#define LOCAL #include using namespace std; #pragma region Macros typedef long long ll; typedef __int128_t i128; typedef unsigned int uint; typedef unsigned long long ull; #define ALL(x) (x).begin(), (x).end() template istream& operator>>(istream& is, vector& v) { for (T& x : v) is >> x; return is; } template ostream& operator<<(ostream& os, const vector& v) { for (int i = 0; i < (int)v.size(); i++) { os << v[i] << (i + 1 == (int)v.size() ? "" : " "); } return os; } template ostream& operator<<(ostream& os, const pair& p) { os << '(' << p.first << ',' << p.second << ')'; return os; } template ostream& operator<<(ostream& os, const tuple& t) { os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ')'; return os; } template ostream& operator<<(ostream& os, const tuple& t) { os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ',' << get<3>(t) << ')'; return os; } template ostream& operator<<(ostream& os, const map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const multiset& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const deque& v) { for (int i = 0; i < (int)v.size(); i++) { os << v[i] << (i + 1 == (int)v.size() ? "" : " "); } return os; } void debug_out() { cerr << '\n'; } template void debug_out(Head&& head, Tail&&... tail) { cerr << head; if (sizeof...(Tail) > 0) cerr << ", "; debug_out(move(tail)...); } #ifdef LOCAL #define debug(...) \ cerr << " "; \ cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \ cerr << " "; \ debug_out(__VA_ARGS__) #else #define debug(...) 42 #endif template T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; } template T lcm(T x, T y) { return x / gcd(x, y) * y; } template inline bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; } #pragma endregion const int INF = 1e9; const long long IINF = 1e18; const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; const char dir[4] = {'D', 'R', 'U', 'L'}; const long long MOD = 1000000007; // const long long MOD = 998244353; int calc(int x, int y) { return !(__builtin_popcount(x * y) & 1); } int f(int P, const vector& X) { int res = 0; for (int i = 0; i < P; i++) { for (int j = 0; j < P; j++) { res += calc(X[i], X[j]); } } return res; } bool check(int N, int M, int P, int Q, const vector& X, const vector& Y) { if (P < 0 || Q < 0) return false; if (P + Q != N) return false; vector used(N + 1, false); for (int x : X) { if (x < 1 || N < x) return false; if (used[x]) return false; used[x] = true; } for (int y : Y) { if (y < 1 || N < y) return false; if (used[y]) return false; used[y] = true; } return f(P, X) - f(Q, Y) == M; } int main() { cin.tie(0); ios::sync_with_stdio(false); int N, M; cin >> N >> M; vector cnt(N, 0); int sum = 0; for (int i = 1; i <= N; i++) { for (int j = 1; j <= N; j++) cnt[i - 1] += calc(i, j); sum += cnt[i - 1]; } M = sum - M; if (M < 0 || (M & 1)) { cout << -1 << '\n'; return 0; } M >>= 1; vector> dp(N + 1, vector(M + 1, 0)); dp[0][0] = 1; for (int i = 0; i < N; i++) { for (int j = 0; j <= M; j++) { if (dp[i][j] == 0) continue; dp[i + 1][j] = 1; if (j + cnt[i] <= M) dp[i + 1][j + cnt[i]] = -1; } } if (dp[N][M] == 0) { cout << -1 << '\n'; return 0; } vector X, Y; int cur = M; for (int i = N; i > 0; i--) { int nxt = dp[i][cur]; if (nxt == 1) X.emplace_back(i); else { Y.emplace_back(i); cur -= cnt[i - 1]; } } reverse(X.begin(), X.end()); reverse(Y.begin(), Y.end()); int P = X.size(), Q = Y.size(); assert(check(N, sum - M * 2, P, Q, X, Y)); cout << P << ' ' << Q << '\n'; for (int i = 0; i < P; i++) cout << X[i] << (i + 1 == P ? '\n' : ' '); for (int i = 0; i < Q; i++) cout << Y[i] << (i + 1 == Q ? '\n' : ' '); return 0; }