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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include "bits/stdc++.h"
 
typedef long long ll;
#define int ll
#define fi first
#define se second
#define SORT(a) sort(a.begin(),a.end())
#define rep(i,n) for(int i = 0;i < (n) ; i++) 
#define REP(i,n) for(int i = 0;i < (n) ; i++) 
#define MP(a,b) make_pair(a,b)
#define pb(a) push_back(a)
#define INF LLONG_MAX/2

using namespace std;

int MOD = 1000000007;
int l[1000000]={1,
2,
3,
4,
5,
6,
7,
8,
9,
19,
29,
39,
49,
59,
69,
79,
89,
99,
199,
299,
399,
499,
599,
699,
799,
899,
999,
1099,
1199,
1299,
1399,
1499,
1599,
1699,
1799,
1899,
1999,
2999,
3999,
4999,
5999,
6999,
7999,
8999,
9999,
10999,
11999,
12999,
13999,
14999,
15999,
16999,
17999,
18999,
19999,
20999,
21999,
22999,
23999,
24999,
25999,
26999,
27999,
28999,
29999,
39999,
49999,
59999,
69999,
79999,
89999,
99999,
109999,
119999,
129999,
139999,
149999,
159999,
169999,
179999,
189999,
199999,
209999,
219999,
229999,
239999,
249999,
259999,
269999,
279999,
289999,
299999,
309999,
319999,
329999,
339999,
349999,
359999,
369999,
379999,
389999,
399999,
499999,
599999,
699999,
799999,
899999,
999999,
1099999,
1199999,
1299999,
1399999,
1499999,
1599999,
1699999,
1799999,
1899999,
1999999,
2099999,
2199999,
2299999,
2399999,
2499999,
2599999,
2699999,
2799999,
2899999,
2999999,
3099999,
3199999,
3299999,
3399999,
3499999,
3599999,
3699999,
3799999,
3899999,
3999999,
4099999,
4199999,
4299999,
4399999,
4499999,
4599999,
4699999,
4799999,
4899999,
4999999,
5999999,
6999999,
7999999,
8999999,
9999999,
10999999,
11999999,
12999999,
13999999,
14999999,
15999999,
16999999,
17999999,
18999999,
19999999,
20999999,
21999999,
22999999,
23999999,
24999999,
25999999,
26999999,
27999999,
28999999,
29999999,
30999999,
31999999,
32999999,
33999999,
34999999,
35999999,
36999999,
37999999,
38999999,
39999999,
40999999,
41999999,
42999999,
43999999,
44999999,
45999999,
46999999,
47999999,
48999999,
49999999,
50999999,
51999999,
52999999,
53999999,
54999999,
55999999,
56999999,
57999999,
58999999,
59999999,
69999999,
79999999,
89999999,
99999999,
109999999,
119999999,
129999999,
139999999,
149999999,
159999999,
169999999,
179999999,
189999999,
199999999,
209999999,
219999999,
229999999,
239999999,
249999999,
259999999,
269999999,
279999999,
289999999,
299999999,
309999999,
319999999,
329999999,
339999999,
349999999,
359999999,
369999999,
379999999,
389999999,
399999999,
409999999,
419999999,
429999999,
439999999,
449999999,
459999999,
469999999,
479999999,
489999999,
499999999,
509999999,
519999999,
529999999,
539999999,
549999999,
559999999,
569999999,
579999999,
589999999,
599999999,
609999999,
619999999,
629999999,
639999999,
649999999,
659999999,
669999999,
679999999,
689999999,
699999999,
799999999,
899999999,
999999999,
1099999999,
1199999999,
1299999999,
1399999999,
1499999999,
1599999999,
1699999999,
1799999999,
1899999999,
1999999999,
2099999999,
2199999999,
2299999999,
2399999999,
2499999999,
2599999999,
2699999999,
2799999999,
2899999999,
2999999999,
3099999999,
3199999999,
3299999999,
3399999999,
3499999999,
3599999999,
3699999999,
3799999999,
3899999999,
3999999999,
4099999999,
4199999999,
4299999999,
4399999999,
4499999999,
4599999999,
4699999999,
4799999999,
4899999999,
4999999999,
5099999999,
5199999999,
5299999999,
5399999999,
5499999999,
5599999999,
5699999999,
5799999999,
5899999999,
5999999999,
6099999999,
6199999999,
6299999999,
6399999999,
6499999999,
6599999999,
6699999999,
6799999999,
6899999999,
6999999999,
7099999999,
7199999999,
7299999999,
7399999999,
7499999999,
7599999999,
7699999999,
7799999999,
7899999999,
7999999999,
8999999999,
9999999999,
10999999999,
11999999999,
12999999999,
13999999999,
14999999999,
15999999999,
16999999999,
17999999999,
18999999999,
19999999999,
20999999999,
21999999999,
22999999999,
23999999999,
24999999999,
25999999999,
26999999999,
27999999999,
28999999999,
29999999999,
30999999999,
31999999999,
32999999999,
33999999999,
34999999999,
35999999999,
36999999999,
37999999999,
38999999999,
39999999999,
40999999999,
41999999999,
42999999999,
43999999999,
44999999999,
45999999999,
46999999999,
47999999999,
48999999999,
49999999999,
50999999999,
51999999999,
52999999999,
53999999999,
54999999999,
55999999999,
56999999999,
57999999999,
58999999999,
59999999999,
60999999999,
61999999999,
62999999999,
63999999999,
64999999999,
65999999999,
66999999999,
67999999999,
68999999999,
69999999999,
70999999999,
71999999999,
72999999999,
73999999999,
74999999999,
75999999999,
76999999999,
77999999999,
78999999999,
79999999999,
80999999999,
81999999999,
82999999999,
83999999999,
84999999999,
85999999999,
86999999999,
87999999999,
88999999999,
89999999999,
99999999999,
109999999999,
119999999999,
129999999999,
139999999999,
149999999999,
159999999999,
169999999999,
179999999999,
189999999999,
199999999999,
209999999999,
219999999999,
229999999999,
239999999999,
249999999999,
259999999999,
269999999999,
279999999999,
289999999999,
299999999999,
309999999999,
319999999999,
329999999999,
339999999999,
349999999999,
359999999999,
369999999999,
379999999999,
389999999999,
399999999999,
409999999999,
419999999999,
429999999999,
439999999999,
449999999999,
459999999999,
469999999999,
479999999999,
489999999999,
499999999999,
509999999999,
519999999999,
529999999999,
539999999999,
549999999999,
559999999999,
569999999999,
579999999999,
589999999999,
599999999999,
609999999999,
619999999999,
629999999999,
639999999999,
649999999999,
659999999999,
669999999999,
679999999999,
689999999999,
699999999999,
709999999999,
719999999999,
729999999999,
739999999999,
749999999999,
759999999999,
769999999999,
779999999999,
789999999999,
799999999999,
809999999999,
819999999999,
829999999999,
839999999999,
849999999999,
859999999999,
869999999999,
879999999999,
889999999999,
899999999999,
909999999999,
919999999999,
929999999999,
939999999999,
949999999999,
959999999999,
969999999999,
979999999999,
989999999999,
999999999999,
1099999999999,
1199999999999,
1299999999999,
1399999999999,
1499999999999,
1599999999999,
1699999999999,
1799999999999,
1899999999999,
1999999999999,
2099999999999,
2199999999999,
2299999999999,
2399999999999,
2499999999999,
2599999999999,
2699999999999,
2799999999999,
2899999999999,
2999999999999,
3099999999999,
3199999999999,
3299999999999,
3399999999999,
3499999999999,
3599999999999,
3699999999999,
3799999999999,
3899999999999,
3999999999999,
4099999999999,
4199999999999,
4299999999999,
4399999999999,
4499999999999,
4599999999999,
4699999999999,
4799999999999,
4899999999999,
4999999999999,
5099999999999,
5199999999999,
5299999999999,
5399999999999,
5499999999999,
5599999999999,
5699999999999,
5799999999999,
5899999999999,
5999999999999,
6099999999999,
6199999999999,
6299999999999,
6399999999999,
6499999999999,
6599999999999,
6699999999999,
6799999999999,
6899999999999,
6999999999999,
7099999999999,
7199999999999,
7299999999999,
7399999999999,
7499999999999,
7599999999999,
7699999999999,
7799999999999,
7899999999999,
7999999999999,
8099999999999,
8199999999999,
8299999999999,
8399999999999,
8499999999999,
8599999999999,
8699999999999,
8799999999999,
8899999999999,
8999999999999,
9099999999999,
9199999999999,
9299999999999,
9399999999999,
9499999999999,
9599999999999,
9699999999999,
9799999999999,
9899999999999,
9999999999999,
10999999999999,
11999999999999,
12999999999999,
13999999999999,
14999999999999,
15999999999999,
16999999999999,
17999999999999,
18999999999999,
19999999999999,
20999999999999,
21999999999999,
22999999999999,
23999999999999,
24999999999999,
25999999999999,
26999999999999,
27999999999999,
28999999999999,
29999999999999,
30999999999999,
31999999999999,
32999999999999,
33999999999999,
34999999999999,
35999999999999,
36999999999999,
37999999999999,
38999999999999,
39999999999999,
40999999999999,
41999999999999,
42999999999999,
43999999999999,
44999999999999,
45999999999999,
46999999999999,
47999999999999,
48999999999999,
49999999999999,
50999999999999,
51999999999999,
52999999999999,
53999999999999,
54999999999999,
55999999999999,
56999999999999,
57999999999999,
58999999999999,
59999999999999,
60999999999999,
61999999999999,
62999999999999,
63999999999999,
64999999999999,
65999999999999,
66999999999999,
67999999999999,
68999999999999,
69999999999999,
70999999999999,
71999999999999,
72999999999999,
73999999999999,
74999999999999,
75999999999999,
76999999999999,
77999999999999,
78999999999999,
79999999999999,
80999999999999,
81999999999999,
82999999999999,
83999999999999,
84999999999999,
85999999999999,
86999999999999,
87999999999999,
88999999999999,
89999999999999,
90999999999999,
91999999999999,
92999999999999,
93999999999999,
94999999999999,
95999999999999,
96999999999999,
97999999999999,
98999999999999,
99999999999999,
100999999999999,
101999999999999,
102999999999999,
103999999999999,
104999999999999,
105999999999999,
106999999999999,
107999999999999,
108999999999999,
109999999999999,
119999999999999,
129999999999999,
139999999999999,
149999999999999,
159999999999999,
169999999999999,
179999999999999,
189999999999999,
199999999999999,
209999999999999,
219999999999999,
229999999999999,
239999999999999,
249999999999999,
259999999999999,
269999999999999,
279999999999999,
289999999999999,
299999999999999,
309999999999999,
319999999999999,
329999999999999,
339999999999999,
349999999999999,
359999999999999,
369999999999999,
379999999999999,
389999999999999,
399999999999999,
409999999999999,
419999999999999,
429999999999999,
439999999999999,
449999999999999,
459999999999999,
469999999999999,
479999999999999,
489999999999999,
499999999999999,
509999999999999,
519999999999999,
529999999999999,
539999999999999,
549999999999999,
559999999999999,
569999999999999,
579999999999999,
589999999999999,
599999999999999,
609999999999999,
619999999999999,
629999999999999,
639999999999999,
649999999999999,
659999999999999,
669999999999999,
679999999999999,
689999999999999,
699999999999999,
709999999999999,
719999999999999,
729999999999999,
739999999999999,
749999999999999,
759999999999999,
769999999999999,
779999999999999,
789999999999999,
799999999999999,
809999999999999,
819999999999999,
829999999999999,
839999999999999,
849999999999999,
859999999999999,
869999999999999,
879999999999999,
889999999999999,
899999999999999,
909999999999999,
919999999999999,
929999999999999,
939999999999999,
949999999999999,
959999999999999,
969999999999999,
979999999999999,
989999999999999};
signed main(){
    
    int k;
    cin >> k;
    rep(i,k){
        cout << l[i] << endl;
    }
    
    
    return 0;
}
// g++ -std=c++14 code1.cpp
// rm -r -f test;oj dl