Problem:
Score : 300 points

Problem Statement

The problem set at CODE FESTIVAL 20XX Finals consists of N problems.

The score allocated to the i-th (1≦i≦N) problem is i points.

Takahashi, a contestant, is trying to score exactly N points. For that, he is deciding which problems to solve.

As problems with higher scores are harder, he wants to minimize the highest score of a problem among the ones solved by him.

Determine the set of problems that should be solved.

Constraints

1≦N≦10^7

Partial Score

200 points will be awarded for passing the test set satisfying 1≦N≦1000.

Additional 100 points will be awarded for passing the test set without additional constraints.

Input

The input is given from Standard Input in the following format:

N

Output

Among the sets of problems with the total score of N, find a set in which the highest score of a problem is minimum, then print the indices of the problems in the set in any order, one per line.

If there exists more than one such set, any of them will be accepted.

Sample Input 1

4

Sample Output 1

1
3

Solving only the 4-th problem will also result in the total score of 4 points, but solving the 1-st and 3-rd problems will lower the highest score of a solved problem.

Sample Input 2

7

Sample Output 2

1
2
4

The set \{3,4\} will also be accepted.

Sample Input 3

1

Sample Output 3

1

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

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
//using System.Numerics;  //comment out if AOJ
using System.Text;

using Problem = Tmp.Problem;
using MyIO;

#pragma warning disable   //for AOJ

namespace Tmp
{
    class Problem : IDisposable
    {
        bool IsGCJ;
        int Repeat;
        Scanner sc;
        Printer pr;
        public Problem(bool isGCJ, Scanner scanner, Printer printer)
        {
            sc = scanner;
            pr = printer;
            IsGCJ = isGCJ;
            if (isGCJ) Repeat = sc.nextInt();
            else Read();
        }
        public Problem(bool isGCJ) : this(isGCJ, new Scanner(), new Printer()) { }
        public Problem(bool isGCJ, Scanner scanner) : this(isGCJ, scanner, new Printer()) { }
        public Problem(bool isGCJ, Printer printer) : this(isGCJ, new Scanner(), printer) { }
        public void Solve()
        {
            if (IsGCJ) for (var i = 0; i < Repeat; i++) { Read(); pr.Write("Case #" + (i + 1) + ": "); SolveOne(); }
            else SolveOne();
        }
        public void Dispose()
        {
            sc.Dispose();
            pr.Dispose();
        }
        public int Size { get { return 1; } }
        public const long Mod = 1000000007;

        // 使用する変数をここに書く
        // string S;
        // int a;
        /// <summary>
        /// 読み込み処理をここに書く
        /// </summary>
        void Read()
        {

        }
        /// <summary>
        /// メイン処理をここに書く
        /// </summary>
        void SolveOne()
        {
            long n = sc.nextLong();
            for (long max = 1; max < 100000; max++)
            {
                long sum = max * (max + 1) / 2;
                if(sum>=n)
                {
                    long tmp = n;
                    for (long cnt = max; cnt > 0; cnt--)
                    {
                        if(cnt<=tmp)
                        {
                            Console.WriteLine(cnt);
                            tmp -= cnt;
                        }
                    }
                    break;
                }
            }
        }
    }
}
class Program
{
    //public static RandomSFMT rand = new RandomSFMT();
    public static bool IsJudgeMode = true;
    public static bool IsGCJMode = false;
    public static bool IsSolveCreated = true;
    static void Main()
    {
        if (IsJudgeMode)
            if (IsGCJMode) using (var problem = new Problem(true, new Scanner("C-large-practice.in.txt"), new Printer("output.txt"))) problem.Solve();
            else using (var problem = new Problem(false, new Printer())) problem.Solve();
        else
        {
            var num = 1;
            int size = 0;
            decimal time = 0;
            for (var tmp = 0; tmp < num; tmp++)
            {
                using (var P = IsSolveCreated ? new Problem(false, new Scanner("input.txt"), new Printer()) : new Problem(false))
                {
                    size = P.Size;
                    //time += Func.MeasureTime(() => P.Solve());
                }
            }
            Console.WriteLine("{0}, {1}ms", size, time / num);
        }
    }
}

/// <summary>
/// カスタマイズしたIO
/// </summary>
namespace MyIO
{
    class Printer : IDisposable
    {
        bool isConsole;
        TextWriter file;
        public Printer() { file = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }; isConsole = true; }
        public Printer(string path) { file = new StreamWriter(path, false) { AutoFlush = false }; isConsole = false; }
        public void Write<T>(T value) { file.Write(value); }
        public void Write(bool b) { file.Write(b ? "YES" : "NO"); }
        public void Write(string str, params object[] args) { file.Write(str, args); }
        public void WriteLine() { file.WriteLine(); }
        public void WriteLine<T>(T value) { file.WriteLine(value); }
        public void WriteLine(bool b) { file.WriteLine(b ? "YES" : "NO"); }
        public void WriteLine<T>(IEnumerable<T> list) { foreach (var x in list) file.WriteLine(x); }
        public void WriteLine<T>(List<T> list) { foreach (var x in list) file.WriteLine(x); }
        public void WriteLine<T>(T[] list) { foreach (var x in list) file.WriteLine(x); }
        public void WriteLine(string str, params object[] args) { file.WriteLine(str, args); }
        public void Dispose() { file.Flush(); if (!isConsole) file.Dispose(); }
    }
    class Scanner : IDisposable
    {
        bool isConsole;
        TextReader file;
        public Scanner() { file = Console.In; }
        public Scanner(string path) { file = new StreamReader(path); isConsole = false; }
        public void Dispose() { if (!isConsole) file.Dispose(); }

        #region next読み込み
        string[] nextBuffer = new string[0];
        int BufferCnt = 0;

        char[] cs = new char[] { ' ' };

        public string next()
        {
            while (BufferCnt >= nextBuffer.Length)
            {
                string st = file.ReadLine();
                while (st == "") st = file.ReadLine();
                nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
                BufferCnt = 0;
            }
            return nextBuffer[BufferCnt++];
        }

        public int nextInt()
        {
            return int.Parse(next());
        }

        public long nextLong()
        {
            return long.Parse(next());
        }

        public double nextDouble()
        {
            return double.Parse(next());
        }

        private T[] enumerate<T>(int n, Func<T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f();
            return a;
        }

        public string[] next(int n) { return enumerate(n, next); }
        public double[] nextDouble(int n) { return enumerate(n, nextDouble); }
        public int[] nextInt(int n) { return enumerate(n, nextInt); }
        public long[] nextLong(int n) { return enumerate(n, nextLong); }
        #endregion
    }
}