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: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

ll digit(ll n){
  ll num = 0;
  while(n != 0){
    n /= 10;
    num++;
  }
  return num;
}

double snuke(ll n){
  ll N = n;
  ll sum = 0;
  while(n != 0){
    sum += n % 10;
    n /= 10;
  }
  return (double)N / (double)sum;
}

ll f(ll N){
  ll d = digit(N) + 2;
  ll m = N;
  for(int i = 0; i <= d; i++){
    ll c = pow(10,i+1)*(N/pow(10,i+1) + 1) - 1;
    if(snuke(c) < snuke(m)) m = c;
  }
  return m;
}

int main(){
  ll K;
  cin >> K;
  ll N = 1;
  cout << 1 << endl;
  for(int i = 1; i < K; i++){
    cout << f(N+1) << endl;
    N = f(N+1);
  }
  return 0;
}