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 Python (3.4.3) (judge verdict: Wrong Answer)

m=float("INF")
sunukes=[]
for i in range(15,-1,-1):
    for j in range(100,10,-1):
        #print(i,j)
        sunuke=j*(10**i)-1
        s=str(sunuke)
        sn=0
        for k in range(len(s)):
            sn+=int(s[k])
        x=sunuke/sn
        #print(sn,x,i,j,j*10**i-1)
        if x<=m :
            m=x
            sunukes.append(sunuke)
for i in range(9,0,-1):
    sunukes.append(i)
sunukes=sunukes[::-1]
k=int(input())
#print(sunukes)
for i in range(k):
    print(sunukes[i])