1727. Znaika's Magic Numbers-优快云博客

Znaika通过计算一组不同正整数的所有数字之和来寻找魔法数字。Neznaika认为任何数字都能找到这样的组合，并为此打赌。任务是为给定的数字构造这样一个整数集合。

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原题链接: http://acm.timus.ru/problem.aspx?space=1&num=1727

//使用 C# 语言解答如下：

using System;

// http://acm.timus.ru/problem.aspx?space=1&num=1727
static class Timus
{
  static void Main()
  {
    int n = int.Parse(Console.ReadLine());
    int count = Compute(ref n), tops = count;
    for (int i = 0; n > 9; i++, n -= 10) count++;
    int tens = count - tops;
    Console.WriteLine(count += ((n > 0) ? 1 : 0));
    for (int i = 99999; tops-- > 0; i--) Console.Write(i + " ");
    while (tens-- > 0) Console.Write("19 28 37 46 ".Substring(tens * 3, 3));
    if (n > 0) Console.Write(n);
  }
  
  static int Compute(ref int n)
  {
    int count = 0;
    for (int sum = 45; n >= 45; )
    {
      n -= sum--;
      if (++count % 10 == 0) sum += 9;
      if (count % 100 == 0) sum += 9;
      if (count % 1000 == 0) sum += 9; 
    }
    return count;
  }
}

1727. Znaika's Magic Numbers

Time limit: 0.5 second
Memory limit: 64 MB

Znaika has many interests. For example, now he is investigating the properties of number sets. Znaika writes down some set consisting of different positive integers (he calls this set a generating set), calculates the sum of all the written digits, and writes down the result in a special notebook. For example, for a generating set 7, 12, 43, he will write down the number 17 = 7 + 1 + 2 + 4 + 3 . Znaika is sure that only magic numbers can appear as a result of this operation.

Neznaika laughs at Znaika. He thinks that there is a generating set for every number, and he even made a bet with Znaika that he would be able to construct such a set.

Help Neznaika win the bet and construct a generating set for a given number.

Input

The only input line contains an integer n (0 < n < 10 5).

Output

If it is possible to construct a generating set for the number n, output the number of elements in this set in the first line. In the second line output a space-separated list of these elements. The elements of the set must be different positive integers strictly less than 10 5. If there are several generating sets, output any of them. If there are no generating sets, output −1.