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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; typedef vector vi; typedef pair pii; typedef long long ll; typedef unsigned long long ull; typedef short int sint; #define FOR(x, b, e) for(int x=(b); x<=(e); ++x) #define FORD(x, b, e) for(int x=((int)(b))-1; x>=(e); --x) #define REP(x, n) for(int x=0; x<(n); ++x) #define ALL(c) c.begin(),c.end() #define SIZE(x) ((int)((x).size())) #define PB push_back #define ST first #define ND second #define mp(x,y) make_pair(x,y) #define DEBUG 1 #define debug(x) {if (DEBUG)cerr <<#x <<" = " < vals; } F[N]; vi res; ll n, k; ull f(ll nn, ll inw) { ll maksInw = ((nn * (nn - 1)) /2); if (inw > maksInw) { return 0; } ll tinw = min(maksInw - inw, inw); if (nn == 0) { return 0; } if (tinw > F[nn].goodLastInd) { return inf; } return F[nn].vals[tinw]; } void solve(ll inw, ll kk) { FOR(nnn, 1, n - 1) { ll nn = n - nnn + 1; int index = 0; ll maksInw = ((nn - 2) * (nn - 1)) / 2; index = max(0LL, inw - maksInw); while (true) { ull ifThis = f(nn - 1, inw - index); if (ifThis >= kk) { res.PB(index + 1); inw = inw - index; break; } else { kk -= ifThis; ++index; } } } res.PB(1); } void precompute() { F[1].goodLastInd = 0; F[1].vals.PB(1); for (ll n = 2; n < N; ++n) { ll limit = (n * (n - 1)) / 2; ll inw = 0; while (inw <= limit) { ll temp = 0; for (ll i = max(inw - (n - 1), 0LL); i <= inw; ++i) { temp = temp + f(n - 1, i); if (temp >= inf) { break; } } if (temp >= inf) { break; } else { F[n].goodLastInd = inw; F[n].vals.PB(temp); } ++inw; } } } const int NNN = 1 << 18; int tree[2 * NNN], P; int get(int kt, int ind = 1) { if (ind >= P) { int res = ind - P + 1; while (ind) { --tree[ind]; ind>>=1; } return res; } if (kt <= tree[2 * ind]) { return get(kt, 2 * ind); } else { return get(kt - tree[2 * ind], 2 * ind + 1); } } int main() { precompute(); scanf("%lld %lld", &n, &k); if ((n * (n - 1)) % 4 != 0) { printf("NIE\n"); } else { ull required = (n * (n - 1)) / 4; ull howMany = f(n, required); if (howMany < k) { printf("NIE\n"); } else { solve(required, k); P = 1; while (P < n) { P <<= 1; } REP(i, n) tree[P + i] = 1; FORD(i, P, 1) { tree[i] = tree[2 * i] + tree[2 * i + 1]; } printf("TAK\n"); REP(i, n) printf("%d ", get(res[i])); printf("\n"); } } return 0; }