15修正）

$A_0\ A_1\ A_2\ \dots\ A_{N - 1}$

出力

操作を行なってできる数列の $\sum_{i = 0}^{N - 1} abs(A_i - i)$ の最大値を求めよ.また, 末尾に改行も出力せよ.

サンプル

サンプル入力 1

5 2
0 3 2 1 4

サンプル出力 1

12

$0$ 番目の要素と $4$ 番目の要素に操作を行うと，操作後の数列は $(4, 3, 2, 1, 0)$ となり， $|4 - 0| + |3 - 1| + |2 - 2| + |1 - 3| + |0 - 4| = 12$ で最大となる．必ずしも操作を $M$ 回行う必要がないことに注意せよ．

サンプル入力 2

3 2
0 0 0

サンプル出力 2

3

操作を行うことなく最大値となる．

サンプル入力 3

6 2
1 0 3 6 5 4

サンプル出力 3

20

Solution in C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using SB = System.Text.StringBuilder;
//using System.Text.RegularExpressions;
//using System.Globalization;
//using System.Diagnostics;
using static System.Console;
using System.Numerics;
using static System.Math;
using pair = Pair<int, int>;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    readonly Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;
    readonly int dom = 998244353;
    bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (b.CompareTo(a) < 0) { a = b; return true; } return false; }

    void solve()
    {
        int N = cin.nextint;
        int M = cin.nextint;
        var A = cin.scanint;
        var P = new PriorityQueue<long>(-1); //小さいのを消す
        var Q = new PriorityQueue<long>(); //大きいのを消す
        for (int i = 0; i < N; i++)
        {
            P.Enqueue(Max(i, A[i]));
            Q.Enqueue(Min(i, A[i]));
        }
        for (int i = 0; i < M; i++)
        {
            if (P.Peek() < Q.Peek())
            {
                Q.Enqueue(P.Dequeue());
                P.Enqueue(Q.Dequeue());
            }
        }
        WriteLine(P.Item.Sum() - Q.Item.Sum());
    }
    
}
/// <summary>
/// Original Author: 蟻本
/// </summary>
/// <typeparam name="T"></typeparam>
class PriorityQueue<T> where T : IComparable<T>
{
    List<T> heap;
    readonly int cmp;
    public PriorityQueue(int cmp = 1) { heap = new List<T>(); this.cmp = cmp; }
    public void Enqueue(T x)
    {
        heap.Add(x);
        int i = Count++;
        while (i > 0)
        {
            int p = (i - 1) >> 1;
            if (x.CompareTo(heap[p]) * cmp <= 0) break;
            heap[i] = heap[p]; i = p;
        }
        heap[i] = x;
    }
    public T Dequeue()
    {
        T ret = heap[0]; T x = heap[--Count];
        int i = 0;
        while ((i << 1) + 1 < Count)
        {
            int a = (i << 1) + 1; int b = (i << 1) + 2;
            if (b < Count && heap[a].CompareTo(heap[b]) * cmp < 0) a = b;
            if (x.CompareTo(heap[a]) * cmp >= 0) break;
            heap[i] = heap[a]; i = a;
        }
        heap[i] = x; heap.RemoveAt(Count);
        return ret;
    }
    public int Count { get; private set; }
    public bool Any() => Count > 0;
    public T Peek() => heap[0];
    public List<T> Item => heap;
}


static class Ex
{
    public static void join<T>(this IEnumerable<T> values, string sep = " ") => WriteLine(string.Join(sep, values));
    public static string concat<T>(this IEnumerable<T> values) => string.Concat(values);
    public static string reverse(this string s) { var t = s.ToCharArray(); Array.Reverse(t); return t.concat(); }

    public static int lower_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) < 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
    public static int upper_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) <= 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
}

class Pair<T, U> : IComparable<Pair<T, U>> where T : IComparable<T> where U : IComparable<U>
{
    public T f; public U s;
    public Pair(T f, U s) { this.f = f; this.s = s; }
    public int CompareTo(Pair<T, U> a) => f.CompareTo(a.f) != 0 ? f.CompareTo(a.f) : s.CompareTo(a.s);
    public override string ToString() => $"{f} {s}";
}

class Scanner
{
    string[] s; int i;
    readonly char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan => ReadLine().Split();
    public int[] scanint => Array.ConvertAll(scan, int.Parse);
    public long[] scanlong => Array.ConvertAll(scan, long.Parse);
    public double[] scandouble => Array.ConvertAll(scan, double.Parse);
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint => int.Parse(next);
    public long nextlong => long.Parse(next);
    public double nextdouble => double.Parse(next);
}