結果
| 問題 | No.1783 Remix Sum |
| ユーザー |
👑  hitonanode
|
| 提出日時 | 2021-12-12 01:13:40 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 20,866 bytes |
| コンパイル時間 | 2,020 ms |
| コンパイル使用メモリ | 171,700 KB |
| 実行使用メモリ | 31,996 KB |
| 最終ジャッジ日時 | 2023-09-27 15:33:06 |
| 合計ジャッジ時間 | 57,730 ms |
|
ジャッジサーバーID （参考情報） |
judge11 / judge15 |
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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 | AC | 1 ms
4,376 KB |
| testcase_01 | AC | 1 ms
4,376 KB |
| testcase_02 | AC | 2 ms
4,380 KB |
| testcase_03 | AC | 1 ms
4,376 KB |
| testcase_04 | AC | 242 ms
5,712 KB |
| testcase_05 | AC | 193 ms
5,492 KB |
| testcase_06 | AC | 284 ms
5,644 KB |
| testcase_07 | AC | 582 ms
8,644 KB |
| testcase_08 | AC | 249 ms
5,392 KB |
| testcase_09 | AC | 252 ms
5,392 KB |
| testcase_10 | AC | 193 ms
5,608 KB |
| testcase_11 | AC | 151 ms
5,600 KB |
| testcase_12 | AC | 707 ms
8,908 KB |
| testcase_13 | AC | 361 ms
8,656 KB |
| testcase_14 | AC | 207 ms
5,632 KB |
| testcase_15 | AC | 553 ms
31,544 KB |
| testcase_16 | AC | 592 ms
8,728 KB |
| testcase_17 | AC | 711 ms
8,692 KB |
| testcase_18 | AC | 148 ms
5,488 KB |
| testcase_19 | AC | 303 ms
5,436 KB |
| testcase_20 | AC | 278 ms
5,732 KB |
| testcase_21 | AC | 304 ms
5,412 KB |
| testcase_22 | AC | 303 ms
5,492 KB |
| testcase_23 | AC | 339 ms
5,648 KB |
| testcase_24 | AC | 171 ms
5,884 KB |
| testcase_25 | AC | 281 ms
5,640 KB |
| testcase_26 | AC | 712 ms
8,912 KB |
| testcase_27 | AC | 287 ms
5,628 KB |
| testcase_28 | AC | 191 ms
5,752 KB |
| testcase_29 | AC | 273 ms
5,696 KB |
| testcase_30 | AC | 280 ms
5,804 KB |
| testcase_31 | AC | 309 ms
5,496 KB |
| testcase_32 | AC | 801 ms
31,436 KB |
| testcase_33 | AC | 277 ms
5,684 KB |
| testcase_34 | AC | 177 ms
6,160 KB |
| testcase_35 | AC | 362 ms
8,992 KB |
| testcase_36 | AC | 418 ms
31,996 KB |
| testcase_37 | AC | 418 ms
31,836 KB |
| testcase_38 | AC | 372 ms
8,976 KB |
| testcase_39 | AC | 174 ms
6,124 KB |
| testcase_40 | AC | 151 ms
6,088 KB |
| testcase_41 | AC | 182 ms
6,076 KB |
| testcase_42 | AC | 182 ms
6,076 KB |
| testcase_43 | AC | 378 ms
9,060 KB |
| testcase_44 | AC | 4,009 ms
6,540 KB |
| testcase_45 | AC | 3,872 ms
7,296 KB |
| testcase_46 | AC | 4,097 ms
6,452 KB |
| testcase_47 | AC | 4,496 ms
6,776 KB |
| testcase_48 | AC | 9,717 ms
9,488 KB |
| testcase_49 | TLE | - |
| testcase_50 | AC | 3,918 ms
6,700 KB |
| testcase_51 | AC | 3,975 ms
7,292 KB |
| testcase_52 | AC | 4,096 ms
6,384 KB |
| testcase_53 | AC | 4,578 ms
6,804 KB |
| testcase_54 | AC | 9,528 ms
9,724 KB |
| testcase_55 | TLE | - |
| testcase_56 | AC | 5,519 ms
6,856 KB |
| testcase_57 | AC | 5,417 ms
7,192 KB |
| testcase_58 | AC | 5,761 ms
6,596 KB |
| testcase_59 | AC | 6,413 ms
6,968 KB |
| testcase_60 | TLE | - |
| testcase_61 | -- | - |
| testcase_62 | -- | - |
| testcase_63 | -- | - |
| testcase_64 | -- | - |
| testcase_65 | -- | - |
| testcase_66 | -- | - |
| testcase_67 | -- | - |
| testcase_68 | -- | - |
| testcase_69 | -- | - |
| testcase_70 | -- | - |
| testcase_71 | -- | - |
| testcase_72 | -- | - |
| testcase_73 | -- | - |
| testcase_74 | -- | - |
| testcase_75 | -- | - |
| testcase_76 | -- | - |
| testcase_77 | -- | - |
| testcase_78 | -- | - |
| testcase_79 | -- | - |
ソースコード
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr)
#else
#define dbg(x) (x)
#define dbgif(cond, x) 0
#endif
template <int md> struct ModInt {
#if __cplusplus >= 201402L
#define MDCONST constexpr
#else
#define MDCONST
#endif
using lint = long long;
MDCONST static int mod() { return md; }
static int get_primitive_root() {
static int primitive_root = 0;
if (!primitive_root) {
primitive_root = [&]() {
std::set<int> fac;
int v = md - 1;
for (lint i = 2; i * i <= v; i++)
while (v % i == 0) fac.insert(i), v /= i;
if (v > 1) fac.insert(v);
for (int g = 1; g < md; g++) {
bool ok = true;
for (auto i : fac)
if (ModInt(g).pow((md - 1) / i) == 1) {
ok = false;
break;
}
if (ok) return g;
}
return -1;
}();
}
return primitive_root;
}
int val;
MDCONST ModInt() : val(0) {}
MDCONST ModInt &_setval(lint v) { return val = (v >= md ? v - md : v), *this; }
MDCONST ModInt(lint v) { _setval(v % md + md); }
MDCONST explicit operator bool() const { return val != 0; }
MDCONST ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }
MDCONST ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + md); }
MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % md); }
MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % md); }
MDCONST ModInt operator-() const { return ModInt()._setval(md - val); }
MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
friend MDCONST ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % md + x.val); }
friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % md - x.val + md); }
friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.val % md); }
friend MDCONST ModInt operator/(lint a, const ModInt &x) {
return ModInt()._setval(a % md * x.inv() % md);
}
MDCONST bool operator==(const ModInt &x) const { return val == x.val; }
MDCONST bool operator!=(const ModInt &x) const { return val != x.val; }
MDCONST bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map<ModInt, T>
friend std::istream &operator>>(std::istream &is, ModInt &x) {
lint t;
return is >> t, x = ModInt(t), is;
}
MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val; }
MDCONST ModInt pow(lint n) const {
ModInt ans = 1, tmp = *this;
while (n) {
if (n & 1) ans *= tmp;
tmp *= tmp, n >>= 1;
}
return ans;
}
static std::vector<ModInt> facs, facinvs, invs;
MDCONST static void _precalculation(int N) {
int l0 = facs.size();
if (N > md) N = md;
if (N <= l0) return;
facs.resize(N), facinvs.resize(N), invs.resize(N);
for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;
facinvs[N - 1] = facs.back().pow(md - 2);
for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);
for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];
}
MDCONST lint inv() const {
if (this->val < std::min(md >> 1, 1 << 21)) {
while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
return invs[this->val].val;
} else {
return this->pow(md - 2).val;
}
}
MDCONST ModInt fac() const {
while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
return facs[this->val];
}
MDCONST ModInt facinv() const {
while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
return facinvs[this->val];
}
MDCONST ModInt doublefac() const {
lint k = (this->val + 1) / 2;
return (this->val & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac())
: ModInt(k).fac() * ModInt(2).pow(k);
}
MDCONST ModInt nCr(const ModInt &r) const {
return (this->val < r.val) ? 0 : this->fac() * (*this - r).facinv() * r.facinv();
}
MDCONST ModInt nPr(const ModInt &r) const {
return (this->val < r.val) ? 0 : this->fac() * (*this - r).facinv();
}
ModInt sqrt() const {
if (val == 0) return 0;
if (md == 2) return val;
if (pow((md - 1) / 2) != 1) return 0;
ModInt b = 1;
while (b.pow((md - 1) / 2) == 1) b += 1;
int e = 0, m = md - 1;
while (m % 2 == 0) m >>= 1, e++;
ModInt x = pow((m - 1) / 2), y = (*this) * x * x;
x *= (*this);
ModInt z = b.pow(m);
while (y != 1) {
int j = 0;
ModInt t = y;
while (t != 1) j++, t *= t;
z = z.pow(1LL << (e - j - 1));
x *= z, z *= z, y *= z;
e = j;
}
return ModInt(std::min(x.val, md - x.val));
}
};
template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};
using mint = ModInt<(115 << 20) + 1>;
constexpr int root = 6;
// Integer convolution for arbitrary mod
// with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class.
// We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`.
// input: a (size: n), b (size: m)
// return: vector (size: n + m - 1)
template <typename MODINT>
std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner);
constexpr int nttprimes[3] = {(115 << 20) + 1, 998244353, 167772161};
// Integer FFT (Fast Fourier Transform) for ModInt class
// (Also known as Number Theoretic Transform, NTT)
// is_inverse: inverse transform
// ** Input size must be 2^n **
template <typename MODINT> void ntt(std::vector<MODINT> &a, bool is_inverse = false) {
int n = a.size();
if (n == 1) return;
static const int mod = MODINT::mod();
static const MODINT root = MODINT::get_primitive_root();
assert(__builtin_popcount(n) == 1 and (mod - 1) % n == 0);
static std::vector<MODINT> w{1}, iw{1};
for (int m = w.size(); m < n / 2; m *= 2) {
MODINT dw = root.pow((mod - 1) / (4 * m)), dwinv = 1 / dw;
w.resize(m * 2), iw.resize(m * 2);
for (int i = 0; i < m; i++) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv;
}
if (!is_inverse) {
for (int m = n; m >>= 1;) {
for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
for (int i = s; i < s + m; i++) {
MODINT x = a[i], y = a[i + m] * w[k];
a[i] = x + y, a[i + m] = x - y;
}
}
}
} else {
for (int m = 1; m < n; m *= 2) {
for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
for (int i = s; i < s + m; i++) {
MODINT x = a[i], y = a[i + m];
a[i] = x + y, a[i + m] = (x - y) * iw[k];
}
}
}
int n_inv = MODINT(n).inv();
for (auto &v : a) v *= n_inv;
}
}
template <int MOD> std::vector<ModInt<MOD>> nttconv_(const std::vector<int> &a, const std::vector<int> &b) {
int sz = a.size();
assert(a.size() == b.size() and __builtin_popcount(sz) == 1);
std::vector<ModInt<MOD>> ap(sz), bp(sz);
for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i];
ntt(ap, false);
if (a == b)
bp = ap;
else
ntt(bp, false);
for (int i = 0; i < sz; i++) ap[i] *= bp[i];
ntt(ap, true);
return ap;
}
long long garner_ntt_(int r0, int r1, int r2, int mod) {
using mint2 = ModInt<nttprimes[2]>;
static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];
static const long long m0_inv_m1 = ModInt<nttprimes[1]>(nttprimes[0]).inv();
static const long long m01_inv_m2 = mint2(m01).inv();
int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];
auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * m01_inv_m2;
return (r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val) % mod;
}
template <typename MODINT>
std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner) {
if (a.empty() or b.empty()) return {};
int sz = 1, n = a.size(), m = b.size();
while (sz < n + m) sz <<= 1;
if (sz <= 16) {
std::vector<MODINT> ret(n + m - 1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) ret[i + j] += a[i] * b[j];
}
return ret;
}
int mod = MODINT::mod();
if (skip_garner or std::find(std::begin(nttprimes), std::end(nttprimes), mod) != std::end(nttprimes)) {
a.resize(sz), b.resize(sz);
if (a == b) {
ntt(a, false);
b = a;
} else {
ntt(a, false), ntt(b, false);
}
for (int i = 0; i < sz; i++) a[i] *= b[i];
ntt(a, true);
a.resize(n + m - 1);
} else {
std::vector<int> ai(sz), bi(sz);
for (int i = 0; i < n; i++) ai[i] = a[i].val;
for (int i = 0; i < m; i++) bi[i] = b[i].val;
auto ntt0 = nttconv_<nttprimes[0]>(ai, bi);
auto ntt1 = nttconv_<nttprimes[1]>(ai, bi);
auto ntt2 = nttconv_<nttprimes[2]>(ai, bi);
a.resize(n + m - 1);
for (int i = 0; i < n + m - 1; i++) a[i] = garner_ntt_(ntt0[i].val, ntt1[i].val, ntt2[i].val, mod);
}
return a;
}
template <typename MODINT>
std::vector<MODINT> nttconv(const std::vector<MODINT> &a, const std::vector<MODINT> &b) {
return nttconv<MODINT>(a, b, false);
}
// Multivariate convolution (Linear, overflow cutoff)
// Complexity: (kN \log N + k^2 N)$
// Note that the vectors store the infomation in **column-major order**
// Implementation idea: https://rushcheyo.blog.uoj.ac/blog/6547
// Details of my implementation: https://hitonanode.github.io/cplib-cpp/convolution/multivar_ntt.hpp
template <typename MODINT> struct multivar_ntt {
int K, N, fftlen;
std::vector<int> dim;
std::vector<int> chi;
MODINT invfftlen;
private:
void _initialize(const std::vector<int> &dim_) {
dim = dim_;
K = dim_.size();
N = std::accumulate(dim_.begin(), dim_.end(), 1, [&](int l, int r) { return l * r; });
fftlen = 1;
while (fftlen < N * 2) fftlen <<= 1;
invfftlen = MODINT(fftlen).inv();
chi.resize(fftlen);
int t = 1;
for (auto d : dim_) {
t *= d;
for (int s = t; s < fftlen; s += t) chi[s] += 1;
}
for (int i = 0; i + 1 < fftlen; i++) {
chi[i + 1] += chi[i];
if (chi[i + 1] >= K) chi[i + 1] -= K;
}
}
std::vector<MODINT> _convolve(const std::vector<MODINT> &f, const std::vector<MODINT> &g) const {
assert(int(f.size()) == N);
assert(int(g.size()) == N);
if (dim.empty()) return {f[0] * g[0]};
std::vector<std::vector<MODINT>> fex(K, std::vector<MODINT>(fftlen)), gex(K, std::vector<MODINT>(fftlen));
for (int i = 0; i < N; i++) fex[chi[i]][i] = f[i], gex[chi[i]][i] = g[i];
for (auto &vec : fex) ntt(vec, false);
for (auto &vec : gex) ntt(vec, false);
std::vector<std::vector<MODINT>> hex(K, std::vector<MODINT>(fftlen));
for (int df = 0; df < K; df++) {
for (int dg = 0; dg < K; dg++) {
int dh = (df + dg < K) ? df + dg : df + dg - K;
for (int i = 0; i < fftlen; i++) hex[dh][i] += fex[df][i] * gex[dg][i];
}
}
for (auto &vec : hex) ntt(vec, true);
std::vector<MODINT> ret(N);
for (int i = 0; i < N; i++) ret[i] = hex[chi[i]][i];
return ret;
}
public:
multivar_ntt(const std::vector<int> &dim_) { _initialize(dim_); }
std::vector<MODINT> operator()(const std::vector<MODINT> &f, const std::vector<MODINT> &g) const {
return _convolve(f, g);
}
};
// 元ネタが分からないんですが，OpenCup の 7 乗根のやつですか？
constexpr int E = 10;
const mint r10 = 9142366;
template <typename T, typename Int> T pow(T x, Int n) {
T ans = 1;
while (n) {
if (n & 1) ans *= x;
x *= x;
n >>= 1;
}
return ans;
}
int main() {
int N, K;
lint M;
int T;
cin >> N >> K >> M >> T;
int K10 = 1;
REP(t, K) K10 *= 10;
vector<int> A(N);
cin >> A;
vector<int> diminfo(T, E); // T 桁切捨，K - T 桁周期
multivar_ntt<mint> mntt(diminfo);
vector nttmat(E, vector<mint>(E));
REP(i, nttmat.size()) REP(j, nttmat[i].size()) nttmat[i][j] = r10.pow(i * j);
auto inttmat = nttmat;
for (auto &vec : inttmat) for (auto &x : vec) x = x.inv() / mint(10);
auto ntt10 = [&](const vector<mint> &v) -> vector<mint> {
vector<mint> ret(E);
REP(i, E) REP(j, E) ret[i] += nttmat[i][j] * v[j];
return ret;
};
auto intt10 = [&](const vector<mint> &v) -> vector<mint> {
vector<mint> ret(E);
REP(i, E) REP(j, E) ret[i] += inttmat[i][j] * v[j];
return ret;
};
auto multiconv = [&](vector<mint> f, vector<mint> g) -> vector<mint> {
for (int di = mntt.N; di < K10; di *= 10) {
for (int l = 0; l < K10; l += di * 10) {
for (int i = l; i < l + di; ++i) {
// [i, i + di, i + 2di, ..., i + 9di] を NTT
auto impose_ntt = [&](vector<mint> &v) {
vector<mint> ntttmp(E);
REP(k, E) ntttmp[k] = v[i + k * di];
ntttmp = ntt10(ntttmp);
REP(k, E) v[i + k * di] = ntttmp[k];
};
impose_ntt(f);
impose_ntt(g);
}
}
}
vector<mint> ret;
for (int l = 0; l < K10; l += mntt.N) {
vector<mint> fsub(f.begin() + l, f.begin() + l + mntt.N);
vector<mint> gsub(g.begin() + l, g.begin() + l + mntt.N);
auto c = mntt(fsub, gsub);
ret.insert(ret.end(), c.begin(), c.end());
}
for (int di = mntt.N; di < K10; di *= 10) {
for (int l = 0; l < K10; l += di * 10) {
for (int i = l; i < l + di; ++i) {
// [i, i + di, i + 2di, ..., i + 9di] を NTT
auto impose_intt = [&](vector<mint> &v) {
vector<mint> ntttmp(E);
REP(k, E) ntttmp[k] = v[i + k * di];
ntttmp = intt10(ntttmp);
REP(k, E) v[i + k * di] = ntttmp[k];
};
impose_intt(ret);
}
}
}
return ret;
};
vector<mint> dp(K10), trans(K10);
dp[0] = 1;
for (auto a : A) trans[a] += 1;
while (M) {
if (M & 1) dp = multiconv(dp, trans);
trans = multiconv(trans, trans);
M /= 2;
}
// while (M--) dp = multiconv(dp, trans);
for (auto x : dp) cout << x << '\n';
}