#line 1 "test/yj_rectangle_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/rectangle_sum"
#include <cstdint>
#include <cstdio>
#include <algorithm>
#include <tuple>
#include <vector>
#line 1 "DataStructure/rectangle_query.cpp"
/**
* @brief 矩形クエリ
* @author えびちゃん
*/
#include <cstddef>
#line 11 "DataStructure/rectangle_query.cpp"
#include <array>
#include <optional>
#line 15 "DataStructure/rectangle_query.cpp"
#line 1 "DataStructure/bit_vector.cpp"
/**
* @brief rank/select 辞書
* @author えびちゃん
*/
#include <climits>
#line 13 "DataStructure/bit_vector.cpp"
#line 1 "utility/literals.cpp"
/**
* @brief ユーザ定義リテラル
* @author えびちゃん
*/
#line 11 "utility/literals.cpp"
constexpr intmax_t operator ""_jd(unsigned long long n) { return n; }
constexpr uintmax_t operator ""_ju(unsigned long long n) { return n; }
constexpr size_t operator ""_zu(unsigned long long n) { return n; }
constexpr ptrdiff_t operator ""_td(unsigned long long n) { return n; }
constexpr int8_t operator ""_i8(unsigned long long n) { return n; }
constexpr int16_t operator ""_i16(unsigned long long n) { return n; }
constexpr int32_t operator ""_i32(unsigned long long n) { return n; }
constexpr int64_t operator ""_i64(unsigned long long n) { return n; }
constexpr uint8_t operator ""_u8(unsigned long long n) { return n; }
constexpr uint16_t operator ""_u16(unsigned long long n) { return n; }
constexpr uint32_t operator ""_u32(unsigned long long n) { return n; }
constexpr uint64_t operator ""_u64(unsigned long long n) { return n; }
#line 15 "DataStructure/bit_vector.cpp"
class bit_vector {
public:
using underlying_type = uintmax_t;
using size_type = size_t;
using difference_type = ptrdiff_t;
private:
static const size_type S_ws = CHAR_BIT * sizeof(underlying_type);
std::vector<underlying_type> M_c;
std::vector<size_type> M_r;
std::vector<size_type> M_s0, M_s1;
std::vector<std::vector<size_type>> M_ss0, M_ss1;
static size_type S_popcount(underlying_type n) {
return __builtin_popcountll(n);
}
static underlying_type S_least_n_bits(size_type n) {
return (1_ju << n) - 1;
}
template <int Bp>
static size_type S_rank_small(underlying_type x, size_type n) {
if (Bp == 0) x = ~x;
return S_popcount(x & S_least_n_bits(n));
}
template <int Bp>
static size_type S_select_small(underlying_type x, size_type n) {
if (n == 0) return 0;
size_type lb = 0;
size_type ub = S_ws;
while (ub-lb > 1) {
size_type mid = (lb+ub) >> 1;
((S_rank_small<Bp>(x, mid) < n)? lb: ub) = mid;
}
return ub;
}
template <int Bp>
size_type M_rank_large(size_type n) const {
// if (n == 0) return 0;
size_type res = M_r[n];
if (Bp == 0) res = n * S_ws - res;
return res;
}
template <int Bp>
void M_prepare_select(std::vector<bool> const& bv,
std::vector<size_type>& s,
std::vector<std::vector<size_type>>& ss) {
size_type z = 0;
size_type n = bv.size();
s.push_back(0);
std::vector<size_type> tmp;
for (size_type i = 0; i < n; ++i) {
if (bv[i] != Bp) continue;
tmp.push_back(i);
if (++z == S_ws) {
size_type len = i+1 - s.back();
s.push_back(i+1);
ss.emplace_back();
if (len >= S_ws * S_ws) ss.back() = std::move(tmp);
tmp.clear();
z = 0;
}
}
ss.push_back(std::move(tmp));
}
template <int Bp>
size_type M_select(size_type n,
std::vector<size_type> const& s,
std::vector<std::vector<size_type>> const& ss) const {
if (n-- == 0) return 0;
size_type j0 = n / S_ws;
size_type j1 = n % S_ws;
if (j0 >= s.size()) return -1_zu;
if (j0+1 == s.size() && j1 >= ss[j0].size()) return -1_zu;
if (!ss[j0].empty()) return ss[j0][j1] + 1;
size_type lb = s[j0] / S_ws;
size_type ub = (j0+1 < s.size())? (s[j0+1]+S_ws-1) / S_ws: M_r.size();
while (ub-lb > 1) {
size_type mid = (lb+ub) >> 1;
((M_rank_large<Bp>(mid) <= n)? lb: ub) = mid;
}
return lb * S_ws + S_select_small<Bp>(M_c[lb], n+1 - M_rank_large<Bp>(lb));
}
public:
bit_vector() = default;
bit_vector(bit_vector const&) = default;
bit_vector(bit_vector&&) = default;
template <typename InputIt>
bit_vector(InputIt first, InputIt last) { assign(first, last); }
bit_vector& operator =(bit_vector const&) = default;
bit_vector& operator =(bit_vector&&) = default;
template <typename InputIt>
void assign(InputIt first, InputIt last) {
std::vector<bool> tmp(first, last);
M_c.resize(tmp.size() / S_ws + 1);
for (size_type i = 0; i < tmp.size(); ++i) {
if (!tmp[i]) continue;
size_type j0 = i / S_ws;
size_type j1 = i % S_ws;
M_c[j0] |= 1_ju << j1;
}
// rank
M_r.assign(M_c.size(), 0);
for (size_type i = 1; i < M_c.size(); ++i)
M_r[i] += M_r[i-1] + S_popcount(M_c[i-1]);
// select
M_prepare_select<0>(tmp, M_s0, M_ss0);
M_prepare_select<1>(tmp, M_s1, M_ss1);
}
size_type rank0(size_type t) const {
return t - rank1(t);
}
size_type rank1(size_type t) const {
size_type j0 = t / S_ws;
size_type j1 = t % S_ws;
return M_r[j0] + S_popcount(S_least_n_bits(j1) & M_c[j0]);
}
size_type rank0(size_type s, size_type t) const {
return (t-s) - rank1(s, t);
}
size_type rank1(size_type s, size_type t) const {
if (s == t) return 0;
return rank1(t) - rank1(s);
}
size_type select0(size_type n) const {
return M_select<0>(n, M_s0, M_ss0);
}
size_type select1(size_type n) const {
return M_select<1>(n, M_s1, M_ss1);
}
size_type select0(size_type n, size_type s) const {
n += rank0(0, s);
return M_select<0>(n, M_s0, M_ss0);
}
size_type select1(size_type n, size_type s) const {
n += rank1(0, s);
return M_select<1>(n, M_s1, M_ss1);
}
};
#line 17 "DataStructure/rectangle_query.cpp"
template <size_t Nb, typename Group = uintmax_t, typename Int = uintmax_t>
class rectangle_query {
public:
using int_type = Int;
using value_type = Group;
using size_type = size_t;
using optional_type = std::optional<int_type>;
private:
std::array<bit_vector, Nb> M_a = {};
std::array<std::vector<value_type>, Nb> M_s = {};
std::array<size_type, Nb> M_z = {};
size_type M_startpos(int_type x) const {
size_type s = 0, t = 0;
for (size_type i = Nb; i-- > 1;) {
size_type j = Nb-i-1;
if (x >> i & 1) {
s = M_z[j] + M_a[j].rank1(s);
t = M_z[j] + M_a[j].rank1(t);
} else {
s = M_a[j].rank0(s);
t = M_a[j].rank0(t);
}
}
return s;
}
public:
rectangle_query() = default;
template <typename InputItY, typename InputItZ>
rectangle_query(
InputItY y_first, InputItY y_last, InputItZ z_first, InputItZ z_last
) { assign(y_first, y_last, z_first, z_last); }
rectangle_query(
std::initializer_list<int_type> y_il,
std::initializer_list<value_type> z_il
) { assign(y_il, z_il); }
template <typename ForwardIt>
rectangle_query(ForwardIt first, ForwardIt last) { assign(first, last); }
template <typename InputItY, typename InputItZ>
void assign(InputItY y_first, InputItY y_last, InputItZ z_first, InputItZ z_last) {
std::vector<int_type> y_whole(y_first, y_last);
std::vector<value_type> z_whole(z_first, z_last);
M_z = {};
M_s = {};
size_type n = y_whole.size();
for (size_type i = Nb; i--;) {
std::vector<int_type> y_zero, y_one;
std::vector<value_type> z_zero, z_one;
std::vector<bool> vb(n);
for (size_type j = 0; j < n; ++j) {
((y_whole[j] >> i & 1)? y_one: y_zero).push_back(y_whole[j]);
((y_whole[j] >> i & 1)? z_one: z_zero).push_back(z_whole[j]);
vb[j] = (y_whole[j] >> i & 1);
}
M_z[Nb-i-1] = y_zero.size();
M_a[Nb-i-1] = bit_vector(vb.begin(), vb.end());
y_whole = std::move(y_zero);
y_whole.insert(y_whole.end(), y_one.begin(), y_one.end());
z_whole = std::move(z_zero);
z_whole.insert(z_whole.end(), z_one.begin(), z_one.end());
M_s[Nb-i-1] = z_whole;
M_s[Nb-i-1].insert(M_s[Nb-i-1].begin(), value_type{});
for (size_type j = 1; j <= n; ++j) M_s[Nb-i-1][j] += M_s[Nb-i-1][j-1];
}
}
void assign(
std::initializer_list<int_type> y_il, std::initializer_list<value_type> z_il
) { assign(y_il.begin(), y_il.end(), z_il.begin(), z_il.end()); }
void assign(std::initializer_list<int_type> il) { assign(il, il); }
template <typename ForwardIt>
void assign(ForwardIt first, ForwardIt last) { assign(first, last, first, last); }
size_type rank(size_type s, size_type t, int_type x) const {
if (s == t) return 0;
for (size_type i = Nb; i--;) {
size_type j = Nb-i-1;
if (x >> i & 1) {
s = M_z[j] + M_a[j].rank1(s);
t = M_z[j] + M_a[j].rank1(t);
} else {
s = M_a[j].rank0(s);
t = M_a[j].rank0(t);
}
}
return t - s;
}
size_type select(value_type x, int_type k) const {
if (k == 0) return 0;
if (rank(0, M_z.size(), x) < k) return -1;
size_type si = M_startpos(x);
if (x & 1) {
k += M_a[Nb-1].rank1(si);
k = M_a[Nb-1].select1(k);
} else {
k += M_a[Nb-1].rank0(si);
k = M_a[Nb-1].select0(k);
}
for (size_type i = 1; i < Nb; ++i) {
size_type j = Nb-i-1;
if (x >> i & 1) {
k -= M_z[j];
k = M_a[j].select1(k);
} else {
k = M_a[j].seelct0(k);
}
}
return k;
}
size_type select(int_type x, size_type k, size_type s) const {
if (k == 0) return s;
k += rank(0, s, x);
return select(x, k);
}
std::array<size_type, 3> count_3way(size_type s, size_type t, int_type x) const {
if (s == t) return {0, 0, 0};
size_type lt = 0, eq = t-s, gt = 0;
for (size_type i = Nb; i--;) {
size_type j = Nb-i-1;
size_type tmp = t-s;
if (x >> i & 1) {
s = M_z[j] + M_a[j].rank1(s);
t = M_z[j] + M_a[j].rank1(t);
} else {
s = M_a[j].rank0(s);
t = M_a[j].rank0(t);
}
size_type d = tmp - (t-s);
eq -= d;
((x >> i & 1)? lt: gt) += d;
}
return {lt, eq, gt};
}
int_type quantile(size_type s, size_type t, size_type k) const {
int_type res = 0;
for (size_type i = Nb; i--;) {
size_type j = Nb-i-1;
size_type z = M_a[j].rank0(s, t);
if (k < z) {
s = M_a[j].rank0(s);
t = M_a[j].rank0(t);
} else {
res |= static_cast<value_type>(1) << i;
s = M_z[j] + M_a[j].rank1(s);
t = M_z[j] + M_a[j].rank1(t);
k -= z;
}
}
return res;
}
optional_type min_greater(size_type s, size_type t, int_type x) const {
auto [lt, eq, gt] = count_3way(s, t, x);
if (lt+eq == t-s) return {};
return quantile(s, t, lt+eq);
}
optional_type min_greater_equal(size_type s, size_type t, int_type x) const {
auto [lt, eq, gt] = count_3way(s, t, x);
if (lt == t-s) return {};
return quantile(s, t, lt);
}
optional_type max_less(size_type s, size_type t, int_type x) const {
auto [lt, eq, gt] = count_3way(s, t, x);
if (lt == 0) return {};
return quantile(s, t, lt-1);
}
optional_type max_less_equal(size_type s, size_type t, int_type x) const {
auto [lt, eq, gt] = count_3way(s, t, x);
if (lt+eq == 0) return {};
return quantile(s, t, lt+eq-1);
}
std::array<value_type, 3> sum_3way(size_type s, size_type t, int_type x) const {
value_type lt{}, eq{}, gt{};
if (s == t) return {lt, eq, gt};
for (size_type i = Nb; i--;) {
size_type j = Nb-i-1;
size_type s1 = M_z[j] + M_a[j].rank1(s);
size_type t1 = M_z[j] + M_a[j].rank1(t);
size_type s0 = M_a[j].rank0(s);
size_type t0 = M_a[j].rank0(t);
if (x >> i & 1) {
lt += M_s[j][t0] - M_s[j][s0];
s = s1, t = t1;
} else {
gt += M_s[j][t1] - M_s[j][s1];
s = s0, t = t0;
}
}
eq = M_s[Nb-1][t] - M_s[Nb-1][s];
return {lt, eq, gt};
}
value_type sum_within(size_type s, size_type t, int_type x, int_type y) {
value_type x_lt = sum_3way(s, t, x)[0];
auto tmp = sum_3way(s, t, y);
value_type y_lt = tmp[0], y_eq = tmp[1];
return y_eq + y_lt - x_lt;
}
};
#line 10 "test/yj_rectangle_sum.test.cpp"
int main() {
size_t n, q;
scanf("%zu %zu", &n, &q);
std::vector<std::tuple<int, int, intmax_t>> xyz(n);
for (auto& [x, y, z]: xyz)
scanf("%d %d %jd", &x, &y, &z);
std::sort(xyz.begin(), xyz.end());
std::vector<int> x(n), y(n);
std::vector<intmax_t> z(n);
for (size_t i = 0; i < n; ++i)
std::tie(x[i], y[i], z[i]) = xyz[i];
rectangle_query<30, intmax_t> rq(y.begin(), y.end(), z.begin(), z.end());
for (size_t i = 0; i < q; ++i) {
int l, d, r, u;
scanf("%d %d %d %d", &l, &d, &r, &u);
size_t il = std::lower_bound(x.begin(), x.end(), l) - x.begin();
size_t ir = std::lower_bound(x.begin(), x.end(), r) - x.begin();
intmax_t res = rq.sum_within(il, ir, d, u-1);
printf("%jd\n", res);
}
}
test/yj_rectangle_sum.test.cpp