結果
| 問題 | No.1783 Remix Sum |
| ユーザー |
 NyaanNyaan
|
| 提出日時 | 2021-12-12 09:24:53 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 7,440 ms / 10,000 ms |
| コード長 | 57,312 bytes |
| コンパイル時間 | 4,433 ms |
| コンパイル使用メモリ | 284,312 KB |
| 実行使用メモリ | 31,268 KB |
| 最終ジャッジ日時 | 2024-07-20 19:25:17 |
| 合計ジャッジ時間 | 83,203 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
（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 | AC | 27 ms
17,652 KB |
| testcase_01 | AC | 27 ms
17,648 KB |
| testcase_02 | AC | 26 ms
17,648 KB |
| testcase_03 | AC | 27 ms
17,648 KB |
| testcase_04 | AC | 72 ms
17,540 KB |
| testcase_05 | AC | 70 ms
17,648 KB |
| testcase_06 | AC | 127 ms
17,652 KB |
| testcase_07 | AC | 311 ms
17,648 KB |
| testcase_08 | AC | 127 ms
17,648 KB |
| testcase_09 | AC | 123 ms
17,612 KB |
| testcase_10 | AC | 68 ms
17,644 KB |
| testcase_11 | AC | 67 ms
17,648 KB |
| testcase_12 | AC | 359 ms
17,652 KB |
| testcase_13 | AC | 199 ms
17,644 KB |
| testcase_14 | AC | 112 ms
17,648 KB |
| testcase_15 | AC | 286 ms
30,748 KB |
| testcase_16 | AC | 306 ms
17,520 KB |
| testcase_17 | AC | 352 ms
17,648 KB |
| testcase_18 | AC | 67 ms
17,648 KB |
| testcase_19 | AC | 137 ms
17,648 KB |
| testcase_20 | AC | 145 ms
17,648 KB |
| testcase_21 | AC | 137 ms
17,644 KB |
| testcase_22 | AC | 147 ms
17,648 KB |
| testcase_23 | AC | 176 ms
17,648 KB |
| testcase_24 | AC | 105 ms
17,644 KB |
| testcase_25 | AC | 125 ms
17,564 KB |
| testcase_26 | AC | 352 ms
17,776 KB |
| testcase_27 | AC | 123 ms
17,648 KB |
| testcase_28 | AC | 103 ms
17,648 KB |
| testcase_29 | AC | 147 ms
17,648 KB |
| testcase_30 | AC | 150 ms
17,648 KB |
| testcase_31 | AC | 142 ms
17,644 KB |
| testcase_32 | AC | 407 ms
30,748 KB |
| testcase_33 | AC | 145 ms
17,652 KB |
| testcase_34 | AC | 111 ms
17,776 KB |
| testcase_35 | AC | 200 ms
18,028 KB |
| testcase_36 | AC | 234 ms
31,140 KB |
| testcase_37 | AC | 253 ms
31,268 KB |
| testcase_38 | AC | 212 ms
17,904 KB |
| testcase_39 | AC | 116 ms
17,772 KB |
| testcase_40 | AC | 98 ms
17,648 KB |
| testcase_41 | AC | 117 ms
17,644 KB |
| testcase_42 | AC | 118 ms
17,648 KB |
| testcase_43 | AC | 208 ms
17,904 KB |
| testcase_44 | AC | 287 ms
17,644 KB |
| testcase_45 | AC | 1,099 ms
17,644 KB |
| testcase_46 | AC | 1,446 ms
17,648 KB |
| testcase_47 | AC | 1,887 ms
17,648 KB |
| testcase_48 | AC | 4,376 ms
17,776 KB |
| testcase_49 | AC | 5,188 ms
31,268 KB |
| testcase_50 | AC | 281 ms
17,544 KB |
| testcase_51 | AC | 1,071 ms
17,648 KB |
| testcase_52 | AC | 1,385 ms
17,644 KB |
| testcase_53 | AC | 1,913 ms
17,644 KB |
| testcase_54 | AC | 4,463 ms
17,904 KB |
| testcase_55 | AC | 5,326 ms
31,140 KB |
| testcase_56 | AC | 366 ms
17,644 KB |
| testcase_57 | AC | 1,537 ms
17,772 KB |
| testcase_58 | AC | 1,950 ms
17,648 KB |
| testcase_59 | AC | 2,558 ms
17,648 KB |
| testcase_60 | AC | 6,262 ms
17,904 KB |
| testcase_61 | AC | 7,440 ms
31,144 KB |
| testcase_62 | AC | 282 ms
17,644 KB |
| testcase_63 | AC | 1,110 ms
17,520 KB |
| testcase_64 | AC | 1,412 ms
17,648 KB |
| testcase_65 | AC | 1,892 ms
17,520 KB |
| testcase_66 | AC | 4,404 ms
17,904 KB |
| testcase_67 | AC | 5,205 ms
31,268 KB |
| testcase_68 | AC | 93 ms
17,652 KB |
| testcase_69 | AC | 180 ms
17,524 KB |
| testcase_70 | AC | 220 ms
17,648 KB |
| testcase_71 | AC | 261 ms
17,652 KB |
| testcase_72 | AC | 556 ms
17,900 KB |
| testcase_73 | AC | 655 ms
31,264 KB |
| testcase_74 | AC | 93 ms
17,572 KB |
| testcase_75 | AC | 181 ms
17,644 KB |
| testcase_76 | AC | 214 ms
17,644 KB |
| testcase_77 | AC | 161 ms
17,644 KB |
| testcase_78 | AC | 411 ms
17,904 KB |
| testcase_79 | AC | 415 ms
31,140 KB |
ソースコード
/**
* date : 2021-12-12 09:24:48
*/
#define NDEBUG
/**
* date : 2021-10-22 22:08:24
*/
#define NDEBUG
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T, typename U>
struct P : pair<T, U> {
template <typename... Args>
P(Args... args) : pair<T, U>(args...) {}
using pair<T, U>::first;
using pair<T, U>::second;
T &x() { return first; }
const T &x() const { return first; }
U &y() { return second; }
const U &y() const { return second; }
P &operator+=(const P &r) {
first += r.first;
second += r.second;
return *this;
}
P &operator-=(const P &r) {
first -= r.first;
second -= r.second;
return *this;
}
P &operator*=(const P &r) {
first *= r.first;
second *= r.second;
return *this;
}
P operator+(const P &r) const { return P(*this) += r; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator*(const P &r) const { return P(*this) *= r; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
vector<T> ret(v.size() + 1);
if (rev) {
for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
} else {
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
}
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N, F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
int max_val = *max_element(begin(v), end(v));
vector<int> inv(max_val + 1, -1);
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
} // namespace Nyaan
// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
} // namespace Nyaan
// inout
namespace Nyaan {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &... u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &... u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
void outr() {}
template <typename T, class... U, char sep = ' '>
void outr(const T &t, const U &... u) {
cout << t;
outr(u...);
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
} // namespace Nyaan
// debug
namespace DebugImpl {
template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, typename U::iterator, void>::type>
: true_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, decltype(U::first), void>::type>
: true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};
void dump(const char& t) { cerr << t; }
void dump(const string& t) { cerr << t; }
void dump(const bool& t) { cerr << (t ? "true" : "false"); }
template <typename U,
enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
cerr << t;
}
template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
string res;
if (t == Nyaan::inf) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::inf) res = "-inf";
}
if constexpr (sizeof(T) == 8) {
if (t == Nyaan::infLL) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::infLL) res = "-inf";
}
}
if (res.empty()) res = to_string(t);
cerr << res;
}
template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);
template <typename T>
void dump(const T& t,
enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
cerr << "[ ";
for (auto it = t.begin(); it != t.end();) {
dump(*it);
cerr << (++it == t.end() ? "" : ", ");
}
cerr << " ]";
}
template <typename T, typename U>
void dump(const pair<T, U>& t) {
cerr << "( ";
dump(t.first);
cerr << ", ";
dump(t.second);
cerr << " )";
}
template <typename T>
void dump(const pair<T*, int>& t) {
cerr << "[ ";
for (int i = 0; i < t.second; i++) {
dump(t.first[i]);
cerr << (i == t.second - 1 ? "" : ", ");
}
cerr << " ]";
}
void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
cerr << " ";
dump(head);
if (sizeof...(tail) != 0) cerr << ",";
trace(forward<Tail>(tail)...);
}
} // namespace DebugImpl
#ifdef NyaanDebug
#define trc(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc(...) (void(0))
#endif
// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
//
__attribute__((target("sse4.2"))) inline __m128i my128_mullo_epu32(
const __m128i &a, const __m128i &b) {
return _mm_mullo_epi32(a, b);
}
__attribute__((target("sse4.2"))) inline __m128i my128_mulhi_epu32(
const __m128i &a, const __m128i &b) {
__m128i a13 = _mm_shuffle_epi32(a, 0xF5);
__m128i b13 = _mm_shuffle_epi32(b, 0xF5);
__m128i prod02 = _mm_mul_epu32(a, b);
__m128i prod13 = _mm_mul_epu32(a13, b13);
__m128i prod = _mm_unpackhi_epi64(_mm_unpacklo_epi32(prod02, prod13),
_mm_unpackhi_epi32(prod02, prod13));
return prod;
}
__attribute__((target("sse4.2"))) inline __m128i montgomery_mul_128(
const __m128i &a, const __m128i &b, const __m128i &r, const __m128i &m1) {
return _mm_sub_epi32(
_mm_add_epi32(my128_mulhi_epu32(a, b), m1),
my128_mulhi_epu32(my128_mullo_epu32(my128_mullo_epu32(a, b), r), m1));
}
__attribute__((target("sse4.2"))) inline __m128i montgomery_add_128(
const __m128i &a, const __m128i &b, const __m128i &m2, const __m128i &m0) {
__m128i ret = _mm_sub_epi32(_mm_add_epi32(a, b), m2);
return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0, ret), m2), ret);
}
__attribute__((target("sse4.2"))) inline __m128i montgomery_sub_128(
const __m128i &a, const __m128i &b, const __m128i &m2, const __m128i &m0) {
__m128i ret = _mm_sub_epi32(a, b);
return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0, ret), m2), ret);
}
__attribute__((target("avx2"))) inline __m256i my256_mullo_epu32(
const __m256i &a, const __m256i &b) {
return _mm256_mullo_epi32(a, b);
}
__attribute__((target("avx2"))) inline __m256i my256_mulhi_epu32(
const __m256i &a, const __m256i &b) {
__m256i a13 = _mm256_shuffle_epi32(a, 0xF5);
__m256i b13 = _mm256_shuffle_epi32(b, 0xF5);
__m256i prod02 = _mm256_mul_epu32(a, b);
__m256i prod13 = _mm256_mul_epu32(a13, b13);
__m256i prod = _mm256_unpackhi_epi64(_mm256_unpacklo_epi32(prod02, prod13),
_mm256_unpackhi_epi32(prod02, prod13));
return prod;
}
__attribute__((target("avx2"))) inline __m256i montgomery_mul_256(
const __m256i &a, const __m256i &b, const __m256i &r, const __m256i &m1) {
return _mm256_sub_epi32(
_mm256_add_epi32(my256_mulhi_epu32(a, b), m1),
my256_mulhi_epu32(my256_mullo_epu32(my256_mullo_epu32(a, b), r), m1));
}
__attribute__((target("avx2"))) inline __m256i montgomery_add_256(
const __m256i &a, const __m256i &b, const __m256i &m2, const __m256i &m0) {
__m256i ret = _mm256_sub_epi32(_mm256_add_epi32(a, b), m2);
return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0, ret), m2),
ret);
}
__attribute__((target("avx2"))) inline __m256i montgomery_sub_256(
const __m256i &a, const __m256i &b, const __m256i &m2, const __m256i &m0) {
__m256i ret = _mm256_sub_epi32(a, b);
return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0, ret), m2),
ret);
}
namespace ntt_inner {
using u64 = uint64_t;
constexpr uint32_t get_pr(uint32_t mod) {
if (mod == 2) return 1;
u64 ds[32] = {};
int idx = 0;
u64 m = mod - 1;
for (u64 i = 2; i * i <= m; ++i) {
if (m % i == 0) {
ds[idx++] = i;
while (m % i == 0) m /= i;
}
}
if (m != 1) ds[idx++] = m;
uint32_t pr = 2;
while (1) {
int flg = 1;
for (int i = 0; i < idx; ++i) {
u64 a = pr, b = (mod - 1) / ds[i], r = 1;
while (b) {
if (b & 1) r = r * a % mod;
a = a * a % mod;
b >>= 1;
}
if (r == 1) {
flg = 0;
break;
}
}
if (flg == 1) break;
++pr;
}
return pr;
}
constexpr int SZ_FFT_BUF = 1 << 23;
uint32_t _buf1[SZ_FFT_BUF] __attribute__((aligned(64)));
uint32_t _buf2[SZ_FFT_BUF] __attribute__((aligned(64)));
} // namespace ntt_inner
template <typename mint>
struct NTT {
static constexpr uint32_t mod = mint::get_mod();
static constexpr uint32_t pr = ntt_inner::get_pr(mint::get_mod());
static constexpr int level = __builtin_ctzll(mod - 1);
mint dw[level], dy[level];
mint *buf1, *buf2;
constexpr NTT() {
setwy(level);
union raw_cast {
mint dat;
uint32_t _;
};
buf1 = &(((raw_cast *)(ntt_inner::_buf1))->dat);
buf2 = &(((raw_cast *)(ntt_inner::_buf2))->dat);
}
constexpr void setwy(int k) {
mint w[level], y[level];
w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
y[k - 1] = w[k - 1].inverse();
for (int i = k - 2; i > 0; --i)
w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
dw[0] = dy[0] = w[1] * w[1];
dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
for (int i = 3; i < k; ++i) {
dw[i] = dw[i - 1] * y[i - 2] * w[i];
dy[i] = dy[i - 1] * w[i - 2] * y[i];
}
}
__attribute__((target("avx2"))) void ntt(mint *a, int n) {
int k = n ? __builtin_ctz(n) : 0;
if (k == 0) return;
if (k == 1) {
mint a1 = a[1];
a[1] = a[0] - a[1];
a[0] = a[0] + a1;
return;
}
if (k & 1) {
int v = 1 << (k - 1);
if (v < 8) {
for (int j = 0; j < v; ++j) {
mint ajv = a[j + v];
a[j + v] = a[j] - ajv;
a[j] += ajv;
}
} else {
const __m256i m0 = _mm256_set1_epi32(0);
const __m256i m2 = _mm256_set1_epi32(mod + mod);
int j0 = 0;
int j1 = v;
for (; j0 < v; j0 += 8, j1 += 8) {
__m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
__m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
__m256i naj = montgomery_add_256(T0, T1, m2, m0);
__m256i najv = montgomery_sub_256(T0, T1, m2, m0);
_mm256_storeu_si256((__m256i *)(a + j0), naj);
_mm256_storeu_si256((__m256i *)(a + j1), najv);
}
}
}
int u = 1 << (2 + (k & 1));
int v = 1 << (k - 2 - (k & 1));
mint one = mint(1);
mint imag = dw[1];
while (v) {
if (v == 1) {
mint ww = one, xx = one, wx = one;
for (int jh = 0; jh < u;) {
ww = xx * xx, wx = ww * xx;
mint t0 = a[jh + 0], t1 = a[jh + 1] * xx;
mint t2 = a[jh + 2] * ww, t3 = a[jh + 3] * wx;
mint t0p2 = t0 + t2, t1p3 = t1 + t3;
mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
a[jh + 0] = t0p2 + t1p3, a[jh + 1] = t0p2 - t1p3;
a[jh + 2] = t0m2 + t1m3, a[jh + 3] = t0m2 - t1m3;
xx *= dw[__builtin_ctz((jh += 4))];
}
} else if (v == 4) {
const __m128i m0 = _mm_set1_epi32(0);
const __m128i m1 = _mm_set1_epi32(mod);
const __m128i m2 = _mm_set1_epi32(mod + mod);
const __m128i r = _mm_set1_epi32(mint::r);
const __m128i Imag = _mm_set1_epi32(imag.a);
mint ww = one, xx = one, wx = one;
for (int jh = 0; jh < u;) {
if (jh == 0) {
int j0 = 0;
int j1 = v;
int j2 = j1 + v;
int j3 = j2 + v;
int je = v;
for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
const __m128i T0P2 = montgomery_add_128(T0, T2, m2, m0);
const __m128i T1P3 = montgomery_add_128(T1, T3, m2, m0);
const __m128i T0M2 = montgomery_sub_128(T0, T2, m2, m0);
const __m128i T1M3 = montgomery_mul_128(
montgomery_sub_128(T1, T3, m2, m0), Imag, r, m1);
_mm_storeu_si128((__m128i *)(a + j0),
montgomery_add_128(T0P2, T1P3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j1),
montgomery_sub_128(T0P2, T1P3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j2),
montgomery_add_128(T0M2, T1M3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j3),
montgomery_sub_128(T0M2, T1M3, m2, m0));
}
} else {
ww = xx * xx, wx = ww * xx;
const __m128i WW = _mm_set1_epi32(ww.a);
const __m128i WX = _mm_set1_epi32(wx.a);
const __m128i XX = _mm_set1_epi32(xx.a);
int j0 = jh * v;
int j1 = j0 + v;
int j2 = j1 + v;
int j3 = j2 + v;
int je = j1;
for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
const __m128i MT1 = montgomery_mul_128(T1, XX, r, m1);
const __m128i MT2 = montgomery_mul_128(T2, WW, r, m1);
const __m128i MT3 = montgomery_mul_128(T3, WX, r, m1);
const __m128i T0P2 = montgomery_add_128(T0, MT2, m2, m0);
const __m128i T1P3 = montgomery_add_128(MT1, MT3, m2, m0);
const __m128i T0M2 = montgomery_sub_128(T0, MT2, m2, m0);
const __m128i T1M3 = montgomery_mul_128(
montgomery_sub_128(MT1, MT3, m2, m0), Imag, r, m1);
_mm_storeu_si128((__m128i *)(a + j0),
montgomery_add_128(T0P2, T1P3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j1),
montgomery_sub_128(T0P2, T1P3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j2),
montgomery_add_128(T0M2, T1M3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j3),
montgomery_sub_128(T0M2, T1M3, m2, m0));
}
}
xx *= dw[__builtin_ctz((jh += 4))];
}
} else {
const __m256i m0 = _mm256_set1_epi32(0);
const __m256i m1 = _mm256_set1_epi32(mod);
const __m256i m2 = _mm256_set1_epi32(mod + mod);
const __m256i r = _mm256_set1_epi32(mint::r);
const __m256i Imag = _mm256_set1_epi32(imag.a);
mint ww = one, xx = one, wx = one;
for (int jh = 0; jh < u;) {
if (jh == 0) {
int j0 = 0;
int j1 = v;
int j2 = j1 + v;
int j3 = j2 + v;
int je = v;
for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
const __m256i T0P2 = montgomery_add_256(T0, T2, m2, m0);
const __m256i T1P3 = montgomery_add_256(T1, T3, m2, m0);
const __m256i T0M2 = montgomery_sub_256(T0, T2, m2, m0);
const __m256i T1M3 = montgomery_mul_256(
montgomery_sub_256(T1, T3, m2, m0), Imag, r, m1);
_mm256_storeu_si256((__m256i *)(a + j0),
montgomery_add_256(T0P2, T1P3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j1),
montgomery_sub_256(T0P2, T1P3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j2),
montgomery_add_256(T0M2, T1M3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j3),
montgomery_sub_256(T0M2, T1M3, m2, m0));
}
} else {
ww = xx * xx, wx = ww * xx;
const __m256i WW = _mm256_set1_epi32(ww.a);
const __m256i WX = _mm256_set1_epi32(wx.a);
const __m256i XX = _mm256_set1_epi32(xx.a);
int j0 = jh * v;
int j1 = j0 + v;
int j2 = j1 + v;
int j3 = j2 + v;
int je = j1;
for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
const __m256i MT1 = montgomery_mul_256(T1, XX, r, m1);
const __m256i MT2 = montgomery_mul_256(T2, WW, r, m1);
const __m256i MT3 = montgomery_mul_256(T3, WX, r, m1);
const __m256i T0P2 = montgomery_add_256(T0, MT2, m2, m0);
const __m256i T1P3 = montgomery_add_256(MT1, MT3, m2, m0);
const __m256i T0M2 = montgomery_sub_256(T0, MT2, m2, m0);
const __m256i T1M3 = montgomery_mul_256(
montgomery_sub_256(MT1, MT3, m2, m0), Imag, r, m1);
_mm256_storeu_si256((__m256i *)(a + j0),
montgomery_add_256(T0P2, T1P3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j1),
montgomery_sub_256(T0P2, T1P3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j2),
montgomery_add_256(T0M2, T1M3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j3),
montgomery_sub_256(T0M2, T1M3, m2, m0));
}
}
xx *= dw[__builtin_ctz((jh += 4))];
}
}
u <<= 2;
v >>= 2;
}
}
__attribute__((target("avx2"))) void intt(mint *a, int n,
int normalize = true) {
int k = n ? __builtin_ctz(n) : 0;
if (k == 0) return;
if (k == 1) {
mint a1 = a[1];
a[1] = a[0] - a[1];
a[0] = a[0] + a1;
if (normalize) {
a[0] *= mint(2).inverse();
a[1] *= mint(2).inverse();
}
return;
}
int u = 1 << (k - 2);
int v = 1;
mint one = mint(1);
mint imag = dy[1];
while (u) {
if (v == 1) {
mint ww = one, xx = one, yy = one;
u <<= 2;
for (int jh = 0; jh < u;) {
ww = xx * xx, yy = xx * imag;
mint t0 = a[jh + 0], t1 = a[jh + 1];
mint t2 = a[jh + 2], t3 = a[jh + 3];
mint t0p1 = t0 + t1, t2p3 = t2 + t3;
mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
a[jh + 0] = t0p1 + t2p3, a[jh + 2] = (t0p1 - t2p3) * ww;
a[jh + 1] = t0m1 + t2m3, a[jh + 3] = (t0m1 - t2m3) * ww;
xx *= dy[__builtin_ctz(jh += 4)];
}
} else if (v == 4) {
const __m128i m0 = _mm_set1_epi32(0);
const __m128i m1 = _mm_set1_epi32(mod);
const __m128i m2 = _mm_set1_epi32(mod + mod);
const __m128i r = _mm_set1_epi32(mint::r);
const __m128i Imag = _mm_set1_epi32(imag.a);
mint ww = one, xx = one, yy = one;
u <<= 2;
for (int jh = 0; jh < u;) {
if (jh == 0) {
int j0 = 0;
int j1 = v;
int j2 = v + v;
int j3 = j2 + v;
for (; j0 < v; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
const __m128i T0P1 = montgomery_add_128(T0, T1, m2, m0);
const __m128i T2P3 = montgomery_add_128(T2, T3, m2, m0);
const __m128i T0M1 = montgomery_sub_128(T0, T1, m2, m0);
const __m128i T2M3 = montgomery_mul_128(
montgomery_sub_128(T2, T3, m2, m0), Imag, r, m1);
_mm_storeu_si128((__m128i *)(a + j0),
montgomery_add_128(T0P1, T2P3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j2),
montgomery_sub_128(T0P1, T2P3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j1),
montgomery_add_128(T0M1, T2M3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j3),
montgomery_sub_128(T0M1, T2M3, m2, m0));
}
} else {
ww = xx * xx, yy = xx * imag;
const __m128i WW = _mm_set1_epi32(ww.a);
const __m128i XX = _mm_set1_epi32(xx.a);
const __m128i YY = _mm_set1_epi32(yy.a);
int j0 = jh * v;
int j1 = j0 + v;
int j2 = j1 + v;
int j3 = j2 + v;
int je = j1;
for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
const __m128i T0P1 = montgomery_add_128(T0, T1, m2, m0);
const __m128i T2P3 = montgomery_add_128(T2, T3, m2, m0);
const __m128i T0M1 = montgomery_mul_128(
montgomery_sub_128(T0, T1, m2, m0), XX, r, m1);
__m128i T2M3 = montgomery_mul_128(
montgomery_sub_128(T2, T3, m2, m0), YY, r, m1);
_mm_storeu_si128((__m128i *)(a + j0),
montgomery_add_128(T0P1, T2P3, m2, m0));
_mm_storeu_si128(
(__m128i *)(a + j2),
montgomery_mul_128(montgomery_sub_128(T0P1, T2P3, m2, m0), WW,
r, m1));
_mm_storeu_si128((__m128i *)(a + j1),
montgomery_add_128(T0M1, T2M3, m2, m0));
_mm_storeu_si128(
(__m128i *)(a + j3),
montgomery_mul_128(montgomery_sub_128(T0M1, T2M3, m2, m0), WW,
r, m1));
}
}
xx *= dy[__builtin_ctz(jh += 4)];
}
} else {
const __m256i m0 = _mm256_set1_epi32(0);
const __m256i m1 = _mm256_set1_epi32(mod);
const __m256i m2 = _mm256_set1_epi32(mod + mod);
const __m256i r = _mm256_set1_epi32(mint::r);
const __m256i Imag = _mm256_set1_epi32(imag.a);
mint ww = one, xx = one, yy = one;
u <<= 2;
for (int jh = 0; jh < u;) {
if (jh == 0) {
int j0 = 0;
int j1 = v;
int j2 = v + v;
int j3 = j2 + v;
for (; j0 < v; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
const __m256i T0P1 = montgomery_add_256(T0, T1, m2, m0);
const __m256i T2P3 = montgomery_add_256(T2, T3, m2, m0);
const __m256i T0M1 = montgomery_sub_256(T0, T1, m2, m0);
const __m256i T2M3 = montgomery_mul_256(
montgomery_sub_256(T2, T3, m2, m0), Imag, r, m1);
_mm256_storeu_si256((__m256i *)(a + j0),
montgomery_add_256(T0P1, T2P3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j2),
montgomery_sub_256(T0P1, T2P3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j1),
montgomery_add_256(T0M1, T2M3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j3),
montgomery_sub_256(T0M1, T2M3, m2, m0));
}
} else {
ww = xx * xx, yy = xx * imag;
const __m256i WW = _mm256_set1_epi32(ww.a);
const __m256i XX = _mm256_set1_epi32(xx.a);
const __m256i YY = _mm256_set1_epi32(yy.a);
int j0 = jh * v;
int j1 = j0 + v;
int j2 = j1 + v;
int j3 = j2 + v;
int je = j1;
for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
const __m256i T0P1 = montgomery_add_256(T0, T1, m2, m0);
const __m256i T2P3 = montgomery_add_256(T2, T3, m2, m0);
const __m256i T0M1 = montgomery_mul_256(
montgomery_sub_256(T0, T1, m2, m0), XX, r, m1);
const __m256i T2M3 = montgomery_mul_256(
montgomery_sub_256(T2, T3, m2, m0), YY, r, m1);
_mm256_storeu_si256((__m256i *)(a + j0),
montgomery_add_256(T0P1, T2P3, m2, m0));
_mm256_storeu_si256(
(__m256i *)(a + j2),
montgomery_mul_256(montgomery_sub_256(T0P1, T2P3, m2, m0), WW,
r, m1));
_mm256_storeu_si256((__m256i *)(a + j1),
montgomery_add_256(T0M1, T2M3, m2, m0));
_mm256_storeu_si256(
(__m256i *)(a + j3),
montgomery_mul_256(montgomery_sub_256(T0M1, T2M3, m2, m0), WW,
r, m1));
}
}
xx *= dy[__builtin_ctz(jh += 4)];
}
}
u >>= 4;
v <<= 2;
}
if (k & 1) {
v = 1 << (k - 1);
if (v < 8) {
for (int j = 0; j < v; ++j) {
mint ajv = a[j] - a[j + v];
a[j] += a[j + v];
a[j + v] = ajv;
}
} else {
const __m256i m0 = _mm256_set1_epi32(0);
const __m256i m2 = _mm256_set1_epi32(mod + mod);
int j0 = 0;
int j1 = v;
for (; j0 < v; j0 += 8, j1 += 8) {
const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
__m256i naj = montgomery_add_256(T0, T1, m2, m0);
__m256i najv = montgomery_sub_256(T0, T1, m2, m0);
_mm256_storeu_si256((__m256i *)(a + j0), naj);
_mm256_storeu_si256((__m256i *)(a + j1), najv);
}
}
}
if (normalize) {
mint invn = mint(n).inverse();
for (int i = 0; i < n; i++) a[i] *= invn;
}
}
__attribute__((target("avx2"))) void inplace_multiply(
int l1, int l2, int zero_padding = true) {
int l = l1 + l2 - 1;
int M = 4;
while (M < l) M <<= 1;
if (zero_padding) {
for (int i = l1; i < M; i++) ntt_inner::_buf1[i] = 0;
for (int i = l2; i < M; i++) ntt_inner::_buf2[i] = 0;
}
const __m256i m0 = _mm256_set1_epi32(0);
const __m256i m1 = _mm256_set1_epi32(mod);
const __m256i r = _mm256_set1_epi32(mint::r);
const __m256i N2 = _mm256_set1_epi32(mint::n2);
for (int i = 0; i < l1; i += 8) {
__m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf1 + i));
__m256i b = montgomery_mul_256(a, N2, r, m1);
_mm256_storeu_si256((__m256i *)(ntt_inner::_buf1 + i), b);
}
for (int i = 0; i < l2; i += 8) {
__m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf2 + i));
__m256i b = montgomery_mul_256(a, N2, r, m1);
_mm256_storeu_si256((__m256i *)(ntt_inner::_buf2 + i), b);
}
ntt(buf1, M);
ntt(buf2, M);
for (int i = 0; i < M; i += 8) {
__m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf1 + i));
__m256i b = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf2 + i));
__m256i c = montgomery_mul_256(a, b, r, m1);
_mm256_storeu_si256((__m256i *)(ntt_inner::_buf1 + i), c);
}
intt(buf1, M, false);
const __m256i INVM = _mm256_set1_epi32((mint(M).inverse()).a);
for (int i = 0; i < l; i += 8) {
__m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf1 + i));
__m256i b = montgomery_mul_256(a, INVM, r, m1);
__m256i c = my256_mulhi_epu32(my256_mullo_epu32(b, r), m1);
__m256i d = _mm256_and_si256(_mm256_cmpgt_epi32(c, m0), m1);
__m256i e = _mm256_sub_epi32(d, c);
_mm256_storeu_si256((__m256i *)(ntt_inner::_buf1 + i), e);
}
}
void ntt(vector<mint> &a) {
int M = (int)a.size();
for (int i = 0; i < M; i++) buf1[i].a = a[i].a;
ntt(buf1, M);
for (int i = 0; i < M; i++) a[i].a = buf1[i].a;
}
void intt(vector<mint> &a) {
int M = (int)a.size();
for (int i = 0; i < M; i++) buf1[i].a = a[i].a;
intt(buf1, M, true);
for (int i = 0; i < M; i++) a[i].a = buf1[i].a;
}
vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
if (a.size() == 0 && b.size() == 0) return vector<mint>{};
int l = a.size() + b.size() - 1;
if (min<int>(a.size(), b.size()) <= 40) {
vector<mint> s(l);
for (int i = 0; i < (int)a.size(); ++i)
for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];
return s;
}
assert(l <= ntt_inner::SZ_FFT_BUF);
int M = 4;
while (M < l) M <<= 1;
for (int i = 0; i < (int)a.size(); ++i) buf1[i].a = a[i].a;
for (int i = (int)a.size(); i < M; ++i) buf1[i].a = 0;
for (int i = 0; i < (int)b.size(); ++i) buf2[i].a = b[i].a;
for (int i = (int)b.size(); i < M; ++i) buf2[i].a = 0;
ntt(buf1, M);
ntt(buf2, M);
for (int i = 0; i < M; ++i)
buf1[i].a = mint::reduce(uint64_t(buf1[i].a) * buf2[i].a);
intt(buf1, M, false);
vector<mint> s(l);
mint invm = mint(M).inverse();
for (int i = 0; i < l; ++i) s[i] = buf1[i] * invm;
return s;
}
void ntt_doubling(vector<mint> &a) {
int M = (int)a.size();
for (int i = 0; i < M; i++) buf1[i].a = a[i].a;
intt(buf1, M);
mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
for (int i = 0; i < M; i++) buf1[i] *= r, r *= zeta;
ntt(buf1, M);
a.resize(2 * M);
for (int i = 0; i < M; i++) a[M + i].a = buf1[i].a;
}
};
template <typename mint>
struct FormalPowerSeries : vector<mint> {
using vector<mint>::vector;
using FPS = FormalPowerSeries;
FPS &operator+=(const FPS &r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];
return *this;
}
FPS &operator+=(const mint &r) {
if (this->empty()) this->resize(1);
(*this)[0] += r;
return *this;
}
FPS &operator-=(const FPS &r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];
return *this;
}
FPS &operator-=(const mint &r) {
if (this->empty()) this->resize(1);
(*this)[0] -= r;
return *this;
}
FPS &operator*=(const mint &v) {
for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v;
return *this;
}
FPS &operator/=(const FPS &r) {
if (this->size() < r.size()) {
this->clear();
return *this;
}
int n = this->size() - r.size() + 1;
if ((int)r.size() <= 64) {
FPS f(*this), g(r);
g.shrink();
mint coeff = g.back().inverse();
for (auto &x : g) x *= coeff;
int deg = (int)f.size() - (int)g.size() + 1;
int gs = g.size();
FPS quo(deg);
for (int i = deg - 1; i >= 0; i--) {
quo[i] = f[i + gs - 1];
for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j];
}
*this = quo * coeff;
this->resize(n, mint(0));
return *this;
}
return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();
}
FPS &operator%=(const FPS &r) {
*this -= *this / r * r;
shrink();
return *this;
}
FPS operator+(const FPS &r) const { return FPS(*this) += r; }
FPS operator+(const mint &v) const { return FPS(*this) += v; }
FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
FPS operator-(const mint &v) const { return FPS(*this) -= v; }
FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
FPS operator*(const mint &v) const { return FPS(*this) *= v; }
FPS operator/(const FPS &r) const { return FPS(*this) /= r; }
FPS operator%(const FPS &r) const { return FPS(*this) %= r; }
FPS operator-() const {
FPS ret(this->size());
for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i];
return ret;
}
void shrink() {
while (this->size() && this->back() == mint(0)) this->pop_back();
}
FPS rev() const {
FPS ret(*this);
reverse(begin(ret), end(ret));
return ret;
}
FPS dot(FPS r) const {
FPS ret(min(this->size(), r.size()));
for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i];
return ret;
}
FPS pre(int sz) const {
return FPS(begin(*this), begin(*this) + min((int)this->size(), sz));
}
FPS operator>>(int sz) const {
if ((int)this->size() <= sz) return {};
FPS ret(*this);
ret.erase(ret.begin(), ret.begin() + sz);
return ret;
}
FPS operator<<(int sz) const {
FPS ret(*this);
ret.insert(ret.begin(), sz, mint(0));
return ret;
}
FPS diff() const {
const int n = (int)this->size();
FPS ret(max(0, n - 1));
mint one(1), coeff(1);
for (int i = 1; i < n; i++) {
ret[i - 1] = (*this)[i] * coeff;
coeff += one;
}
return ret;
}
FPS integral() const {
const int n = (int)this->size();
FPS ret(n + 1);
ret[0] = mint(0);
if (n > 0) ret[1] = mint(1);
auto mod = mint::get_mod();
for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i);
for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i];
return ret;
}
mint eval(mint x) const {
mint r = 0, w = 1;
for (auto &v : *this) r += w * v, w *= x;
return r;
}
FPS log(int deg = -1) const {
assert((*this)[0] == mint(1));
if (deg == -1) deg = (int)this->size();
return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
}
FPS pow(int64_t k, int deg = -1) const {
const int n = (int)this->size();
if (deg == -1) deg = n;
for (int i = 0; i < n; i++) {
if ((*this)[i] != mint(0)) {
if (i * k > deg) return FPS(deg, mint(0));
mint rev = mint(1) / (*this)[i];
FPS ret =
(((*this * rev) >> i).log(deg) * k).exp(deg) * ((*this)[i].pow(k));
ret = (ret << (i * k)).pre(deg);
if ((int)ret.size() < deg) ret.resize(deg, mint(0));
return ret;
}
}
return FPS(deg, mint(0));
}
static void *ntt_ptr;
static void set_fft();
FPS &operator*=(const FPS &r);
void ntt();
void intt();
void ntt_doubling();
static int ntt_pr();
FPS inv(int deg = -1) const;
FPS exp(int deg = -1) const;
};
template <typename mint>
void *FormalPowerSeries<mint>::ntt_ptr = nullptr;
/**
* @brief 多項式/形式的冪級数ライブラリ
* @docs docs/fps/formal-power-series.md
*/
template <typename mint>
void FormalPowerSeries<mint>::set_fft() {
if (!ntt_ptr) ntt_ptr = new NTT<mint>;
}
template <typename mint>
FormalPowerSeries<mint>& FormalPowerSeries<mint>::operator*=(
const FormalPowerSeries<mint>& r) {
if (this->empty() || r.empty()) {
this->clear();
return *this;
}
set_fft();
auto ret = static_cast<NTT<mint>*>(ntt_ptr)->multiply(*this, r);
return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());
}
template <typename mint>
void FormalPowerSeries<mint>::ntt() {
set_fft();
static_cast<NTT<mint>*>(ntt_ptr)->ntt(*this);
}
template <typename mint>
void FormalPowerSeries<mint>::intt() {
set_fft();
static_cast<NTT<mint>*>(ntt_ptr)->intt(*this);
}
template <typename mint>
void FormalPowerSeries<mint>::ntt_doubling() {
set_fft();
static_cast<NTT<mint>*>(ntt_ptr)->ntt_doubling(*this);
}
template <typename mint>
int FormalPowerSeries<mint>::ntt_pr() {
set_fft();
return static_cast<NTT<mint>*>(ntt_ptr)->pr;
}
template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {
assert((*this)[0] != mint(0));
if (deg == -1) deg = (int)this->size();
FormalPowerSeries<mint> res(deg);
res[0] = {mint(1) / (*this)[0]};
for (int d = 1; d < deg; d <<= 1) {
FormalPowerSeries<mint> f(2 * d), g(2 * d);
for (int j = 0; j < min((int)this->size(), 2 * d); j++) f[j] = (*this)[j];
for (int j = 0; j < d; j++) g[j] = res[j];
f.ntt();
g.ntt();
for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
f.intt();
for (int j = 0; j < d; j++) f[j] = 0;
f.ntt();
for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
f.intt();
for (int j = d; j < min(2 * d, deg); j++) res[j] = -f[j];
}
return res.pre(deg);
}
template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {
using fps = FormalPowerSeries<mint>;
assert((*this).size() == 0 || (*this)[0] == mint(0));
if (deg == -1) deg = this->size();
fps inv;
inv.reserve(deg + 1);
inv.push_back(mint(0));
inv.push_back(mint(1));
auto inplace_integral = [&](fps& F) -> void {
const int n = (int)F.size();
auto mod = mint::get_mod();
while ((int)inv.size() <= n) {
int i = inv.size();
inv.push_back((-inv[mod % i]) * (mod / i));
}
F.insert(begin(F), mint(0));
for (int i = 1; i <= n; i++) F[i] *= inv[i];
};
auto inplace_diff = [](fps& F) -> void {
if (F.empty()) return;
F.erase(begin(F));
mint coeff = 1, one = 1;
for (int i = 0; i < (int)F.size(); i++) {
F[i] *= coeff;
coeff += one;
}
};
fps b{1, 1 < (int)this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};
for (int m = 2; m < deg; m *= 2) {
auto y = b;
y.resize(2 * m);
y.ntt();
z1 = z2;
fps z(m);
for (int i = 0; i < m; ++i) z[i] = y[i] * z1[i];
z.intt();
fill(begin(z), begin(z) + m / 2, mint(0));
z.ntt();
for (int i = 0; i < m; ++i) z[i] *= -z1[i];
z.intt();
c.insert(end(c), begin(z) + m / 2, end(z));
z2 = c;
z2.resize(2 * m);
z2.ntt();
fps x(begin(*this), begin(*this) + min<int>(this->size(), m));
x.resize(m);
inplace_diff(x);
x.push_back(mint(0));
x.ntt();
for (int i = 0; i < m; ++i) x[i] *= y[i];
x.intt();
x -= b.diff();
x.resize(2 * m);
for (int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = mint(0);
x.ntt();
for (int i = 0; i < 2 * m; ++i) x[i] *= z2[i];
x.intt();
x.pop_back();
inplace_integral(x);
for (int i = m; i < min<int>(this->size(), 2 * m); ++i) x[i] += (*this)[i];
fill(begin(x), begin(x) + m, mint(0));
x.ntt();
for (int i = 0; i < 2 * m; ++i) x[i] *= y[i];
x.intt();
b.insert(end(b), begin(x) + m, end(x));
}
return fps{begin(b), begin(b) + deg};
}
/**
* @brief NTT mod用FPSライブラリ
* @docs docs/fps/ntt-friendly-fps.md
*/
constexpr uint32_t PrimitiveRoot(uint32_t mod) {
using u64 = uint64_t;
if (mod == 2) return 1;
u64 ds[32] = {};
int idx = 0;
u64 m = mod - 1;
for (u64 i = 2; i * i <= m; ++i) {
if (m % i == 0) {
ds[idx++] = i;
while (m % i == 0) m /= i;
}
}
if (m != 1) ds[idx++] = m;
uint32_t pr = 2;
while (1) {
int flg = 1;
for (int i = 0; i < idx; ++i) {
u64 a = pr, b = (mod - 1) / ds[i], r = 1;
while (b) {
if (b & 1) r = r * a % mod;
a = a * a % mod;
b >>= 1;
}
if (r == 1) {
flg = 0;
break;
}
}
if (flg == 1) break;
++pr;
}
return pr;
}
/**
* @brief 原始根
*/
template <uint32_t mod>
struct LazyMontgomeryModInt {
using mint = LazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod) % mod;
static_assert(r * mod == 1, "invalid, r * mod != 1");
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
u32 a;
constexpr LazyMontgomeryModInt() : a(0) {}
constexpr LazyMontgomeryModInt(const int64_t &b)
: a(reduce(u64(b % mod + mod) * n2)){};
static constexpr u32 reduce(const u64 &b) {
return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
}
constexpr mint &operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
constexpr mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
constexpr bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
constexpr bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
constexpr mint operator-() const { return mint() - mint(*this); }
constexpr mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
constexpr mint inverse() const { return pow(mod - 2); }
friend ostream &operator<<(ostream &os, const mint &b) {
return os << b.get();
}
friend istream &operator>>(istream &is, mint &b) {
int64_t t;
is >> t;
b = LazyMontgomeryModInt<mod>(t);
return (is);
}
constexpr u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static constexpr u32 get_mod() { return mod; }
};
template <typename T>
struct Binomial {
vector<T> f, g, h;
Binomial(int MAX = 0) : f(1, T(1)), g(1, T(1)), h(1, T(1)) {
while (MAX >= (int)f.size()) extend();
}
void extend() {
int n = f.size();
int m = n * 2;
f.resize(m);
g.resize(m);
h.resize(m);
for (int i = n; i < m; i++) f[i] = f[i - 1] * T(i);
g[m - 1] = f[m - 1].inverse();
h[m - 1] = g[m - 1] * f[m - 2];
for (int i = m - 2; i >= n; i--) {
g[i] = g[i + 1] * T(i + 1);
h[i] = g[i] * f[i - 1];
}
}
T fac(int i) {
if (i < 0) return T(0);
while (i >= (int)f.size()) extend();
return f[i];
}
T finv(int i) {
if (i < 0) return T(0);
while (i >= (int)g.size()) extend();
return g[i];
}
T inv(int i) {
if (i < 0) return -inv(-i);
while (i >= (int)h.size()) extend();
return h[i];
}
T C(int n, int r) {
if (n < 0 || n < r || r < 0) return T(0);
return fac(n) * finv(n - r) * finv(r);
}
inline T operator()(int n, int r) { return C(n, r); }
template <typename I>
T multinomial(const vector<I>& r) {
static_assert(is_integral<I>::value == true);
int n = 0;
for (auto& x : r) {
if(x < 0) return T(0);
n += x;
}
T res = fac(n);
for (auto& x : r) res *= finv(x);
return res;
}
template <typename I>
T operator()(const vector<I>& r) {
return multinomial(r);
}
T C_naive(int n, int r) {
if (n < 0 || n < r || r < 0) return T(0);
T ret = T(1);
r = min(r, n - r);
for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--);
return ret;
}
T P(int n, int r) {
if (n < 0 || n < r || r < 0) return T(0);
return fac(n) * finv(n - r);
}
T H(int n, int r) {
if (n < 0 || r < 0) return T(0);
return r == 0 ? 1 : C(n + r - 1, r);
}
};
template <typename T, typename F>
struct MultidimensionalFourierTransform {
vector<int> base;
F dft1d;
MultidimensionalFourierTransform(const vector<int>& bs, const F& f)
: base(bs), dft1d(f) {}
bool ascend(vector<int>& v) {
int i = 0;
v[i] += 1;
while (v[i] == base[i]) {
if (i == (int)v.size() - 1) return false;
v[i] = 0;
v[++i] += 1;
}
return true;
}
int operator()(vector<int>& a) {
int res = a[0], coeff = 1;
for (int i = 1; i < (int)a.size(); i++)
coeff *= base[i - 1], res += coeff * a[i];
return res;
}
void inner(vector<T>& a, int dim, bool rev = false) {
int i = 0, shift = 1, n = base[dim];
vector<T> f(n);
vector<int> id(base.size());
for (int j = 0; j < dim; j++) shift *= base[j];
do {
if (id[dim] != 0) continue;
for (int j = 0, t = i; j < n; j++, t += shift) f[j] = a[t];
dft1d(f, rev);
for (int j = 0, t = i; j < n; j++, t += shift) a[t] = f[j];
id[dim] = 0;
} while (++i && ascend(id));
}
void fft(vector<T>& a, bool rev = false) {
if (!rev)
for (int i = 0; i < (int)base.size(); i++) inner(a, i);
else
for (int i = (int)base.size(); i--;) inner(a, i, true);
}
};
/**
* @brief 多次元FFT
*/
template <typename fps>
fps multivariate_multiplication(const fps& f, const fps& g,
const vector<int>& base) {
int n = f.size(), s = base.size(), W = 1;
if (s == 0) return fps{f[0] * g[0]};
while (W < 2 * n) W *= 2;
vector<int> chi(n);
for (int i = 0; i < n; i++) {
int x = i;
for (int j = 0; j < s - 1; j++) chi[i] += (x /= base[j]);
chi[i] %= s;
}
vector<fps> F(s, fps(W)), G(s, fps(W));
for (int i = 0; i < n; i++) F[chi[i]][i] = f[i], G[chi[i]][i] = g[i];
for (auto& x : F) x.ntt();
for (auto& x : G) x.ntt();
fps a(s);
for (int k = 0; k < W; k++) {
fill(begin(a), end(a), typename fps::value_type());
for (int i = 0; i < s; i++)
for (int j = 0; j < s; j++) {
a[i + j - (i + j >= s ? s : 0)] += F[i][k] * G[j][k];
}
for (int i = 0; i < s; i++) F[i][k] = a[i];
}
for (auto& x : F) x.intt();
fps h(n);
for (int i = 0; i < n; i++) h[i] = F[chi[i]][i];
return h;
}
/**
* @brief Multivariate Multiplication
* @docs docs/ntt/multivariate-multiplication.md
*/
using namespace Nyaan;
constexpr int mod = 120586241;
using mint = LazyMontgomeryModInt<mod>;
using vm = vector<mint>;
using fps = FormalPowerSeries<mint>;
Binomial<mint> C(700700);
fps multi_diff(const fps& f) {
fps g{begin(f), end(f)};
for (int i = 0; i < (int)f.size(); i++) g[i] *= i;
return g;
}
fps multi_int(const fps& f) {
assert(f[0] == 0);
fps g{begin(f), end(f)};
for (int i = 1; i < (int)f.size(); i++) g[i] *= C.inv(i);
return g;
}
fps multi_inv(const fps& f, const vector<int>& base) {
assert(!f.empty() && f[0] != 0);
assert(base.empty() == false);
int n = f.size(), s = base.size(), W = 1;
while (W < 2 * n) W *= 2;
vector<int> chi(W);
for (int i = 0; i < W; i++) {
int x = i;
for (int j = 0; j < s - 1; j++) chi[i] += (x /= base[j]);
chi[i] %= s;
}
auto hadamard_prod = [&s](vector<fps>& F, vector<fps>& G, vector<fps>& H) {
fps a(s);
for (int k = 0; k < (int)F[0].size(); k++) {
fill(begin(a), end(a), typename fps::value_type());
for (int i = 0; i < s; i++)
for (int j = 0; j < s; j++) {
a[i + j - (i + j >= s ? s : 0)] += F[i][k] * G[j][k];
}
for (int i = 0; i < s; i++) H[i][k] = a[i];
}
};
fps g(W);
g.ntt();
g.intt();
g[0] = f[0].inverse();
for (int d = 1; d < n; d *= 2) {
vector<fps> F(s, fps(2 * d)), G(s, fps(2 * d)), H(s, fps(2 * d));
for (int j = 0; j < min((int)f.size(), 2 * d); j++) F[chi[j]][j] = f[j];
for (int j = 0; j < d; j++) G[chi[j]][j] = g[j];
for (auto& x : F) x.ntt();
for (auto& x : G) x.ntt();
hadamard_prod(F, G, H);
for (auto& x : H) x.intt();
for (auto& x : F) fill(begin(x), end(x), typename fps::value_type());
for (int j = d; j < 2 * d; j++) F[chi[j]][j] = H[chi[j]][j];
for (auto& x : F) x.ntt();
hadamard_prod(F, G, H);
for (auto& x : H) x.intt();
for (int j = d; j < 2 * d; j++) g[j] = -H[chi[j]][j];
}
return {begin(g), begin(g) + n};
}
fps multi_log(const fps f, const vector<int>& base) {
auto df = multi_diff(f);
auto invf = multi_inv(f, base);
auto g = multivariate_multiplication(df, invf, base);
return multi_int(g);
}
fps multi_exp(const fps& f, const vector<int>& base) {
if (f.size() == 0) return {};
assert(f[0] == mint(0));
int n = f.size();
fps g{mint(1)};
for (int d = 1; d < n; d *= 2) {
g.resize(2 * d, mint());
fps lg_g = multi_log(g, base);
fps h = fps{mint(1)} - lg_g + fps{begin(f), begin(f) + min(n, d * 2)};
h.resize(2 * d, mint());
g = multivariate_multiplication(g, h, base);
}
return {begin(g), begin(g) + n};
}
fps naive_pow(fps f, long long e, const vector<int>& base) {
// e >= 50の場合0が確定する
// if (e > 50) return fps(f.size());
fps res(f.size());
res[0] = 1;
while (e) {
if (e & 1) res = multivariate_multiplication(res, f, base);
f = multivariate_multiplication(f, f, base);
e >>= 1;
}
return res;
}
fps multi_pow(fps f, long long e, const vector<int>& base) {
assert(!f.empty());
// f.size() == 1の場合は(変数無し)愚直にpow
if (base.empty()) return fps{f[0].pow(e)};
// f[0] == 0の場合も愚直にpow
if (f[0] == 0) return naive_pow(f, e, base);
mint inv = f[0].inverse(), coe = f[0].pow(e);
for (auto& x : f) x *= inv;
fps lg_f = multi_log(f, base);
each(x, lg_f) x *= e;
fps g = multi_exp(lg_f, base);
each(x, g) x *= coe;
return g;
}
void Nyaan::solve() {
int pr = PrimitiveRoot(mod);
vm pr10(110);
pr10[0] = 1;
pr10[1] = mint(pr).pow((mod - 1) / 10);
rep1(i, 102) pr10[i + 1] = pr10[i] * pr10[1];
assert(pr10[10] == 1);
auto dft = [&](vector<mint>& f, bool rev) {
int n = sz(f);
vector<mint> F(n);
if (n == 10) {
rep(i, n) rep(j, n) F[j] += f[i] * pr10[i * j];
} else
exit(1);
if (rev) reverse(begin(F) + 1, end(F));
f.swap(F);
};
long long n, k, m, t;
cin >> n >> k >> m >> t;
vector<int> a(n);
each(x, a) {
cin >> x;
assert(0 <= x and x < TEN(k));
}
vector<int> base(k, 10);
vector<mint> f(TEN(k));
each(x, a) f[x] += 1;
MultidimensionalFourierTransform<mint, decltype(dft)> mntt(base, dft);
for (int i = k - 1; i >= t; i--) mntt.inner(f, i);
for (int i = 0, di = TEN(t); i < TEN(k); i += di) {
fps g{begin(f) + i, begin(f) + i + di};
// g[0]の場合でもm<=45なら愚直にpowをする必要がある
g = naive_pow(g, m, vi(t, 10));
for (int j = 0; j < di; j++) f[i + j] = g[j];
}
for (int i = t; i < k; i++) mntt.inner(f, i, true);
mint coe = mint(10).inverse().pow(k - t);
// rep(i, TEN(k)) if (f[i] != 0) cout << i << " " << f[i] * coe << endl;
each(x, f) cout << x * coe << "\n";
}