1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
#include <bits/stdc++.h>
using namespace std;

#include <ext/pb_ds/tag_and_trait.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace __gnu_pbds;

typedef
tree<
  int,
  null_type,
  less<int>,
  rb_tree_tag,
  tree_order_statistics_node_update>
set_t;


typedef long long ll;
const ll inf = 1e18 + 1;
const int N = 250001;
vector<ll> dp[N];

ll get(ll n, ll k)
{
    if(k < dp[n].size()) return dp[n][k];
    k = n * (n - 1) / 2 - k;
    if(k < 0) return 0;
    if(k < dp[n].size()) return dp[n][k];
    return inf;
}

int main()
{
    ll n, k;
    scanf("%lld %lld", &n, &k);
    dp[0] = { 1LL };
    for(int i = 1; i <= n; i++)
    {
        long long m = 1LL * i * (i - 1) / 2;
        for(int j = 0; j <= m; j++)
        {
            ll t = 0;
            for(int k = j; k >= 0 && k > j - i; k--)
            {
                t += get(i - 1, k);
                if(t >= inf)
                {
                    t = inf;
                    break;
                }
            }
            if(t == inf) break;
            dp[i].push_back(t);
        }
    }
    if(n * (n - 1) % 4 || get(n, n * (n - 1) / 4) < k)
    {
        puts("NIE");
        return 0;
    }
    ll inv = n * (n - 1) / 4;
    puts("TAK");
    set_t l;
    for(int i = 1; i <= n; i++)
        l.insert(i);
    for(int i = 1; i <= n; i++)
    {
        ll nz = (n - i) * (n - i - 1) / 2;
        for(int j = max(0LL, inv - nz); ; j++)
            if(get(n - i, inv - j) >= k)
            {
                inv -= j;
                auto it = l.find_by_order(j);
                printf("%d ", *it);
                l.erase(it);
                break;
            }
            else k -= get(n - i, inv - j);
    }
    puts("");
}