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 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
   
int main(void){
    int k,count=0;
    long long x=1,n=1;
    scanf("%d",&k);
    printf("1\n");
    for (int i=1; i<k; i++){
        long long m=x+n,s=0;
        while(m!=0){
            s+=m%10;
            m/=10;
        }
        if((i-count)%9==0){
            if(x+n>n*s){
                n=n*10;
                count=0;
            } else {
                count++;
            }
        }
        x+=n;
        printf("%lld\n",x);
    }
    return 0;
}