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 PyPy3 (2.4.0) (judge verdict: Accepted)


import sys
#sys.stdin=open("data.txt")
input=sys.stdin.readline

nums=[]

num=0
pow10=1

# add a few possible answers
for i in range(16):
    t="9"*i
    if t!="": nums.append(int(t))
    for j in range(1,1000):
        t=str(j)+"9"*i
        if len(t)>15: continue
        nums.append(int(t))

def dsum(x):
    t=0
    while x:
        t+=x%10
        x//=10
    return t

# remove some bad numbers
out=[]
rat=[]
for i in sorted(set(nums)):
    j=i/dsum(i)
    while rat and rat[-1]>j:
        out.pop(-1)
        rat.pop(-1)
    out.append(i)
    rat.append(j)

#print(len(out))

#for i in range(len(out)): print(i,out[i],rat[i])

#for i in range(len(nums)):
#    print(i,dsum(nums[i]),nums[i]/dsum(nums[i]))

k=int(input())
for i in range(k):
    print(out[i])