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>
#include<vector>
using namespace std;
int dsum(long long int x){
    int ret = 0;
    while(x>0){
        ret+= x%10;
        x/=10;
    }
    return ret;
}
int main(){
    vector<long long> a;
    vector<long long> b;
    for(int i=0;i<16;++i){
        for(int j=1;j<10;++j){
           long long x=j;
           for(int k=0;k<i;++k){
               x=x*10+9;
           }
           a.push_back(x);
           b.push_back(dsum(x));
        }
    }
    int k;
    cin>>k;
    for(int i=0;i<k;++i){
        cout<<a[i]<<"\n";
    }
    

}