cp-library
競技プログラミング用 C++ ライブラリ
test/generalized_floor_sum_yuki.test.cpp
test/generalized_floor_sum_yuki.test.cpp · GitHub で見る
依存ライブラリ
コード
#define PROBLEM "https://yukicoder.me/problems/no/2996"
#include "../math/generalized_floor_sum.hpp"
#include "../math/mint.hpp"
#include "../components/fast_io.hpp"
template <int D>
mint solve(int p, int q, std::int64_t n, std::int64_t m, std::int64_t a, std::int64_t b) {
auto sums = generalized_floor_sum_moments<D, mint>(n + 1, m, a, b);
return sums[p][q];
}
int main() {
FastInput in;
FastOutput out;
int t = 0;
in.read(t);
while (t--) {
int p = 0, q = 0;
std::int64_t n = 0, m = 1, a = 0, b = 0;
in.read(p); in.read(q); in.read(n); in.read(m); in.read(a); in.read(b);
auto result = p <= 2 && q <= 2 ? solve<4>(p, q, n, m, a, b) : solve<20>(p, q, n, m, a, b);
out.println(result.val());
}
}
#line 1 "test/generalized_floor_sum_yuki.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/2996"
#line 1 "math/generalized_floor_sum.hpp"
#include <array>
#include <cassert>
#include <cstdint>
#include <type_traits>
#include <utility>
namespace generalized_floor_sum_detail {
using U = std::uint64_t;
template <class T>
constexpr bool integer = std::is_integral_v<T> || std::is_same_v<T, __int128_t> || std::is_same_v<T, __uint128_t>;
template <int N, class T>
T divide(T value) {
if constexpr (integer<T>) return value / T(N);
else {
static const T inverse = T(1) / T(N);
return value * inverse;
}
}
template <int D, class T>
using Table = std::array<std::array<T, D + 1>, D + 1>;
template <int D, class T>
struct Coefficients {
std::array<std::array<T, D + 2>, D + 1> sums{};
std::array<std::array<T, D + 2>, D + 2> choose{};
std::array<T, D + 1> denominator{}, inverse{};
Coefficients() {
for (int i = 0; i <= D + 1; ++i) {
choose[i][0] = choose[i][i] = T(1);
for (int j = 1; j < i; ++j) choose[i][j] = choose[i - 1][j - 1] + choose[i - 1][j];
}
T factorial = 1;
for (int p = 0; p <= D; ++p) {
denominator[p] = factorial * T(p + 1);
for (int k = 0; k <= p + 1; ++k) {
T value = factorial * choose[p + 1][k];
for (int j = 0; j < p; ++j)
if (k <= j + 1) value -= factorial / denominator[j] * choose[p + 1][j] * sums[j][k];
sums[p][k] = value;
}
factorial = denominator[p];
if constexpr (!integer<T>) inverse[p] = T(1) / denominator[p];
}
}
T divide(T value, int p) const {
if constexpr (integer<T>) return value / denominator[p];
else return value * inverse[p];
}
};
template <int D, class T>
const Coefficients<D, T> &coefficients() {
static const Coefficients<D, T> value;
return value;
}
template <int D, class T, class A, class B>
[[gnu::always_inline]] inline void translate(Table<D, T> &result, const Coefficients<D, T> &c, A a, B b,
std::array<T, D + 1> &ak, std::array<T, D + 1> &bk) {
if (a != A(0)) {
ak[0] = T(1);
for (int i = 1; i <= D; ++i) ak[i] = ak[i - 1] * T(a);
for (int q = D; q >= 1; --q)
for (int p = 0; p + q <= D; ++p)
for (int j = 0; j < q; ++j) result[p][q] += c.choose[q][j] * ak[q - j] * result[p + q - j][j];
}
if (b != B(0)) {
bk[0] = T(1);
for (int i = 1; i <= D; ++i) bk[i] = bk[i - 1] * T(b);
for (int q = D; q >= 1; --q)
for (int p = 0; p + q <= D; ++p)
for (int j = 0; j < q; ++j) result[p][q] += c.choose[q][j] * bk[q - j] * result[p][j];
}
}
template <int D, class T>
Table<D, T> euclidean(U n, U m, U a, U b) {
Table<D, T> result{};
if (!n) return result;
if (n == 1) {
result[0][0] = T(1);
T value = T(b / m);
for (int q = 1; q <= D; ++q) result[0][q] = result[0][q - 1] * value;
return result;
}
const auto &c = coefficients<D, T>();
std::array<T, D + 1> sums{}, ak{}, bk{}, kp{};
T x = T(n - 1);
for (int p = 0; p <= D; ++p) {
T value = c.sums[p][p + 1];
for (int j = p; j >= 0; --j) value = value * x + c.sums[p][j];
sums[p] = c.divide(value, p);
}
U u = a / m, v = b / m;
a %= m;
b %= m;
if (a) {
__uint128_t z = __uint128_t(a) * (n - 1) + b;
U k = z >> 64 ? U(z / m) : U(z) / m;
if (k) {
auto child = euclidean<D, T>(k, a, m, m - b - 1);
kp[0] = T(1);
for (int j = 1; j <= D; ++j) kp[j] = kp[j - 1] * T(k);
for (int p = 0; p < D; ++p) {
std::array<T, D + 1> inner{};
for (int i = 0; i < D - p; ++i) {
T value = 0;
for (int j = 0; j <= p + 1; ++j) value += c.sums[p][j] * child[i][j];
inner[i] = c.divide(value, p);
}
for (int q = 1; p + q <= D; ++q) {
T value = sums[p] * kp[q];
for (int i = 0; i < q; ++i) value -= c.choose[q][i] * inner[i];
result[p][q] = value;
}
}
}
}
for (int p = 0; p <= D; ++p) result[p][0] = sums[p];
translate<D>(result, c, u, v, ak, bk);
return result;
}
template <class A, class B>
using Signed = std::enable_if_t<std::is_integral_v<A> && std::is_integral_v<B> &&
(std::is_signed_v<A> || std::is_signed_v<B>), int>;
template <class A>
bool negative(A value) {
if constexpr (std::is_signed_v<A>) return value < 0;
else return false;
}
template <class T, class A>
std::pair<U, T> normalize(A value, U m) {
U x = static_cast<U>(value);
if (!negative(value)) return {x % m, T(x / m)};
x = U(0) - x;
U r = x % m, q = x / m + (r != 0);
if constexpr (integer<T>) return {r ? m - r : 0, T(-__int128_t(q))};
else return {r ? m - r : 0, -T(q)};
}
template <class T, bool Full = false>
auto quadratic(U n, U m, U a, U b) {
std::conditional_t<Full, Table<2, T>, std::array<T, 3>> result{};
if (!n) return result;
T count = T(n), s1 = T(n >> 1) * T(n - 1 + (n & 1)), s2 = divide<3>(s1 * (T(2) * count - T(1)));
U u = a / m, v = b / m;
a %= m;
b %= m;
T f = 0, g = 0, h = 0;
if (a) {
__uint128_t z = __uint128_t(a) * (n - 1) + b;
U k = z >> 64 ? U(z / m) : U(z) / m;
if (k) {
auto child = quadratic<T>(k, a, m, m - b - 1);
T height = T(k);
f = T(n - 1) * height - child[0];
g = s1 * height - divide<2>(child[2] + child[0]);
h = T(n - 1) * height * height - child[0] - T(2) * child[1];
}
}
T at = T(u), bt = T(v);
T f0 = f + at * s1 + bt * count;
T f1 = g + at * s2 + bt * s1;
T f2 = h + T(2) * (at * g + bt * f) + at * at * s2 + bt * (T(2) * at * s1 + bt * count);
if constexpr (Full) {
result[0][0] = count;
result[1][0] = s1;
result[2][0] = s2;
result[0][1] = f0;
result[1][1] = f1;
result[0][2] = f2;
} else result = {f0, f1, f2};
return result;
}
template <class T>
T linear(U n, U m, U a, U b) {
T result = 0;
for (;;) {
if (!n) return result;
if (n == 1) return result + T(b / m);
if (a >= m) result += divide<2>(T(n) * T(n - 1)) * T(a / m), a %= m;
if (b >= m) result += T(n) * T(b / m), b %= m;
__uint128_t z = __uint128_t(a) * n + b;
if (z < m) return result;
if (z >> 64) n = z / m, b = z % m;
else {
U value = z;
n = value / m;
b = value % m;
}
std::swap(a, m);
}
}
}
template <int D, class T = __int128_t>
auto generalized_floor_sum_moments(std::uint64_t n, std::uint64_t m, std::uint64_t a, std::uint64_t b) {
static_assert(D >= 0);
assert(m > 0);
if constexpr (D == 0) return generalized_floor_sum_detail::Table<0, T>{std::array<T, 1>{T(n)}};
else if constexpr (D == 1) {
generalized_floor_sum_detail::Table<1, T> result{};
result[0][0] = T(n);
result[1][0] = n ? generalized_floor_sum_detail::divide<2>(T(n) * T(n - 1)) : T(0);
result[0][1] = generalized_floor_sum_detail::linear<T>(n, m, a, b);
return result;
} else if constexpr (D == 2) return generalized_floor_sum_detail::quadratic<T, true>(n, m, a, b);
else return generalized_floor_sum_detail::euclidean<D, T>(n, m, a, b);
}
template <int P, int Q, class T = __int128_t>
T generalized_floor_sum(std::uint64_t n, std::uint64_t m, std::uint64_t a, std::uint64_t b) {
static_assert(P >= 0 && Q >= 0);
assert(m > 0);
if constexpr (Q == 0) {
if (!n) return T(0);
if constexpr (P == 0) return T(n);
else if constexpr (P == 1) return generalized_floor_sum_detail::divide<2>(T(n) * T(n - 1));
else if constexpr (P == 2) return generalized_floor_sum_detail::divide<6>(T(n) * T(n - 1) * (T(2) * T(n) - T(1)));
else {
const auto &c = generalized_floor_sum_detail::coefficients<P, T>();
T value = c.sums[P][P + 1], x = T(n - 1);
for (int j = P; j >= 0; --j) value = value * x + c.sums[P][j];
return c.divide(value, P);
}
} else if constexpr (P == 0 && Q == 1) return generalized_floor_sum_detail::linear<T>(n, m, a, b);
else return generalized_floor_sum_moments<P + Q, T>(n, m, a, b)[P][Q];
}
template <int D, class T = __int128_t, class A, class B, generalized_floor_sum_detail::Signed<A, B> = 0>
auto generalized_floor_sum_moments(std::uint64_t n, std::uint64_t m, A a, B b) {
using namespace generalized_floor_sum_detail;
static_assert(D >= 0);
assert(m > 0);
if (!negative(a) && !negative(b)) return generalized_floor_sum_moments<D, T>(n, m, U(a), U(b));
if constexpr (D == 0) return generalized_floor_sum_moments<0, T>(n, m, U(0), U(0));
else {
if (!n) return Table<D, T>{};
auto [rb, v] = normalize<T>(b, m);
if (n == 1) {
Table<D, T> result{};
result[0][0] = T(1);
for (int q = 1; q <= D; ++q) result[0][q] = result[0][q - 1] * v;
return result;
}
auto [ra, u] = normalize<T>(a, m);
auto result = generalized_floor_sum_moments<D, T>(n, m, ra, rb);
std::array<T, D + 1> ak{}, bk{};
translate<D>(result, coefficients<D, T>(), u, v, ak, bk);
return result;
}
}
template <int P, int Q, class T = __int128_t, class A, class B, generalized_floor_sum_detail::Signed<A, B> = 0>
T generalized_floor_sum(std::uint64_t n, std::uint64_t m, A a, B b) {
using namespace generalized_floor_sum_detail;
static_assert(P >= 0 && Q >= 0);
assert(m > 0);
if constexpr (Q == 0) return generalized_floor_sum<P, Q, T>(n, m, U(0), U(0));
else {
if (!negative(a) && !negative(b)) return generalized_floor_sum<P, Q, T>(n, m, U(a), U(b));
return generalized_floor_sum_moments<P + Q, T>(n, m, a, b)[P][Q];
}
}
#line 1 "math/mint.hpp"
#line 4 "math/mint.hpp"
#include <istream>
#include <ostream>
#line 7 "math/mint.hpp"
#if defined(__GNUC__) && !defined(__clang__) && (defined(__x86_64__) || defined(__i386__))
#pragma GCC push_options
#pragma GCC optimize("O3")
#endif
namespace mint_detail {
template <class I>
constexpr bool mint_integral = std::is_integral_v<I>
#if defined(__SIZEOF_INT128__)
|| std::is_same_v<I, __int128> || std::is_same_v<I, unsigned __int128>
#endif
;
struct [[gnu::warn_unused]] Mint {
using mint = Mint;
unsigned v = 0;
[[nodiscard]] static constexpr unsigned mod() { return 998244353; }
[[nodiscard, gnu::always_inline]] static unsigned reduce(unsigned long long x) {
return (x + (unsigned long long)(unsigned(x) * 998244351u) * mod()) >> 32;
}
[[gnu::always_inline]] Mint() = default;
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
Mint(I x) {
long long r = x % (long long)mod();
if (r < 0) r += mod();
v = reduce((unsigned long long)r * 932051910);
}
[[nodiscard, gnu::always_inline]] static Mint raw(unsigned x) {
Mint a;
a.v = reduce((unsigned long long)x * 932051910);
return a;
}
[[nodiscard, gnu::always_inline]] static Mint word(unsigned x) {
Mint a;
a.v = x;
return a;
}
[[nodiscard, gnu::always_inline]] unsigned val() const {
unsigned r = reduce(v);
return r < mod() ? r : r - mod();
}
friend std::istream &operator>>(std::istream &is, Mint &x) {
long long value;
if (is >> value) x = Mint(value);
return is;
}
friend std::ostream &operator<<(std::ostream &os, const Mint &x) {
return os << x.val();
}
[[gnu::always_inline]] Mint &operator+=(Mint b) {
v += b.v;
if (v >= 2 * mod()) v -= 2 * mod();
return *this;
}
[[gnu::always_inline]] Mint &operator-=(Mint b) {
v -= b.v;
if (v >> 31) v += 2 * mod();
return *this;
}
[[gnu::always_inline]] Mint &operator*=(Mint b) {
v = reduce((unsigned long long)v * b.v);
return *this;
}
Mint &operator/=(Mint b) { return *this *= b.inv(); }
Mint &operator++() { return *this += Mint(1); }
Mint &operator--() { return *this -= Mint(1); }
Mint operator++(int) {
Mint a = *this;
++*this;
return a;
}
Mint operator--(int) {
Mint a = *this;
--*this;
return a;
}
[[nodiscard, gnu::always_inline]] Mint operator+() const { return *this; }
[[nodiscard, gnu::always_inline]] Mint operator-() const { return word(v ? 2 * mod() - v : 0); }
[[nodiscard, gnu::always_inline]] Mint operator+(Mint b) const { return Mint(*this) += b; }
[[nodiscard, gnu::always_inline]] Mint operator-(Mint b) const { return Mint(*this) -= b; }
[[nodiscard, gnu::always_inline]] Mint operator*(Mint b) const { return Mint(*this) *= b; }
[[nodiscard]] Mint operator/(Mint b) const { return Mint(*this) /= b; }
[[nodiscard, gnu::always_inline]] bool operator==(Mint b) const { return (v < mod() ? v : v - mod()) == (b.v < mod() ? b.v : b.v - mod()); }
[[nodiscard, gnu::always_inline]] bool operator!=(Mint b) const { return !(*this == b); }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
[[nodiscard]] friend Mint operator+(I a, Mint b) { return Mint(a) + b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
[[nodiscard]] friend Mint operator-(I a, Mint b) { return Mint(a) - b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
[[nodiscard]] friend Mint operator*(I a, Mint b) { return Mint(a) * b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
[[nodiscard]] friend Mint operator/(I a, Mint b) { return Mint(a) / b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
[[nodiscard]] friend bool operator==(I a, Mint b) { return Mint(a) == b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
[[nodiscard]] friend bool operator!=(I a, Mint b) { return Mint(a) != b; }
[[nodiscard]] Mint pow(long long n) const {
assert(n >= 0);
if (!n) return Mint(1);
Mint r(1), a = *this;
for (; n > 1; n >>= 1, a *= a)
if (n & 1) r *= a;
return r * a;
}
[[nodiscard, gnu::noinline]] Mint inv() const {
assert(*this != Mint(0));
Mint a2 = *this * *this, a3 = a2 * *this;
Mint a7 = a3 * a3 * *this;
Mint a31 = a7;
for (int i = 0; i < 2; ++i) a31 *= a31;
a31 *= a3;
Mint r = a7;
for (int i = 0; i < 3; ++i) r *= r;
r *= a3;
r *= r;
for (int j = 0; j < 4; ++j) {
for (int i = 0; i < 5; ++i) r *= r;
r *= a31;
}
for (int i = 0; i < 3; ++i) r *= r;
return r * a7;
}
};
} // namespace mint_detail
using mint = mint_detail::Mint;
using fps_mint = mint;
#if defined(__GNUC__) && !defined(__clang__) && (defined(__x86_64__) || defined(__i386__))
#pragma GCC pop_options
#endif
#line 1 "components/fast_io.hpp"
#include <algorithm>
#line 6 "components/fast_io.hpp"
#include <bit>
#line 8 "components/fast_io.hpp"
#include <charconv>
#include <cstddef>
#line 11 "components/fast_io.hpp"
#include <cstdio>
#include <cstring>
#include <memory>
#include <stdexcept>
#include <string>
#include <string_view>
#line 18 "components/fast_io.hpp"
#if defined(__unix__) || defined(__APPLE__)
#include <sys/mman.h>
#include <sys/stat.h>
#include <unistd.h>
#endif
namespace fast_io_detail { struct BulkInput; struct BulkOutput; }
class FastInput {
friend struct fast_io_detail::BulkInput;
static constexpr std::size_t capacity = 1 << 16;
FILE *file = nullptr;
std::unique_ptr<char[]> buffer;
const char *current = "", *end = current;
std::string scratch;
void *mapping = nullptr;
std::size_t mapped_size = 0;
bool refill() {
if (!file) return false;
std::size_t n = std::fread(buffer.get(), 1, capacity, file);
current = buffer.get();
end = current + n;
return n;
}
static const char *scan(const char *p, const char *end) {
while (end - p >= 8) {
std::uint64_t x;
std::memcpy(&x, p, 8);
if ((x - 0x2121212121212121ULL) & ~x & 0x8080808080808080ULL) break;
p += 8;
}
while (p != end && static_cast<unsigned char>(*p) > ' ') ++p;
return p;
}
public:
explicit FastInput(FILE *input = stdin) {
#if defined(__unix__) || defined(__APPLE__)
struct stat status;
int fd = fileno(input);
auto offset = ftello(input);
if (fd >= 0 && offset >= 0 && !fstat(fd, &status) && S_ISREG(status.st_mode) && status.st_size > offset) {
mapped_size = status.st_size;
mapping = mmap(nullptr, mapped_size, PROT_READ, MAP_PRIVATE, fd, 0);
if (mapping != MAP_FAILED) {
current = static_cast<const char *>(mapping) + offset;
end = static_cast<const char *>(mapping) + mapped_size;
return;
}
mapping = nullptr;
}
#endif
file = input;
buffer = std::make_unique_for_overwrite<char[]>(capacity);
}
explicit FastInput(std::string_view input) : current(input.empty() ? "" : input.data()), end(current + input.size()) {}
FastInput(const FastInput &) = delete;
FastInput &operator=(const FastInput &) = delete;
~FastInput() {
#if defined(__unix__) || defined(__APPLE__)
if (mapping) munmap(mapping, mapped_size);
#endif
}
std::string_view token() {
while (true) {
while (current != end && static_cast<unsigned char>(*current) <= ' ') ++current;
if (current != end) break;
if (!refill()) return {};
}
const char *begin = current;
current = scan(current, end);
if (current != end || !file) return {begin, std::size_t(current - begin)};
scratch.assign(begin, end);
while (refill()) {
current = scan(current, end);
scratch.append(buffer.get(), std::size_t(current - buffer.get()));
if (current != end) break;
}
return scratch;
}
template <class T>
bool read(T &value) {
if constexpr (std::is_integral_v<T> && !std::is_same_v<T, bool>) {
while (true) {
while (current != end && static_cast<unsigned char>(*current) <= ' ') ++current;
if (current != end) break;
if (!refill()) return false;
}
if constexpr (std::is_unsigned_v<T> && sizeof(T) == 4 && std::endian::native == std::endian::little) {
if (end - current >= 11) {
std::uint64_t x;
std::memcpy(&x, current, 8);
if (!(((x + 0x4646464646464646ULL) | (x - 0x3030303030303030ULL)) & 0x8080808080808080ULL)) {
x &= 0x0f0f0f0f0f0f0f0fULL;
x = (x * 10 + (x >> 8)) & 0x00ff00ff00ff00ffULL;
x = (x * 100 + (x >> 16)) & 0x0000ffff0000ffffULL;
std::uint64_t v = std::uint32_t(x * 10000 + (x >> 32));
int n = 8;
for (; n < 10 && static_cast<unsigned char>(current[n]) - unsigned('0') < 10; ++n)
v = v * 10 + (current[n] - '0');
if (static_cast<unsigned char>(current[n]) <= ' ' && v <= 0xffffffffULL) {
current += n;
value = T(v);
return true;
}
}
}
}
T parsed{};
auto result = std::from_chars(current, end, parsed);
if (result.ec == std::errc{} && (result.ptr != end ? static_cast<unsigned char>(*result.ptr) <= ' ' : !file)) {
current = result.ptr;
value = parsed;
return true;
}
}
auto s = token();
if (s.empty()) return false;
if constexpr (std::is_same_v<T, bool>) {
assert(s == "0" || s == "1");
value = s[0] == '1';
} else if constexpr (std::is_integral_v<T>) {
auto result = std::from_chars(s.data(), s.data() + s.size(), value);
assert(result.ec == std::errc{} && result.ptr == s.data() + s.size());
(void)result;
} else value = T(s);
return true;
}
};
class FastOutput {
friend struct fast_io_detail::BulkOutput;
inline static constexpr auto quads = [] {
std::array<std::array<char, 4>, 10000> table{};
for (int i = 0; i < 10000; ++i)
table[i] = {char('0' + i / 1000), char('0' + i / 100 % 10), char('0' + i / 10 % 10), char('0' + i % 10)};
return table;
}();
FILE *file;
std::unique_ptr<char[]> buffer = std::make_unique_for_overwrite<char[]>(1 << 16);
std::size_t capacity = 1 << 16, length = 0;
char *reserve(std::size_t n) {
if (n > capacity - length) {
if (!flush()) throw std::runtime_error("output failed");
if (n > capacity) {
std::size_t next = std::max(n, 2 * capacity);
buffer = std::make_unique_for_overwrite<char[]>(next);
capacity = next;
}
}
return buffer.get() + length;
}
public:
explicit FastOutput(FILE *output = stdout) : file(output) {}
FastOutput(const FastOutput &) = delete;
FastOutput &operator=(const FastOutput &) = delete;
~FastOutput() { flush(); }
bool flush() {
std::size_t offset = 0;
while (offset < length) {
auto n = std::fwrite(buffer.get() + offset, 1, length - offset, file);
if (!n) {
std::memmove(buffer.get(), buffer.get() + offset, length - offset);
length -= offset;
return false;
}
offset += n;
}
length = 0;
return std::fflush(file) == 0;
}
void write(char c) { *reserve(1) = c; ++length; }
void write(__uint128_t value) {
char digits[40];
char *end = digits + sizeof(digits), *begin = end;
do { *--begin = char('0' + value % 10); value /= 10; } while (value);
write(std::string_view(begin, end - begin));
}
void write(__int128_t value) {
__uint128_t magnitude = __uint128_t(value);
if (value < 0) write('-'), magnitude = 0 - magnitude;
write(magnitude);
}
void write(std::string_view s) {
char *out = reserve(s.size());
if (!s.empty()) std::memcpy(out, s.data(), s.size());
length += s.size();
}
template <class T> requires std::is_integral_v<T>
void write(T value) {
char *out = reserve(32);
if constexpr (std::is_same_v<T, bool>) *out = '0' + value, ++length;
else if constexpr (std::is_unsigned_v<T> && sizeof(T) == 4) {
char *p = out;
if (value >= 100000000) {
auto high = value / 100000000, low = value % 100000000;
p = std::to_chars(p, p + 2, high).ptr;
std::memcpy(p, quads[low / 10000].data(), 4);
std::memcpy(p + 4, quads[low % 10000].data(), 4);
p += 8;
} else if (value >= 10000) {
p = std::to_chars(p, p + 4, value / 10000).ptr;
std::memcpy(p, quads[value % 10000].data(), 4);
p += 4;
} else p = std::to_chars(p, p + 4, value).ptr;
length += p - out;
} else length += std::to_chars(out, out + 32, value).ptr - out;
}
template <class T> requires requires(const T &value, char *out) { value.decimal_capacity(); value.to_chars(out); }
void write(const T &value) {
char *out = reserve(value.decimal_capacity());
length += value.to_chars(out) - out;
}
template <class T>
void println(const T &value) { write(value); write('\n'); }
};
#line 5 "test/generalized_floor_sum_yuki.test.cpp"
template <int D>
mint solve(int p, int q, std::int64_t n, std::int64_t m, std::int64_t a, std::int64_t b) {
auto sums = generalized_floor_sum_moments<D, mint>(n + 1, m, a, b);
return sums[p][q];
}
int main() {
FastInput in;
FastOutput out;
int t = 0;
in.read(t);
while (t--) {
int p = 0, q = 0;
std::int64_t n = 0, m = 1, a = 0, b = 0;
in.read(p); in.read(q); in.read(n); in.read(m); in.read(a); in.read(b);
auto result = p <= 2 && q <= 2 ? solve<4>(p, q, n, m, a, b) : solve<20>(p, q, n, m, a, b);
out.println(result.val());
}
}