Problem:
Score : 500 points

Problem Statement

Let S(n) denote the sum of the digits in the decimal notation of n.
For example, S(123) = 1 + 2 + 3 = 6.

We will call an integer n a Snuke number when, for all positive integers m such that m > n, \frac{n}{S(n)} \leq \frac{m}{S(m)} holds.

Given an integer K, list the K smallest Snuke numbers.

Constraints

1 \leq K

The K-th smallest Snuke number is not greater than 10^{15}.

Input

Input is given from Standard Input in the following format:

K

Output

Print K lines. The i-th line should contain the i-th smallest Snuke number.

Sample Input 1

10

Sample Output 1

1
2
3
4
5
6
7
8
9
19

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
using namespace std;

void QuickSort(int array[], int begin, int end) {
  int i = begin;
  int j = end;
  int pivot;
  int temp;
  
  pivot = array[ ( begin + end ) / 2 ];
  
  while(1) {
    while( array[i] < pivot ){ ++i; }
    while( array[j] > pivot ){ --j; }
    if (i >= j) break;
    
    temp = array[i];
    array[i] = array[j];
    array[j] = temp;
    i++;
    j--;
  }
  if( begin < i - 1 ){ QuickSort( array, begin, i - 1 ); }
  if( j + 1 < end ){ QuickSort( array, j + 1, end ); }
}

int S(int num) {
  int dig, sum = 0;
  
  while (num) {
    dig = num % 10;
    sum += dig;
    num /= 10;
  }
  
  return sum;
}

int SunukeCheck(int n, int m) {
  return (n / S(n) <= m / S(m) ? 1 : 0);
}

int main() {
  int n = 1, m = 2, sun, num, cnt = 0;
  cin >> num;
  
  while (cnt < num) {
    if (sun = SunukeCheck(n++, m++)) {
      cnt++;
      cout << sun << endl;
    }
  }
  
  return 0;
}