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: Wrong Answer)

    #include <stdio.h>
    #include <stdlib.h>
    double fun(long long n)
    {
        long long sum=0;
        long long m=n;
        while(n>0)
        {
            sum+=n%10;
            n/=10;
        }
        return 1.0*m/sum;
    }
    int main()
    {
        long long k,i,j;
        long long count=0;
        scanf("%lld",&k);
        for(i=1;;i++)
        {
            if(fun(i+1)>=fun(i))
            {
                printf("%lld",i);
                count++;
                if(count<k)
                    printf("\n");
            }
            if(count==k)
                break;
        }
        return 0;
    }