結果
| 問題 | No.1907 DETERMINATION |
| ユーザー |
 kiyoshi0205
|
| 提出日時 | 2022-04-15 22:28:26 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 20,924 bytes |
| コンパイル時間 | 4,590 ms |
| コンパイル使用メモリ | 380,348 KB |
| 実行使用メモリ | 13,888 KB |
| 最終ジャッジ日時 | 2024-06-07 03:28:35 |
| 合計ジャッジ時間 | 19,196 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / 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 | 2 ms
12,800 KB |
| testcase_01 | AC | 3 ms
5,248 KB |
| testcase_02 | AC | 3 ms
5,248 KB |
| testcase_03 | AC | 3 ms
5,376 KB |
| testcase_04 | AC | 4 ms
5,376 KB |
| testcase_05 | AC | 3 ms
5,376 KB |
| testcase_06 | AC | 3 ms
6,944 KB |
| testcase_07 | AC | 3,707 ms
7,424 KB |
| testcase_08 | AC | 1,343 ms
5,888 KB |
| testcase_09 | AC | 2,493 ms
6,528 KB |
| testcase_10 | TLE | - |
| testcase_11 | -- | - |
| testcase_12 | -- | - |
| testcase_13 | -- | - |
| testcase_14 | -- | - |
| testcase_15 | -- | - |
| testcase_16 | -- | - |
| testcase_17 | -- | - |
| testcase_18 | -- | - |
| testcase_19 | -- | - |
| testcase_20 | -- | - |
| testcase_21 | -- | - |
| testcase_22 | -- | - |
| testcase_23 | -- | - |
| testcase_24 | -- | - |
| testcase_25 | -- | - |
| testcase_26 | -- | - |
| testcase_27 | -- | - |
| testcase_28 | -- | - |
| testcase_29 | -- | - |
| testcase_30 | -- | - |
| testcase_31 | -- | - |
| testcase_32 | -- | - |
| testcase_33 | -- | - |
| testcase_34 | -- | - |
| testcase_35 | -- | - |
| testcase_36 | -- | - |
| testcase_37 | -- | - |
| testcase_38 | -- | - |
| testcase_39 | -- | - |
| testcase_40 | -- | - |
| testcase_41 | -- | - |
| testcase_42 | -- | - |
| testcase_43 | -- | - |
| testcase_44 | -- | - |
| testcase_45 | -- | - |
| testcase_46 | -- | - |
| testcase_47 | -- | - |
| testcase_48 | -- | - |
| testcase_49 | -- | - |
| testcase_50 | -- | - |
| testcase_51 | -- | - |
| testcase_52 | -- | - |
| testcase_53 | -- | - |
| testcase_54 | -- | - |
| testcase_55 | -- | - |
| testcase_56 | -- | - |
| testcase_57 | -- | - |
| testcase_58 | -- | - |
| testcase_59 | -- | - |
| testcase_60 | -- | - |
| testcase_61 | -- | - |
| testcase_62 | -- | - |
| testcase_63 | -- | - |
| testcase_64 | -- | - |
| testcase_65 | -- | - |
| testcase_66 | -- | - |
コンパイルメッセージ
main.cpp:557:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
557 | montgomery_sub_256(const __m256i &a, const __m256i &b, const __m256i &m2,
| ^~~~~~~~~~~~~~~~~~
main.cpp:549:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
549 | montgomery_add_256(const __m256i &a, const __m256i &b, const __m256i &m2,
| ^~~~~~~~~~~~~~~~~~
main.cpp:541:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
541 | montgomery_mul_256(const __m256i &a, const __m256i &b, const __m256i &r,
| ^~~~~~~~~~~~~~~~~~
main.cpp:530:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
530 | my256_mulhi_epu32(const __m256i &a, const __m256i &b) {
| ^~~~~~~~~~~~~~~~~
main.cpp:525:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
525 | my256_mullo_epu32(const __m256i &a, const __m256i &b) {
| ^~~~~~~~~~~~~~~~~
main.cpp:518:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
518 | montgomery_sub_128(const __m128i &a, const __m128i &b, const __m128i &m2,
| ^~~~~~~~~~~~~~~~~~
main.cpp:511:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
511 | montgomery_add_128(const __m128i &a, const __m128i &b, const __m128i &m2,
| ^~~~~~~~~~~~~~~~~~
main.cpp:503:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
503 | montgomery_mul_128(const __m128i &a, const __m128i &b, const __m128i &r,
| ^~~~~~~~~~~~~~~~~~
main.cpp:492:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
492 | my128_mulhi_epu32(const __m128i &a, const __m128i &b) {
| ^~~~~~~~~~~~~~~~~
main.cpp:487:1: warning: 'always_inline' function might not be inlinable [-Wattributes]
487 | my128_mullo_epu32(const __m128i &a, const __m128i &b) {
| ^~~~~~~~~~~~~~~~~
ソースコード
//拝借、ありがとう………
#define PROBLEM "https://judge.yosupo.jp/problem/matrix_det"
#pragma region kyopro_template
#define Nyaan_template
#include <immintrin.h>
#include <bits/stdc++.h>
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define each(x, v) for (auto &x : v)
#define all(v) (v).begin(), (v).end()
#define sz(v) ((int)(v).size())
#define mem(a, val) memset(a, val, sizeof(a))
#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 inc(...) \
char __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 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 die(...) \
do { \
out(__VA_ARGS__); \
return; \
} while (0)
using namespace std;
using ll = long long;
template <class T>
using V = vector<T>;
using vi = vector<int>;
using vl = vector<long long>;
using vvi = vector<vector<int>>;
using vd = V<double>;
using vs = V<string>;
using vvl = vector<vector<long long>>;
using P = pair<long long, long long>;
using vp = vector<P>;
using pii = pair<int, int>;
using vpi = vector<pair<int, int>>;
constexpr int inf = 1001001001;
constexpr long long infLL = (1LL << 61) - 1;
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, 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>
void out(const T &t, const U &... u) {
cout << t;
if (sizeof...(u)) cout << " ";
out(u...);
}
#ifdef NyaanDebug
#define trc(...) \
do { \
cerr << #__VA_ARGS__ << " = "; \
dbg_out(__VA_ARGS__); \
} while (0)
#define trca(v, N) \
do { \
cerr << #v << " = "; \
array_out(v, N); \
} while (0)
#define trcc(v) \
do { \
cerr << #v << " = {"; \
each(x, v) { cerr << " " << x << ","; } \
cerr << "}" << endl; \
} while (0)
template <typename T>
void _cout(const T &c) {
cerr << c;
}
void _cout(const int &c) {
if (c == 1001001001)
cerr << "inf";
else if (c == -1001001001)
cerr << "-inf";
else
cerr << c;
}
void _cout(const unsigned int &c) {
if (c == 1001001001)
cerr << "inf";
else
cerr << c;
}
void _cout(const long long &c) {
if (c == 1001001001 || c == (1LL << 61) - 1)
cerr << "inf";
else if (c == -1001001001 || c == -((1LL << 61) - 1))
cerr << "-inf";
else
cerr << c;
}
void _cout(const unsigned long long &c) {
if (c == 1001001001 || c == (1LL << 61) - 1)
cerr << "inf";
else
cerr << c;
}
template <typename T, typename U>
void _cout(const pair<T, U> &p) {
cerr << "{ ";
_cout(p.fi);
cerr << ", ";
_cout(p.se);
cerr << " } ";
}
template <typename T>
void _cout(const vector<T> &v) {
int s = v.size();
cerr << "{ ";
for (int i = 0; i < s; i++) {
cerr << (i ? ", " : "");
_cout(v[i]);
}
cerr << " } ";
}
template <typename T>
void _cout(const vector<vector<T>> &v) {
cerr << "[ ";
for (const auto &x : v) {
cerr << endl;
_cout(x);
cerr << ", ";
}
cerr << endl << " ] ";
}
void dbg_out() { cerr << endl; }
template <typename T, class... U>
void dbg_out(const T &t, const U &... u) {
_cout(t);
if (sizeof...(u)) cerr << ", ";
dbg_out(u...);
}
template <typename T>
void array_out(const T &v, int s) {
cerr << "{ ";
for (int i = 0; i < s; i++) {
cerr << (i ? ", " : "");
_cout(v[i]);
}
cerr << " } " << endl;
}
template <typename T>
void array_out(const T &v, int H, int W) {
cerr << "[ ";
for (int i = 0; i < H; i++) {
cerr << (i ? ", " : "");
array_out(v[i], W);
}
cerr << " ] " << endl;
}
#else
#define trc(...)
#define trca(...)
#define trcc(...)
#endif
inline int popcnt(unsigned long long a) { return __builtin_popcountll(a); }
inline int lsb(unsigned long long a) { return __builtin_ctzll(a); }
inline int msb(unsigned long long a) { return 63 - __builtin_clzll(a); }
template <typename T>
inline int getbit(T a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void setbit(T &a, int i) {
a |= (1LL << i);
}
template <typename T>
inline void delbit(T &a, int i) {
a &= ~(1LL << i);
}
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);
}
template <typename T>
int btw(T a, T x, T b) {
return a <= x && x < b;
}
template <typename T, typename U>
T ceil(T a, U b) {
return (a + b - 1) / b;
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
while (n) {
if (n & 1) ret *= x;
x *= x;
n >>= 1;
}
return ret;
}
template <typename T>
vector<T> mkrui(const vector<T> &v) {
vector<T> ret(v.size() + 1);
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 = int>
vector<T> mkiota(int N) {
vector<T> ret(N);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
vector<int> inv(v.size());
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
void solve();
int main() { solve(); }
#pragma endregion
using namespace std;
namespace fastio {
static constexpr int SZ = 1 << 17;
char ibuf[SZ], obuf[SZ];
int pil = 0, pir = 0, por = 0;
struct Pre {
char num[40000];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i * 4 + j] = n % 10 + '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
pil = 0;
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
inline void rd(char& c) { c = ibuf[pil++]; }
template <typename T>
inline void rd(T& x) {
if (pil + 32 > pir) load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if (c == '-') {
minus = 1;
c = ibuf[pil++];
}
x = 0;
while (c >= '0') {
x = x * 10 + (c & 15);
c = ibuf[pil++];
}
if (minus) x = -x;
}
inline void wt(char c) { obuf[por++] = c; }
template <typename T>
inline void wt(T x) {
if (por > SZ - 32) flush();
if (!x) {
obuf[por++] = '0';
return;
}
if (x < 0) {
obuf[por++] = '-';
x = -x;
}
int i = 12;
char buf[16];
while (x >= 10000) {
memcpy(buf + i, pre.num + (x % 10000) * 4, 4);
x /= 10000;
i -= 4;
}
int d = x < 100 ? (x < 10 ? 1 : 2) : (x < 1000 ? 3 : 4);
memcpy(obuf + por, pre.num + x * 4 + 4 - d, d);
por += d;
memcpy(obuf + por, buf + i + 4, 12 - i);
por += 12 - i;
}
struct Dummy {
Dummy() { atexit(flush); }
} dummy;
} // namespace fastio
using fastio::rd;
using fastio::wt;
using namespace std;
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; }
};
using namespace std;
using namespace std;
__attribute__((target("sse4.2"))) __attribute__((always_inline)) __m128i
my128_mullo_epu32(const __m128i &a, const __m128i &b) {
return _mm_mullo_epi32(a, b);
}
__attribute__((target("sse4.2"))) __attribute__((always_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"))) __attribute__((always_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"))) __attribute__((always_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"))) __attribute__((always_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"))) __attribute__((always_inline)) __m256i
my256_mullo_epu32(const __m256i &a, const __m256i &b) {
return _mm256_mullo_epi32(a, b);
}
__attribute__((target("avx2"))) __attribute__((always_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"))) __attribute__((always_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"))) __attribute__((always_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"))) __attribute__((always_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 Gauss {
uint32_t a_buf_[4096][4096] __attribute__((aligned(64)));
// return value: (rank, (-1) ^ (number of swap time))
template <typename mint>
__attribute__((target("avx2"))) pair<int, int> GaussianElimination(
const vector<vector<mint>> &m, int LinearEquation = false) {
mint(&a)[4096][4096] = *reinterpret_cast<mint(*)[4096][4096]>(a_buf_);
int H = m.size(), W = m[0].size(), rank = 0;
int det = 1;
for (int i = 0; i < H; i++)
for (int j = 0; j < W; j++) a[i][j].a = m[i][j].a;
__m256i r = _mm256_set1_epi32(mint::r);
__m256i m0 = _mm256_set1_epi32(0);
__m256i m1 = _mm256_set1_epi32(mint::get_mod());
__m256i m2 = _mm256_set1_epi32(mint::get_mod() << 1);
for (int j = 0; j < (LinearEquation ? (W - 1) : W); j++) {
// find basis
if (rank == H) break;
int idx = -1;
for (int i = rank; i < H; i++) {
if (a[i][j].get() != 0) idx = i;
if (idx != -1) break;
}
if (idx == -1) {
if (LinearEquation)
continue;
else
return {0, 0};
}
// swap
if (rank != idx) {
det = -det;
for (int l = j; l < W; l++) swap(a[rank][l], a[idx][l]);
}
// normalize
if (LinearEquation) {
if (a[rank][j].get() != 1) {
mint coeff = a[rank][j].inverse();
__m256i COEFF = _mm256_set1_epi32(coeff.a);
for (int i = j / 8 * 8; i < W; i += 8) {
__m256i R = _mm256_load_si256((__m256i *)(a[rank] + i));
__m256i RmulC = montgomery_mul_256(R, COEFF, r, m1);
_mm256_store_si256((__m256i *)(a[rank] + i), RmulC);
}
}
}
// elimination
for (int k = (LinearEquation ? 0 : rank + 1); k < H; k++) {
if (k == rank) continue;
if (a[k][rank].get() != 0) {
mint coeff = a[k][j] / a[rank][j];
__m256i COEFF = _mm256_set1_epi32(coeff.a);
for (int i = j / 8 * 8; i < W; i += 8) {
__m256i R = _mm256_load_si256((__m256i *)(a[rank] + i));
__m256i K = _mm256_load_si256((__m256i *)(a[k] + i));
__m256i RmulC = montgomery_mul_256(R, COEFF, r, m1);
__m256i KmnsR = montgomery_sub_256(K, RmulC, m2, m0);
_mm256_store_si256((__m256i *)(a[k] + i), KmnsR);
}
}
}
rank++;
}
return {rank, det};
}
// calculate determinant
template <typename mint>
mint determinant(const vector<vector<mint>> &mat) {
mint(&a)[4096][4096] = *reinterpret_cast<mint(*)[4096][4096]>(a_buf_);
auto p = GaussianElimination(mat);
if (p.first != (int)mat.size()) return mint(0);
mint det = p.second;
for (int i = 0; i < (int)mat.size(); i++) det *= a[i][i];
return det;
}
// return V<V<mint>>
// 0 column ... one of solutions
// 1 ~ (W - rank) column ... bases
// if not exist, return empty vector
template <typename mint>
vector<vector<mint>> LinearEquation(vector<vector<mint>> A, vector<mint> B) {
int H = A.size(), W = A[0].size();
for (int i = 0; i < H; i++) A[i].push_back(B[i]);
auto p = GaussianElimination(A, true);
mint(&a)[4096][4096] = *reinterpret_cast<mint(*)[4096][4096]>(a_buf_);
int rank = p.first;
// check if solutions exist
for (int i = rank; i < H; ++i)
if (a[i][W] != 0) return vector<vector<mint>>{};
vector<vector<mint>> res(1, vector<mint>(W));
vector<int> pivot(W, -1);
for (int i = 0, j = 0; i < rank; ++i) {
while (a[i][j] == 0) ++j;
res[0][j] = a[i][W], pivot[j] = i;
}
for (int j = 0; j < W; ++j) {
if (pivot[j] == -1) {
vector<mint> x(W);
x[j] = -1;
for (int k = 0; k < j; ++k)
if (pivot[k] != -1) x[k] = a[pivot[k]][j];
res.push_back(x);
}
}
return res;
}
} // namespace Gauss
using namespace Gauss;
using mint = LazyMontgomeryModInt<998244353>;
using vm = vector<mint>;
template <typename mint>
std::pair<int, mint> GaussElimination(vector<vector<mint>> &a,
int pivot_end = -1,
bool diagonalize = false) {
int H = a.size(), W = a[0].size();
int rank = 0, je = pivot_end;
if (je == -1) je = W;
mint det = 1;
for (int j = 0; j < je; j++) {
int idx = -1;
for (int i = rank; i < H; i++) {
if (a[i][j] != mint(0)) {
idx = i;
break;
}
}
if (idx == -1) {
det = 0;
continue;
}
if (rank != idx) {
det = -det;
swap(a[rank], a[idx]);
}
det *= a[rank][j];
if (diagonalize && a[rank][j] != mint(1)) {
mint coeff = a[rank][j].inverse();
for (int k = j; k < W; k++) a[rank][k] *= coeff;
}
int is = diagonalize ? 0 : rank + 1;
for (int i = is; i < H; i++) {
if (i == rank) continue;
if (a[i][j] != mint(0)) {
mint coeff = a[i][j] / a[rank][j];
for (int k = j; k < W; k++) a[i][k] -= a[rank][k] * coeff;
}
}
rank++;
}
return make_pair(rank, det);
}
#line 4 "matrix/inverse-matrix.hpp"
template <typename mint>
vector<vector<mint>> inverse_matrix(const vector<vector<mint>>& a) {
int N = a.size();
assert(N > 0);
assert(N == (int)a[0].size());
vector<vector<mint>> m(N, vector<mint>(2 * N));
for (int i = 0; i < N; i++) {
copy(begin(a[i]), end(a[i]), begin(m[i]));
m[i][N + i] = 1;
}
auto [rank, det] = GaussElimination(m, N, true);
if (rank != N) return {};
vector<vector<mint>> b(N);
for (int i = 0; i < N; i++) {
copy(begin(m[i]) + N, end(m[i]), back_inserter(b[i]));
}
return b;
}
void solve() {
int N;
rd(N);
V<vm> a(N, vm(N)),b(N,vm(N));
int buf;
rep(i, N) rep(j, N) {
rd(buf);
a[i][j] = buf;
}
rep(i, N) rep(j, N) {
rd(buf);
b[i][j] = buf;
}
// wt();
vector<vector<mint>> calc(N+1,vector<mint>(N+1));
vector<vector<mint>> ch(N,vector<mint>(N));
vector<mint> res(N+1);
rep(x,N+1){
calc[x][0]=1;
rep(i,N)calc[x][i+1]=calc[x][i]*(x+1);
rep(i,N)rep(j,N)ch[i][j]=a[i][j]+b[i][j]*(x+1);
res[x]=Gauss::determinant(ch).get();
}
auto tmp=inverse_matrix(calc);
rep(i,N+1){
mint ans=0;
rep(j,N+1)ans+=tmp[i][j]*res[j];
cout<<ans<<'\n';
}
}