#include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> using namespace __gnu_pbds; using namespace std; template<class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>; #ifdef LOCAL template <class T, class U> ostream& operator<<(ostream& os, pair<T, U> p) { return os << "(" << p.first << ", " << p.second << ")"; } template<template<class, class...> class C, class... A> typename enable_if<!is_same<C<A...>, string>::value, ostream&>::type operator<<(ostream& os, C<A...> c) { auto i = c.begin(); while (i != c.end()) { os << " {"[i == c.begin()] << *i; os << ",}"[++i == c.end()]; } return os; } #define debug(x) { cerr << #x << " = " << x << endl; } #else #define debug(...) {} #endif vector<int> rozw; long long inf = 1LL<<60; const int N = 250 * 1000 + 5; vector<long long> newt[N]; void preprocess() { int MAX = 0; for (int n = 1; n < N; n ++) { newt[n].push_back(1); for (int k = 1; 2 * k <= n; k ++) { int mno = n - k + 1; int dziel = k; int g = __gcd(mno, dziel); mno /= g; dziel /= g; long long x = newt[n].back() / dziel; if (x >= (inf + mno - 1) / mno) break; x *= mno; if (x <= inf) newt[n].push_back(x); else break; MAX = max(MAX, k); } } debug(MAX); } inline long long newton(int a, int b) { if (b > a) return 0; if (b == 0) return 1; b = min(b, a - b); if (b >= newt[a].size()) return inf; // debug(make_pair(a, b)); // debug(newt[a][b]); return newt[a][b]; } map<pair<pair<int,int>, int>, long long> mem; inline long long int suma(int n) { return ((long long)n * (n - 1)) / 2; } vector<vector<long long>> wzo[N]; long long int wzorek(int n, int d, long long k) { long long int s = suma(n) - suma(d); k = min(k, s - k); if (k < 0) return 0; // if (k == 0) return 1; if (d >= n) return 1; if (k <= d) { return newton(n - d + k - 1, k); } // if (d == 0 && n >= 500 && k >= 10) return inf; if (wzo[n].size() <= d) { assert(wzo[n].size() == d); wzo[n].push_back(vector<long long>(d + 1, 1)); } if (wzo[n][d].size() > k) return wzo[n][d][k]; if (wzo[n][d].back() >= inf) return inf; assert (wzo[n][d].size() == k); long long wynik = 0; // { for (int ile = 0; wynik < inf && ile <= min(k, (long long)d); ile ++) { wynik += wzorek(n, d + 1, k - ile); } wynik = min(inf, wynik); // } wzo[n][d].push_back(wynik); return wynik; } vector<int> solution; bool szukaj(int n, long long k) { solution.resize(n); long long inw = ((long long)n * (n - 1)) / 4; if (((long long)n * (n - 1)) % 4 != 0) return false; int id = 1, ile; for (;id <= n; id ++) { if (suma(id) > inw) { ile = inw - suma(id - 1); break; } } if (id == n + 1) return false; while (inw > 0 && k >= 0) { debug(inw); debug(k); debug(id); debug(ile); if (ile == id) { ile = 0; id ++; } if (id > n) return false; long long w = wzorek(id - 1, 0, inw - ile); debug(w); if (w < k) { k -= w; ile ++; } else if (w == k) { solution[n - id] = ile; inw -= ile; for (int i = id - 1; i > 1; i --) { solution[n - i] = min(inw, (long long)(i - 1)); inw -= i - 1; inw = max(inw, 0LL); } break; } else { inw -= ile; solution[n - id] = ile; for (;id > 0; id --) { if (suma(id - 1) <= inw) { ile = inw - suma(id - 1); break; } } } } debug(solution); return true; } ordered_set<int> numbers; int main() { preprocess(); // debug(wzorek(4, 0, 3)); // debug(wzorek(4, 0, 2)); int last = 0; for (int n = 1; n < N; n ++) { // for (int n = 1; n <= 1000; n ++) { //wzo[n][0][0] = 1 wzo[n].push_back(vector<long long>(1, 1LL)); for (int k = 0; 2 * k <= suma(n); k ++) { long long w = wzorek(n, 0, k); if (w >= inf) { break; } // assert(wzo[n][0].back() <= w); // wzo[n][0].push_back(w); assert(2 * k > suma(n - 1) || wzo[n][0].back() >= wzorek(n - 1, 0, k)); } // debug(n); // debug(wzo[n].size()); } int n; long long k; scanf("%d%lld", &n, &k); for (int i = 1; i <= n; i ++) { numbers.insert(i); } if (not szukaj(n, k)) printf("NIE\n"); else { printf("TAK\n"); for (int x : solution) { int y = *numbers.find_by_order(x); numbers.erase(y); printf("%d ", y); } printf("\n"); debug(solution); } }
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 | #include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> using namespace __gnu_pbds; using namespace std; template<class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>; #ifdef LOCAL template <class T, class U> ostream& operator<<(ostream& os, pair<T, U> p) { return os << "(" << p.first << ", " << p.second << ")"; } template<template<class, class...> class C, class... A> typename enable_if<!is_same<C<A...>, string>::value, ostream&>::type operator<<(ostream& os, C<A...> c) { auto i = c.begin(); while (i != c.end()) { os << " {"[i == c.begin()] << *i; os << ",}"[++i == c.end()]; } return os; } #define debug(x) { cerr << #x << " = " << x << endl; } #else #define debug(...) {} #endif vector<int> rozw; long long inf = 1LL<<60; const int N = 250 * 1000 + 5; vector<long long> newt[N]; void preprocess() { int MAX = 0; for (int n = 1; n < N; n ++) { newt[n].push_back(1); for (int k = 1; 2 * k <= n; k ++) { int mno = n - k + 1; int dziel = k; int g = __gcd(mno, dziel); mno /= g; dziel /= g; long long x = newt[n].back() / dziel; if (x >= (inf + mno - 1) / mno) break; x *= mno; if (x <= inf) newt[n].push_back(x); else break; MAX = max(MAX, k); } } debug(MAX); } inline long long newton(int a, int b) { if (b > a) return 0; if (b == 0) return 1; b = min(b, a - b); if (b >= newt[a].size()) return inf; // debug(make_pair(a, b)); // debug(newt[a][b]); return newt[a][b]; } map<pair<pair<int,int>, int>, long long> mem; inline long long int suma(int n) { return ((long long)n * (n - 1)) / 2; } vector<vector<long long>> wzo[N]; long long int wzorek(int n, int d, long long k) { long long int s = suma(n) - suma(d); k = min(k, s - k); if (k < 0) return 0; // if (k == 0) return 1; if (d >= n) return 1; if (k <= d) { return newton(n - d + k - 1, k); } // if (d == 0 && n >= 500 && k >= 10) return inf; if (wzo[n].size() <= d) { assert(wzo[n].size() == d); wzo[n].push_back(vector<long long>(d + 1, 1)); } if (wzo[n][d].size() > k) return wzo[n][d][k]; if (wzo[n][d].back() >= inf) return inf; assert (wzo[n][d].size() == k); long long wynik = 0; // { for (int ile = 0; wynik < inf && ile <= min(k, (long long)d); ile ++) { wynik += wzorek(n, d + 1, k - ile); } wynik = min(inf, wynik); // } wzo[n][d].push_back(wynik); return wynik; } vector<int> solution; bool szukaj(int n, long long k) { solution.resize(n); long long inw = ((long long)n * (n - 1)) / 4; if (((long long)n * (n - 1)) % 4 != 0) return false; int id = 1, ile; for (;id <= n; id ++) { if (suma(id) > inw) { ile = inw - suma(id - 1); break; } } if (id == n + 1) return false; while (inw > 0 && k >= 0) { debug(inw); debug(k); debug(id); debug(ile); if (ile == id) { ile = 0; id ++; } if (id > n) return false; long long w = wzorek(id - 1, 0, inw - ile); debug(w); if (w < k) { k -= w; ile ++; } else if (w == k) { solution[n - id] = ile; inw -= ile; for (int i = id - 1; i > 1; i --) { solution[n - i] = min(inw, (long long)(i - 1)); inw -= i - 1; inw = max(inw, 0LL); } break; } else { inw -= ile; solution[n - id] = ile; for (;id > 0; id --) { if (suma(id - 1) <= inw) { ile = inw - suma(id - 1); break; } } } } debug(solution); return true; } ordered_set<int> numbers; int main() { preprocess(); // debug(wzorek(4, 0, 3)); // debug(wzorek(4, 0, 2)); int last = 0; for (int n = 1; n < N; n ++) { // for (int n = 1; n <= 1000; n ++) { //wzo[n][0][0] = 1 wzo[n].push_back(vector<long long>(1, 1LL)); for (int k = 0; 2 * k <= suma(n); k ++) { long long w = wzorek(n, 0, k); if (w >= inf) { break; } // assert(wzo[n][0].back() <= w); // wzo[n][0].push_back(w); assert(2 * k > suma(n - 1) || wzo[n][0].back() >= wzorek(n - 1, 0, k)); } // debug(n); // debug(wzo[n].size()); } int n; long long k; scanf("%d%lld", &n, &k); for (int i = 1; i <= n; i ++) { numbers.insert(i); } if (not szukaj(n, k)) printf("NIE\n"); else { printf("TAK\n"); for (int x : solution) { int y = *numbers.find_by_order(x); numbers.erase(y); printf("%d ", y); } printf("\n"); debug(solution); } } |