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 getsn(long long int n)
    {
        int sum=0;
     
        while(n!=0)
        {
            sum=sum+n%10;
            n=n/10;
        }
        return sum;
    }
     
    int main()
    {
        int i, j, k, count;
        long long int x=1, n=1;
        scanf("%d", &k);
        puts("1");
        for(i=1; i<k; i++)
        {
            if((i-count)%9==0)
            {
                if(x+n>n*getsn(x+n))
                {
                    n=n*10;
                    count=0;
                }
                else
                {
                    count++;
                }
            }
            x=x+n;
            printf("%lld\n", x);
        }
        return 0;
    }