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
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
#include <bits/stdc++.h>
using namespace std;
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define e1 first
#define e2 second
#define OUT(x) {cout << x; exit(0); }
#define scanf(...) scanf(__VA_ARGS__)?:0
#define boost ios_base::sync_with_stdio(0); cin.tie(0)
#define FOR(i, a, b) for(int i=(a); i<=(b); ++i)
typedef long long int ll;
typedef unsigned long long ull;
typedef unsigned int ui;
typedef long double ld;
typedef pair <int, int> PII;
typedef pair <int, PII> PIP;
typedef pair <PII, int> PPI;
typedef pair <ll, ll> PLL;
typedef pair <PII, PII> PP;
const int mod = 1e9+7;
const int inf = 1e9+9;
const int MOD = 1e9+696969;
const ll INF = (ll)1e18 + 3;
const int maxn = 250100;
int ktore[maxn], tab[maxn];
ll n, k;
const int R = (1 << 18);
struct segmentTree {
ll dr[2 * R + 5];
segmentTree() {
	fill(dr, dr+2*R+3, 0);
}
inline void insert(int x, ll val) {
	assert(val >= 0);
	x += R;
	while (x) {
		dr[x] += val;
		dr[x] = min(dr[x], INF);
		x >>= 1;
	}
}
inline void czysc(int x) {
	x += R;
	dr[x] = 0;
	x >>= 1;
	while (x) {
		dr[x] = dr[x << 1 | 0] + dr[x << 1 | 1];
		dr[x] = min(dr[x], INF);
		x >>= 1;
	}
}
inline ll query(int x, int y) {
	x += R; y += R;
	if (x > y) return 0;
	if (x == y) return dr[x];
	ll ret = dr[x] + dr[y];
	ret = min(ret, INF);
	while (x + 1 < y) {
		if (!(x & 1)) ret += dr[x + 1];
		if (y & 1) ret += dr[y-1];
		ret = min(ret, INF);
		x >>= 1; y >>= 1;
	}
	return ret;
}

int search(int k) {
	assert(dr[1] >= k);
	int x = 1;
	while (x < R) {
		if (dr[2 * x] >= k) x *= 2;
		else k -= dr[2 * x], x = 2 * x + 1;
	}
	return x - R;
}
};

segmentTree depek;
vector <ll> dp[maxn];
void countDP(int range) {
	dp[0].pb(1);
	depek.insert(0, 1);
	for (ll i=1; i<=range; ++i) {
		for (ll j = 0; j <= i * (i - 1)/2; ++j) {
			int X = 0, Y = (int)dp[i-1].size() - 1;
			X = max(X, (int)(j - i + 1)); 
			Y = min(Y, (int)j);
			ll value = depek.query(X, Y);
			dp[i].pb(value);
			if (value >= INF) break;
		}
		
		for (int j=0; j<(int)dp[i-1].size(); ++j) depek.czysc(j);
		for (int j=0; j<(int)dp[i].size(); ++j) depek.insert(j, dp[i][j]);
	}
}

inline ll getDP(ll n, ll k) {
	ll inve = n * (n - 1) / 2;
	k = min(k, inve - k);
	//cout << "Getting: " << n << ' ' << k << endl;
	if (k < 0) return 0;
	if (k >= (int)dp[n].size()) return INF;
	return dp[n][k];
}

int main()
{
	boost;
	cin >> n >> k;
	ll m = n * (n - 1) / 2;
	if (m % 2 == 1) OUT("NIE");
	m /= 2;
	segmentTree elementy = segmentTree();
	FOR(i, 1, n) elementy.insert(i, 1);
	countDP(250000);
	if (getDP(n, m) < k) OUT("NIE");
	FOR(i, 1, n)
	{
		int skip = 0;
		int pocz = 0, kon = min(m, n - i);
		while (pocz < kon)
		{
			int sr = (pocz + kon)/2;
			if (getDP(n - i, m - sr) == 0) pocz = ++sr;
			else kon = sr;
		}
		skip = pocz;
		while (getDP(n - i, m - skip) < k)
		{
			k -= getDP(n - i, m - skip);
			++skip;
		}

		ktore[i] = elementy.search(1 + skip);
		elementy.czysc(ktore[i]);
		m -= skip;
	}
	cout << "TAK\n";
	FOR(i, 1, n) cout << ktore[i] << ' ';
}