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: Runtime Error)

import math
#import datetime

def s(n):
	sum = 0
	for c in str(n):
		sum += int(c)
	return sum

k = int(input())
found=0

def next_sunuke(n, s_n, s_n_div):

	global found

	if n == 1:
		return

	m = n - 1
	s_mplus1 = s(m + 1)

	while m >= 1:
		s_m = s(m)

		if (s_m < s_mplus1 or (s_n - s_m != 1 and s_n - s_m != -8)) and m > 9:
			m -= 1
			s_mplus1 = s_m
			continue

		# print("check: " + str(m))

		s_m_div = m / s(m)

		if s_m_div <= s_n_div:
			next_sunuke(m, s_m, s_m_div)
			if found >= k:
				return

			found += 1
			# print("{0:5d}".format(m), "{0:2d}".format(s_m), s_m_div)
			print(m)
			break
		# else:
		# 	log_m = int(math.log(m,10))
		# 	if (m + 1) / (10 ** (log_m - 1)) == 19:

		# 		print ("skip: " + str(m) + " to " + str(10 ** log_m - 1))

		# 		m = 10 ** log_m - 1
		# 		s_mplus1 = s(m+1)
		# 		continue
		m -= 1
		s_mplus1 = s_m


# 適当な大きいスヌケ数
current_sunuke = 999999
s_current_sunuke = s(current_sunuke)
s_current_sunuke_div = current_sunuke / s_current_sunuke

#start = datetime.datetime.now()
next_sunuke(current_sunuke, s_current_sunuke, s_current_sunuke_div)
#end = datetime.datetime.now()
print(str(end-start))

# sunukes=[]

# n = current_sunuke - 1

# while(n >= 1):
# 	s_n = n / s(n)
# 	if s_n <= current_sunuke_n:
# 		#sunukes.insert(0,n)
# 		sunukes.append(n)
# 		current_sunuke = n
# 		current_sunuke_n = s_n
# 	n -= 1

# for n in sunukes:
# 	print (n)