結果
| 問題 | No.1783 Remix Sum |
| ユーザー |
 Pachicobue
|
| 提出日時 | 2021-12-12 22:24:28 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 25,998 bytes |
| コンパイル時間 | 2,871 ms |
| コンパイル使用メモリ | 231,500 KB |
| 実行使用メモリ | 50,552 KB |
| 最終ジャッジ日時 | 2024-07-21 10:48:17 |
| 合計ジャッジ時間 | 46,423 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | RE | - |
| testcase_01 | AC | 2 ms
5,376 KB |
| testcase_02 | AC | 2 ms
5,376 KB |
| testcase_03 | RE | - |
| testcase_04 | AC | 257 ms
5,740 KB |
| testcase_05 | AC | 173 ms
5,612 KB |
| testcase_06 | RE | - |
| testcase_07 | RE | - |
| testcase_08 | RE | - |
| testcase_09 | RE | - |
| testcase_10 | AC | 174 ms
5,488 KB |
| testcase_11 | AC | 91 ms
5,376 KB |
| testcase_12 | RE | - |
| testcase_13 | RE | - |
| testcase_14 | RE | - |
| testcase_15 | RE | - |
| testcase_16 | RE | - |
| testcase_17 | RE | - |
| testcase_18 | AC | 91 ms
5,376 KB |
| testcase_19 | RE | - |
| testcase_20 | RE | - |
| testcase_21 | RE | - |
| testcase_22 | RE | - |
| testcase_23 | RE | - |
| testcase_24 | RE | - |
| testcase_25 | RE | - |
| testcase_26 | RE | - |
| testcase_27 | RE | - |
| testcase_28 | RE | - |
| testcase_29 | RE | - |
| testcase_30 | RE | - |
| testcase_31 | RE | - |
| testcase_32 | RE | - |
| testcase_33 | RE | - |
| testcase_34 | RE | - |
| testcase_35 | RE | - |
| testcase_36 | RE | - |
| testcase_37 | RE | - |
| testcase_38 | RE | - |
| testcase_39 | RE | - |
| testcase_40 | RE | - |
| testcase_41 | RE | - |
| testcase_42 | RE | - |
| testcase_43 | RE | - |
| testcase_44 | AC | 6,773 ms
37,240 KB |
| testcase_45 | RE | - |
| testcase_46 | RE | - |
| testcase_47 | RE | - |
| testcase_48 | RE | - |
| testcase_49 | RE | - |
| testcase_50 | AC | 6,773 ms
37,236 KB |
| testcase_51 | RE | - |
| testcase_52 | RE | - |
| testcase_53 | RE | - |
| testcase_54 | RE | - |
| testcase_55 | RE | - |
| testcase_56 | AC | 9,575 ms
50,552 KB |
| testcase_57 | RE | - |
| testcase_58 | RE | - |
| testcase_59 | RE | - |
| testcase_60 | RE | - |
| testcase_61 | RE | - |
| testcase_62 | AC | 6,784 ms
37,240 KB |
| testcase_63 | RE | - |
| testcase_64 | RE | - |
| testcase_65 | RE | - |
| testcase_66 | RE | - |
| testcase_67 | RE | - |
| testcase_68 | AC | 686 ms
7,928 KB |
| testcase_69 | RE | - |
| testcase_70 | RE | - |
| testcase_71 | RE | - |
| testcase_72 | RE | - |
| testcase_73 | RE | - |
| testcase_74 | AC | 602 ms
7,544 KB |
| testcase_75 | RE | - |
| testcase_76 | RE | - |
| testcase_77 | RE | - |
| testcase_78 | RE | - |
| testcase_79 | RE | - |
ソースコード
#include <bits/stdc++.h>
/**
* 上位は1の10乗根でアダマール変換をして、下位はNTTする？
* 多変数FPSでexp.logを経てM乗を計算？
*
* X=(x_0,x_1,...,x_{T-1}), Y=(x_T,x_{T+1},...,x_{K-1})
* f(X,Y) = 上位K-T桁がYで、下位T桁がXである通り数みたいなFPS
* Xについてはmultivariate convolution, YについてはF_10 plus convolution
* https://nyaannyaan.github.io/library/ntt/multivariate-multiplication.hpp
*/
#pragma region Header
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
using f64 = double;
using f80 = long double;
using f128 = __float128;
constexpr i32 operator"" _i32(u64 v)
{
return v;
}
constexpr i32 operator"" _u32(u64 v)
{
return v;
}
constexpr i64 operator"" _i64(u64 v)
{
return v;
}
constexpr u64 operator"" _u64(u64 v)
{
return v;
}
constexpr f64 operator"" _f64(f80 v)
{
return v;
}
constexpr f80 operator"" _f80(f80 v)
{
return v;
}
using Istream = std::istream;
using Ostream = std::ostream;
using Str = std::string;
template<typename T>
using Lt = std::less<T>;
template<typename T>
using Gt = std::greater<T>;
template<typename T>
using IList = std::initializer_list<T>;
template<int n>
using BSet = std::bitset<n>;
template<typename T1, typename T2>
using Pair = std::pair<T1, T2>;
template<typename... Ts>
using Tup = std::tuple<Ts...>;
template<typename T, int N>
using Arr = std::array<T, N>;
template<typename... Ts>
using Deq = std::deque<Ts...>;
template<typename... Ts>
using Set = std::set<Ts...>;
template<typename... Ts>
using MSet = std::multiset<Ts...>;
template<typename... Ts>
using USet = std::unordered_set<Ts...>;
template<typename... Ts>
using UMSet = std::unordered_multiset<Ts...>;
template<typename... Ts>
using Map = std::map<Ts...>;
template<typename... Ts>
using MMap = std::multimap<Ts...>;
template<typename... Ts>
using UMap = std::unordered_map<Ts...>;
template<typename... Ts>
using UMMap = std::unordered_multimap<Ts...>;
template<typename... Ts>
using Vec = std::vector<Ts...>;
template<typename... Ts>
using Stack = std::stack<Ts...>;
template<typename... Ts>
using Queue = std::queue<Ts...>;
template<typename T>
using MaxHeap = std::priority_queue<T>;
template<typename T>
using MinHeap = std::priority_queue<T, Vec<T>, Gt<T>>;
using NSec = std::chrono::nanoseconds;
using USec = std::chrono::microseconds;
using MSec = std::chrono::milliseconds;
using Sec = std::chrono::seconds;
template<typename T>
constexpr T LIMMIN = std::numeric_limits<T>::min();
template<typename T>
constexpr T LIMMAX = std::numeric_limits<T>::max();
template<typename T>
constexpr T INF = (LIMMAX<T> - 1) / 2;
template<typename T>
constexpr T PI = T{3.141592653589793238462643383279502884};
template<typename T = u64>
constexpr T TEN(const int n)
{
return n == 0 ? T{1} : TEN<T>(n - 1) * T{10};
}
Ostream& operator<<(Ostream& os, i128 v)
{
bool minus = false;
if (v < 0) { minus = true, v = -v; }
Str ans;
if (v == 0) { ans = "0"; }
while (v) {
ans.push_back('0' + v % 10), v /= 10;
}
std::reverse(ans.begin(), ans.end());
return os << (minus ? "-" : "") << ans;
}
Ostream& operator<<(Ostream& os, u128 v)
{
Str ans;
if (v == 0) { ans = "0"; }
while (v) {
ans.push_back('0' + v % 10), v /= 10;
}
std::reverse(ans.begin(), ans.end());
return os << ans;
}
template<typename T>
bool chmin(T& a, const T& b)
{
if (a > b) {
a = b;
return true;
} else {
return false;
}
}
template<typename T>
bool chmax(T& a, const T& b)
{
if (a < b) {
a = b;
return true;
} else {
return false;
}
}
template<typename T>
constexpr T floorDiv(T x, T y)
{
if (y < T{}) { x = -x, y = -y; }
return x >= T{} ? x / y : (x - y + 1) / y;
}
template<typename T>
constexpr T ceilDiv(T x, T y)
{
if (y < T{}) { x = -x, y = -y; }
return x >= T{} ? (x + y - 1) / y : x / y;
}
template<typename T, typename I>
constexpr T modPower(T v, I n, T mod)
{
T ans = 1 % mod;
for (; n > 0; n >>= 1, (v *= v) %= mod) {
if (n % 2 == 1) { (ans *= v) %= mod; }
}
return ans;
}
template<typename T, typename I>
constexpr T power(T v, I n)
{
T ans = 1;
for (; n > 0; n >>= 1, v *= v) {
if (n % 2 == 1) { ans *= v; }
}
return ans;
}
template<typename T, typename I>
constexpr T power(T v, I n, const T& e)
{
T ans = e;
for (; n > 0; n >>= 1, v *= v) {
if (n % 2 == 1) { ans *= v; }
}
return ans;
}
template<typename T>
Vec<T> operator+=(Vec<T>& vs1, const Vec<T>& vs2)
{
vs1.insert(vs1.end(), vs2.begin(), vs2.end());
return vs1;
}
template<typename T>
Vec<T> operator+(const Vec<T>& vs1, const Vec<T>& vs2)
{
auto vs = vs1;
vs += vs2;
return vs;
}
template<typename Vs, typename V>
void fillAll(Vs& arr, const V& v)
{
if constexpr (std::is_convertible<V, Vs>::value) {
arr = v;
} else {
for (auto& subarr : arr) {
fillAll(subarr, v);
}
}
}
template<typename Vs>
void sortAll(Vs& vs)
{
std::sort(std::begin(vs), std::end(vs));
}
template<typename Vs, typename C>
void sortAll(Vs& vs, C comp)
{
std::sort(std::begin(vs), std::end(vs), comp);
}
template<typename Vs>
void reverseAll(Vs& vs)
{
std::reverse(std::begin(vs), std::end(vs));
}
template<typename V, typename Vs>
V sumAll(const Vs& vs)
{
if constexpr (std::is_convertible<Vs, V>::value) {
return static_cast<V>(vs);
} else {
V ans = 0;
for (const auto& v : vs) {
ans += sumAll<V>(v);
}
return ans;
}
}
template<typename Vs>
int minInd(const Vs& vs)
{
return std::min_element(std::begin(vs), std::end(vs)) - std::begin(vs);
}
template<typename Vs>
int maxInd(const Vs& vs)
{
return std::max_element(std::begin(vs), std::end(vs)) - std::begin(vs);
}
template<typename Vs, typename V>
int lbInd(const Vs& vs, const V& v)
{
return std::lower_bound(std::begin(vs), std::end(vs), v) - std::begin(vs);
}
template<typename Vs, typename V>
int ubInd(const Vs& vs, const V& v)
{
return std::upper_bound(std::begin(vs), std::end(vs), v) - std::begin(vs);
}
template<typename T, typename F>
Vec<T> genVec(int n, F gen)
{
Vec<T> ans;
std::generate_n(std::back_insert_iterator(ans), n, gen);
return ans;
}
Vec<int> iotaVec(int n, int offset = 0)
{
Vec<int> ans(n);
std::iota(ans.begin(), ans.end(), offset);
return ans;
}
constexpr int popcount(const u64 v)
{
return v ? __builtin_popcountll(v) : 0;
}
constexpr int log2p1(const u64 v)
{
return v ? 64 - __builtin_clzll(v) : 0;
}
constexpr int lsbp1(const u64 v)
{
return __builtin_ffsll(v);
}
constexpr int clog(const u64 v)
{
return v ? log2p1(v - 1) : 0;
}
constexpr u64 ceil2(const u64 v)
{
const int l = clog(v);
return (l == 64) ? 0_u64 : (1_u64 << l);
}
constexpr u64 floor2(const u64 v)
{
return v ? (1_u64 << (log2p1(v) - 1)) : 0_u64;
}
constexpr bool ispow2(const u64 v)
{
return (v > 0) and ((v & (v - 1)) == 0);
}
constexpr bool btest(const u64 mask, const int ind)
{
return (mask >> ind) & 1_u64;
}
template<typename F>
struct Fix : F
{
Fix(F&& f) : F{std::forward<F>(f)} {}
template<typename... Args>
auto operator()(Args&&... args) const
{
return F::operator()(*this, std::forward<Args>(args)...);
}
};
class irange
{
private:
struct itr
{
itr(i64 start = 0, i64 step = 1) : m_cnt{start}, m_step{step} {}
bool operator!=(const itr& it) const
{
return m_cnt != it.m_cnt;
}
int operator*()
{
return m_cnt;
}
itr& operator++()
{
m_cnt += m_step;
return *this;
}
i64 m_cnt, m_step;
};
i64 m_start, m_end, m_step;
public:
irange(i64 start, i64 end, i64 step = 1)
{
assert(step != 0);
const i64 d = std::abs(step);
const i64 l = (step > 0 ? start : end);
const i64 r = (step > 0 ? end : start);
int n = (r - l) / d + ((r - l) % d ? 1 : 0);
if (l >= r) { n = 0; }
m_start = start;
m_end = start + step * n;
m_step = step;
}
itr begin() const
{
return itr{m_start, m_step};
}
itr end() const
{
return itr{m_end, m_step};
}
};
irange rep(int end)
{
return irange(0, end, 1);
}
irange per(int rend)
{
return irange(rend - 1, -1, -1);
}
#pragma COMMENT("[REFS] Xoshiro: https://prng.di.unimi.it")
namespace xoshiro_impl {
u64 x;
u64 next()
{
uint64_t z = (x += 0x9e3779b97f4a7c15);
z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9;
z = (z ^ (z >> 27)) * 0x94d049bb133111eb;
return z ^ (z >> 31);
}
} // namespace xoshiro_impl
class Xoshiro32
{
public:
using result_type = u32;
using T = result_type;
Xoshiro32(T seed = 0)
{
xoshiro_impl::x = seed;
s[0] = xoshiro_impl::next();
s[1] = xoshiro_impl::next();
s[2] = xoshiro_impl::next();
s[3] = xoshiro_impl::next();
}
static constexpr T min()
{
return LIMMIN<T>;
}
static constexpr T max()
{
return LIMMAX<T>;
}
T operator()()
{
return next();
}
private:
static constexpr T rotl(const T x, int k)
{
return (x << k) | (x >> (32 - k));
}
T next()
{
const T ans = rotl(s[1] * 5, 7) * 9;
const T t = s[1] << 9;
s[2] ^= s[0];
s[3] ^= s[1];
s[1] ^= s[2];
s[0] ^= s[3];
s[2] ^= t;
s[3] = rotl(s[3], 11);
return ans;
}
T s[4];
};
class Xoshiro64
{
public:
using result_type = u64;
using T = result_type;
Xoshiro64(T seed = 0)
{
xoshiro_impl::x = seed;
s[0] = xoshiro_impl::next();
s[1] = xoshiro_impl::next();
s[2] = xoshiro_impl::next();
s[3] = xoshiro_impl::next();
}
static constexpr T min()
{
return LIMMIN<T>;
}
static constexpr T max()
{
return LIMMAX<T>;
}
T operator()()
{
return next();
}
private:
static constexpr T rotl(const T x, int k)
{
return (x << k) | (x >> (64 - k));
}
T next()
{
const T ans = rotl(s[1] * 5, 7) * 9;
const T t = s[1] << 17;
s[2] ^= s[0];
s[3] ^= s[1];
s[1] ^= s[2];
s[0] ^= s[3];
s[2] ^= t;
s[3] = rotl(s[3], 45);
return ans;
}
T s[4];
};
template<typename Rng>
class RNG
{
public:
using result_type = typename Rng::result_type;
using T = result_type;
static constexpr T min()
{
return Rng::min();
}
static constexpr T max()
{
return Rng::max();
}
RNG() : RNG(std::random_device{}()) {}
RNG(T seed) : m_rng(seed) {}
T operator()()
{
return m_rng();
}
template<typename T>
T val(T min, T max)
{
return std::uniform_int_distribution<T>(min, max)(m_rng);
}
template<typename T>
Pair<T, T> pair(T min, T max)
{
return std::minmax({val<T>(min, max), val<T>(min, max)});
}
template<typename T>
Vec<T> vec(int n, T min, T max)
{
return genVec<T>(n, [&]() { return val<T>(min, max); });
}
template<typename T>
Vec<Vec<T>> vvec(int n, int m, T min, T max)
{
return genVec<Vec<T>>(n, [&]() { return vec(m, min, max); });
}
private:
Rng m_rng;
};
RNG<std::mt19937> rng;
RNG<std::mt19937_64> rng64;
RNG<Xoshiro32> rng_xo;
RNG<Xoshiro64> rng_xo64;
class Scanner
{
public:
Scanner(Istream& is = std::cin) : m_is{is}
{
m_is.tie(nullptr)->sync_with_stdio(false);
}
template<typename T>
T val()
{
T v;
return m_is >> v, v;
}
template<typename T>
T val(T offset)
{
return val<T>() - offset;
}
template<typename T>
Vec<T> vec(int n)
{
return genVec<T>(n, [&]() { return val<T>(); });
}
template<typename T>
Vec<T> vec(int n, T offset)
{
return genVec<T>(n, [&]() { return val<T>(offset); });
}
template<typename T>
Vec<Vec<T>> vvec(int n, int m)
{
return genVec<Vec<T>>(n, [&]() { return vec<T>(m); });
}
template<typename T>
Vec<Vec<T>> vvec(int n, int m, const T offset)
{
return genVec<Vec<T>>(n, [&]() { return vec<T>(m, offset); });
}
template<typename... Args>
auto tup()
{
return Tup<Args...>{val<Args>()...};
}
template<typename... Args>
auto tup(const Args&... offsets)
{
return Tup<Args...>{val<Args>(offsets)...};
}
private:
Istream& m_is;
};
Scanner in;
class Printer
{
public:
Printer(Ostream& os = std::cout) : m_os{os}
{
m_os << std::fixed << std::setprecision(15);
}
template<typename... Args>
int operator()(const Args&... args)
{
dump(args...);
return 0;
}
template<typename... Args>
int ln(const Args&... args)
{
dump(args...), m_os << '\n';
return 0;
}
template<typename... Args>
int el(const Args&... args)
{
dump(args...), m_os << std::endl;
return 0;
}
private:
template<typename T>
void dump(const T& v)
{
m_os << v;
}
template<typename T>
void dump(const Vec<T>& vs)
{
for (const int i : rep(vs.size())) {
m_os << (i ? " " : ""), dump(vs[i]);
}
}
template<typename T>
void dump(const Vec<Vec<T>>& vss)
{
for (const int i : rep(vss.size())) {
m_os << (i ? "\n" : ""), dump(vss[i]);
}
}
template<typename T, typename... Ts>
int dump(const T& v, const Ts&... args)
{
dump(v), m_os << ' ', dump(args...);
return 0;
}
Ostream& m_os;
};
Printer out;
template<typename T, int n, int i = 0>
auto ndVec(int const (&szs)[n], const T x = T{})
{
if constexpr (i == n) {
return x;
} else {
return std::vector(szs[i], ndVec<T, n, i + 1>(szs, x));
}
}
template<u32 mod_, u32 root_, u32 max2p_>
class modint
{
template<typename U = u32&>
static U modRef()
{
static u32 s_mod = 0;
return s_mod;
}
template<typename U = u32&>
static U rootRef()
{
static u32 s_root = 0;
return s_root;
}
template<typename U = u32&>
static U max2pRef()
{
static u32 s_max2p = 0;
return s_max2p;
}
public:
template<typename U = const u32>
static constexpr std::enable_if_t<mod_ != 0, U> mod()
{
return mod_;
}
template<typename U = const u32>
static std::enable_if_t<mod_ == 0, U> mod()
{
return modRef();
}
template<typename U = const u32>
static constexpr std::enable_if_t<mod_ != 0, U> root()
{
return root_;
}
template<typename U = const u32>
static std::enable_if_t<mod_ == 0, U> root()
{
return rootRef();
}
template<typename U = const u32>
static constexpr std::enable_if_t<mod_ != 0, U> max2p()
{
return max2p_;
}
template<typename U = const u32>
static std::enable_if_t<mod_ == 0, U> max2p()
{
return max2pRef();
}
template<typename U = u32>
static void setMod(std::enable_if_t<mod_ == 0, U> m)
{
modRef() = m;
}
template<typename U = u32>
static void setRoot(std::enable_if_t<mod_ == 0, U> r)
{
rootRef() = r;
}
template<typename U = u32>
static void setMax2p(std::enable_if_t<mod_ == 0, U> m)
{
max2pRef() = m;
}
constexpr modint() : m_val{0} {}
constexpr modint(i64 v) : m_val{normll(v)} {}
constexpr void setRaw(u32 v)
{
m_val = v;
}
constexpr modint operator-() const
{
return modint{0} - (*this);
}
constexpr modint& operator+=(const modint& m)
{
m_val = norm(m_val + m.val());
return *this;
}
constexpr modint& operator-=(const modint& m)
{
m_val = norm(m_val + mod() - m.val());
return *this;
}
constexpr modint& operator*=(const modint& m)
{
m_val = normll((i64)m_val * (i64)m.val() % (i64)mod());
return *this;
}
constexpr modint& operator/=(const modint& m)
{
return *this *= m.inv();
}
constexpr modint operator+(const modint& m) const
{
auto v = *this;
return v += m;
}
constexpr modint operator-(const modint& m) const
{
auto v = *this;
return v -= m;
}
constexpr modint operator*(const modint& m) const
{
auto v = *this;
return v *= m;
}
constexpr modint operator/(const modint& m) const
{
auto v = *this;
return v /= m;
}
constexpr bool operator==(const modint& m) const
{
return m_val == m.val();
}
constexpr bool operator!=(const modint& m) const
{
return not(*this == m);
}
friend Istream& operator>>(Istream& is, modint& m)
{
i64 v;
return is >> v, m = v, is;
}
friend Ostream& operator<<(Ostream& os, const modint& m)
{
return os << m.val();
}
constexpr u32 val() const
{
return m_val;
}
template<typename I>
constexpr modint pow(I n) const
{
return power(*this, n);
}
constexpr modint inv() const
{
return pow(mod() - 2);
}
static modint sinv(u32 n)
{
static Vec<modint> is{1, 1};
for (u32 i = (u32)is.size(); i <= n; i++) {
is.push_back(-is[mod() % i] * (mod() / i));
}
return is[n];
}
static modint fact(u32 n)
{
static Vec<modint> fs{1, 1};
for (u32 i = (u32)fs.size(); i <= n; i++) {
fs.push_back(fs.back() * i);
}
return fs[n];
}
static modint ifact(u32 n)
{
static Vec<modint> ifs{1, 1};
for (u32 i = (u32)ifs.size(); i <= n; i++) {
ifs.push_back(ifs.back() * sinv(i));
}
return ifs[n];
}
static modint comb(int n, int k)
{
return k > n or k < 0 ? modint{0} : fact(n) * ifact(n - k) * ifact(k);
}
private:
static constexpr u32 norm(u32 x)
{
return x < mod() ? x : x - mod();
}
static constexpr u32 normll(i64 x)
{
return norm(u32(x % (i64)mod() + (i64)mod()));
}
u32 m_val;
};
using modint_1000000007 = modint<1000000007, 5, 1>;
using modint_998244353 = modint<998244353, 3, 23>;
template<int id>
using modint_dynamic = modint<0, 0, id>;
#pragma endregion
constexpr int D = 10;
constexpr int Ds[] = {1, 10, 100, 1000, 10000, 100000};
constexpr int ls[] = {0, 4, 7, 10, 14, 17};
constexpr int Ls[] = {1, 16, 128, 1024, 16384, 131072};
constexpr u32 MOD = (1_u32 << 20) * 115 + 1;
constexpr u32 ROOT = 6;
constexpr u32 MAX2P = 20;
using mint = modint<MOD, ROOT, MAX2P>;
const mint omega_10 = mint(ROOT).pow((MOD - 1) / 10);
const mint omega_10s[] = {1,
omega_10,
omega_10.pow(2),
omega_10.pow(3),
omega_10.pow(4),
omega_10.pow(5),
omega_10.pow(6),
omega_10.pow(7),
omega_10.pow(8),
omega_10.pow(9)};
const mint i_omega_10 = omega_10.inv();
const mint i_omega_10s[] = {1,
i_omega_10,
i_omega_10.pow(2),
i_omega_10.pow(3),
i_omega_10.pow(4),
i_omega_10.pow(5),
i_omega_10.pow(6),
i_omega_10.pow(7),
i_omega_10.pow(8),
i_omega_10.pow(9)};
i64 M;
int K; // 桁数
int T; // (mod x^D)で計算する桁数、残りは(mod x^D-1)で計算
int X; // ceil2(D^T)
int lx; // log2(X)
int Y; // D^(K-T)
int ly; // log10(Y)=K-T
/**
* Xの関数としてNTT
*/
void ntt(Vec<Vec<mint>>& f, bool rev)
{
assert((int)f.size() == X);
assert((int)f[0].size() == Y);
static Vec<mint> rs, irs;
if (rs.empty()) {
const mint r = mint(mint::root()), ir = r.inv();
rs.resize(mint::max2p() + 1), irs.resize(mint::max2p() + 1);
rs.back() = -r.pow((mint::mod() - 1) >> mint::max2p()),
irs.back() = -ir.pow((mint::mod() - 1) >> mint::max2p());
for (u32 i : irange(mint::max2p(), 0, -1)) {
rs[i - 1] = -(rs[i] * rs[i]);
irs[i - 1] = -(irs[i] * irs[i]);
}
}
const auto drange = (rev ? irange(0, lx, 1) : irange(lx - 1, -1, -1));
for (const int d : drange) {
const int width = 1 << d;
mint e = 1;
for (int i = 0, j = 1; i < X; i += width * 2, j++) {
for (int l = i, r = i + width; l < i + width; l++, r++) {
for (int y : rep(Y)) {
if (rev) {
const mint v1 = f[l][y], v2 = f[r][y];
f[l][y] = v1 + v2, f[r][y] = (v1 - v2) * e;
} else {
const mint v1 = f[l][y], v2 = f[r][y] * e;
f[l][y] = v1 + v2, f[r][y] = v1 - v2;
}
}
}
e *= (rev ? irs : rs)[lsbp1(j) + 1];
}
}
if (rev) {
const mint iN = mint{X}.inv();
for (auto& as : f) {
for (auto& a : as) {
a *= iN;
}
}
}
}
/* xにおけるbaseに対応する桁 */
int btest_10(int x, int base)
{
return (x / base) % D;
}
/**
* Yの関数としてFHT_10する
*/
void fht_10(Vec<Vec<mint>>& f, bool rev)
{
assert((int)f.size() == X);
assert((int)f[0].size() == Y);
for (int delta = 1; delta < Y; delta *= D) {
for (int j : rep(Y)) {
if (btest_10(j, delta) == 0) {
for (int x : rep(X)) {
Vec<mint> dps(D);
for (int k : rep(D)) {
dps[k] = f[x][j + delta * k];
f[x][j + delta * k] = 0;
}
for (int k : rep(D)) {
for (int l : rep(D)) {
f[x][j + delta * k]
+= (rev ? i_omega_10s[(k * l) % D]
: omega_10s[(k * l) % D])
* dps[l];
}
}
}
}
}
}
if (rev) {
const mint iN = mint(Y).inv();
for (auto& as : f) {
for (auto& a : as) {
a *= iN;
}
}
}
}
/**
* f(X,Y)を変換する
*/
void trans(Vec<Vec<mint>>& f, bool rev)
{
assert((int)f.size() == X);
assert((int)f[0].size() == Y);
ntt(f, rev);
fht_10(f, rev);
}
/**
* f(X,Y)*g(X,Y)
*/
Vec<Vec<mint>> multi_mul(const Vec<Vec<mint>>& f, const Vec<Vec<mint>>& g)
{
assert((int)f.size() == X);
assert((int)f[0].size() == Y);
assert((int)g.size() == X);
assert((int)g[0].size() == Y);
if (T == 0) {
// 全部FHT_10
auto F = f, G = g;
trans(F, false);
trans(G, false);
for (int x : rep(X)) {
for (int y : rep(Y)) {
F[x][y] *= G[x][y];
}
}
trans(F, true);
return F;
} else {
Vec<int> chi(X, 0);
for (int x : rep(X)) {
for (int k : irange(1, T)) {
chi[x] += x / Ds[k];
}
chi[x] %= T; // mod (t^T-1)
}
auto F = ndVec<mint>({T, X, Y}, 0);
auto G = ndVec<mint>({T, X, Y}, 0);
for (int x : rep(X)) {
for (int y : rep(Y)) {
F[chi[x]][x][y] += f[x][y];
G[chi[x]][x][y] += g[x][y];
}
}
for (int k : rep(T)) {
trans(F[k], false);
trans(G[k], false);
}
// F(t),G(t)の各点積
for (int x : rep(X)) {
for (int y : rep(Y)) {
Vec<mint> H_xy(T, 0);
// H_xy(t) = F_xy(t)*G_xy(t) mod (t^T-1)
for (int ki : rep(T)) {
for (int kj : rep(T)) {
H_xy[(ki + kj) % T] += F[ki][x][y] * G[kj][x][y];
}
}
for (int k : rep(T)) {
F[k][x][y] = H_xy[k];
}
}
}
for (int k : rep(T)) {
trans(F[k], true);
}
auto h = ndVec<mint>({X, Y}, 0);
for (int x : rep(X)) {
for (int y : rep(Y)) {
h[x][y] += F[chi[x]][x][y];
}
}
return h;
}
}
/**
* f(X,Y)^M
*/
Vec<Vec<mint>> multi_pow(Vec<Vec<mint>> f, i64 M)
{
if (M == 1) {
return f;
} else if (M % 2 == 0) {
return multi_pow(multi_mul(f, f), M / 2);
} else {
return multi_mul(f, multi_pow(f, M - 1));
}
}
int main()
{
int N;
std::tie(N, K, M, T) = in.tup<int, int, i64, int>();
assert(T == 0);
X = Ls[T];
lx = ls[T];
assert(X == (1 << lx));
Y = Ds[K - T];
ly = K - T;
const auto as = in.vec<int>(N);
auto f = ndVec<mint>({X, Y}, 0);
for (int i : rep(N)) {
const int x = as[i] % Ds[T];
const int y = as[i] / Ds[T];
f[x][y] += 1;
}
const auto g = multi_pow(f, M);
void(0);
Vec<mint> ans(Ds[K], 0);
for (int x : rep(Ds[T])) {
for (int y : rep(Ds[K - T])) {
ans[y * Ds[T] + x] += g[x][y];
}
}
for (auto an : ans) {
out.ln(an);
}
return 0;
}