結果
| 問題 |
No.2907 Business Revealing Dora Tiles
|
| コンテスト | |
| ユーザー |
 hashiryo
|
| 提出日時 | 2024-09-29 20:40:34 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 29,813 bytes |
| コンパイル時間 | 2,596 ms |
| コンパイル使用メモリ | 220,688 KB |
| 最終ジャッジ日時 | 2025-02-24 14:10:34 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 20 TLE * 1 -- * 36 |
ソースコード
// #define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
// clang-format off
std::ostream&operator<<(std::ostream&os,std::int8_t x){return os<<(int)x;}
std::ostream&operator<<(std::ostream&os,std::uint8_t x){return os<<(int)x;}
std::ostream&operator<<(std::ostream&os,const __int128_t &u){if(!u)os<<"0";__int128_t tmp=u<0?(os<<"-",-u):u;std::string s;while(tmp)s+='0'+(tmp%10),tmp/=10;return std::reverse(s.begin(),s.end()),os<<s;}
std::ostream&operator<<(std::ostream&os,const __uint128_t &u){if(!u)os<<"0";__uint128_t tmp=u;std::string s;while(tmp)s+='0'+(tmp%10),tmp/=10;return std::reverse(s.begin(),s.end()),os<<s;}
#define checkpoint() (void(0))
#define debug(...) (void(0))
#define debugArray(x,n) (void(0))
#define debugMatrix(x,h,w) (void(0))
// clang-format on
#include <type_traits>
template <class Int> constexpr inline Int mod_inv(Int a, Int mod) {
static_assert(std::is_signed_v<Int>);
Int x= 1, y= 0, b= mod;
for (Int q= 0, z= 0; b;) z= x, x= y, y= z - y * (q= a / b), z= a, a= b, b= z - b * q;
return assert(a == 1), x < 0 ? mod - (-x) % mod : x % mod;
}
namespace math_internal {
using namespace std;
using u8= unsigned char;
using u32= unsigned;
using i64= long long;
using u64= unsigned long long;
using u128= __uint128_t;
#define CE constexpr
#define IL inline
#define NORM \
if (n >= mod) n-= mod; \
return n
#define PLUS(U, M) \
CE IL U plus(U l, U r) const { return l+= r, l < (M) ? l : l - (M); }
#define DIFF(U, C, M) \
CE IL U diff(U l, U r) const { return l-= r, l >> C ? l + (M) : l; }
#define SGN(U) \
static CE IL U set(U n) { return n; } \
static CE IL U get(U n) { return n; } \
static CE IL U norm(U n) { return n; }
template <class u_t, class du_t, u8 B, u8 A> struct MP_Mo {
u_t mod;
CE MP_Mo(): mod(0), iv(0), r2(0) {}
CE MP_Mo(u_t m): mod(m), iv(inv(m)), r2(-du_t(mod) % mod) {}
CE IL u_t mul(u_t l, u_t r) const { return reduce(du_t(l) * r); }
PLUS(u_t, mod << 1)
DIFF(u_t, A, mod << 1)
CE IL u_t set(u_t n) const { return mul(n, r2); }
CE IL u_t get(u_t n) const {
n= reduce(n);
NORM;
}
CE IL u_t norm(u_t n) const { NORM; }
private:
u_t iv, r2;
static CE u_t inv(u_t n, int e= 6, u_t x= 1) { return e ? inv(n, e - 1, x * (2 - x * n)) : x; }
CE IL u_t reduce(const du_t &w) const { return u_t(w >> B) + mod - ((du_t(u_t(w) * iv) * mod) >> B); }
};
struct MP_Na {
u32 mod;
CE MP_Na(): mod(0){};
CE MP_Na(u32 m): mod(m) {}
CE IL u32 mul(u32 l, u32 r) const { return u64(l) * r % mod; }
PLUS(u32, mod) DIFF(u32, 31, mod) SGN(u32)
};
struct MP_Br { // mod < 2^31
u32 mod;
CE MP_Br(): mod(0), s(0), x(0) {}
CE MP_Br(u32 m): mod(m), s(95 - __builtin_clz(m - 1)), x(((u128(1) << s) + m - 1) / m) {}
CE IL u32 mul(u32 l, u32 r) const { return rem(u64(l) * r); }
PLUS(u32, mod) DIFF(u32, 31, mod) SGN(u32) private: u8 s;
u64 x;
CE IL u64 quo(u64 n) const { return (u128(x) * n) >> s; }
CE IL u32 rem(u64 n) const { return n - quo(n) * mod; }
};
struct MP_Br2 { // 2^20 < mod <= 2^41
u64 mod;
CE MP_Br2(): mod(0), x(0) {}
CE MP_Br2(u64 m): mod(m), x((u128(1) << 84) / m) {}
CE IL u64 mul(u64 l, u64 r) const { return rem(u128(l) * r); }
PLUS(u64, mod << 1)
DIFF(u64, 63, mod << 1)
static CE IL u64 set(u64 n) { return n; }
CE IL u64 get(u64 n) const { NORM; }
CE IL u64 norm(u64 n) const { NORM; }
private:
u64 x;
CE IL u128 quo(const u128 &n) const { return (n * x) >> 84; }
CE IL u64 rem(const u128 &n) const { return n - quo(n) * mod; }
};
struct MP_D2B1 {
u8 s;
u64 mod, d, v;
CE MP_D2B1(): s(0), mod(0), d(0), v(0) {}
CE MP_D2B1(u64 m): s(__builtin_clzll(m)), mod(m), d(m << s), v(u128(-1) / d) {}
CE IL u64 mul(u64 l, u64 r) const { return rem((u128(l) * r) << s) >> s; }
PLUS(u64, mod) DIFF(u64, 63, mod) SGN(u64) private: CE IL u64 rem(const u128 &u) const {
u128 q= (u >> 64) * v + u;
u64 r= u64(u) - (q >> 64) * d - d;
if (r > u64(q)) r+= d;
if (r >= d) r-= d;
return r;
}
};
template <class u_t, class MP> CE u_t pow(u_t x, u64 k, const MP &md) {
for (u_t ret= md.set(1);; x= md.mul(x, x))
if (k & 1 ? ret= md.mul(ret, x) : 0; !(k>>= 1)) return ret;
}
#undef NORM
#undef PLUS
#undef DIFF
#undef SGN
#undef CE
}
namespace math_internal {
struct m_b {};
struct s_b: m_b {};
}
template <class mod_t> constexpr bool is_modint_v= std::is_base_of_v<math_internal::m_b, mod_t>;
template <class mod_t> constexpr bool is_staticmodint_v= std::is_base_of_v<math_internal::s_b, mod_t>;
namespace math_internal {
#define CE constexpr
template <class MP, u64 MOD> struct SB: s_b {
protected:
static CE MP md= MP(MOD);
};
template <class Int, class U, class B> struct MInt: public B {
using Uint= U;
static CE inline auto mod() { return B::md.mod; }
CE MInt(): x(0) {}
template <class T, typename= enable_if_t<is_modint_v<T> && !is_same_v<T, MInt>>> CE MInt(T v): x(B::md.set(v.val() % B::md.mod)) {}
CE MInt(__int128_t n): x(B::md.set((n < 0 ? ((n= (-n) % B::md.mod) ? B::md.mod - n : n) : n % B::md.mod))) {}
CE MInt operator-() const { return MInt() - *this; }
#define FUNC(name, op) \
CE MInt name const { \
MInt ret; \
return ret.x= op, ret; \
}
FUNC(operator+(const MInt & r), B::md.plus(x, r.x))
FUNC(operator-(const MInt & r), B::md.diff(x, r.x))
FUNC(operator*(const MInt & r), B::md.mul(x, r.x))
FUNC(pow(u64 k), math_internal::pow(x, k, B::md))
#undef FUNC
CE MInt operator/(const MInt& r) const { return *this * r.inv(); }
CE MInt& operator+=(const MInt& r) { return *this= *this + r; }
CE MInt& operator-=(const MInt& r) { return *this= *this - r; }
CE MInt& operator*=(const MInt& r) { return *this= *this * r; }
CE MInt& operator/=(const MInt& r) { return *this= *this / r; }
CE bool operator==(const MInt& r) const { return B::md.norm(x) == B::md.norm(r.x); }
CE bool operator!=(const MInt& r) const { return !(*this == r); }
CE bool operator<(const MInt& r) const { return B::md.norm(x) < B::md.norm(r.x); }
CE inline MInt inv() const { return mod_inv<Int>(val(), B::md.mod); }
CE inline Uint val() const { return B::md.get(x); }
friend ostream& operator<<(ostream& os, const MInt& r) { return os << r.val(); }
friend istream& operator>>(istream& is, MInt& r) {
i64 v;
return is >> v, r= MInt(v), is;
}
private:
Uint x;
};
template <u64 MOD> using ModInt= conditional_t < (MOD < (1 << 30)) & MOD, MInt<int, u32, SB<MP_Mo<u32, u64, 32, 31>, MOD>>, conditional_t < (MOD < (1ull << 62)) & MOD, MInt<i64, u64, SB<MP_Mo<u64, u128, 64, 63>, MOD>>, conditional_t<MOD<(1u << 31), MInt<int, u32, SB<MP_Na, MOD>>, conditional_t<MOD<(1ull << 32), MInt<i64, u32, SB<MP_Na, MOD>>, conditional_t<MOD <= (1ull << 41), MInt<i64, u64, SB<MP_Br2, MOD>>, MInt<i64, u64, SB<MP_D2B1, MOD>>>>>>>;
#undef CE
}
using math_internal::ModInt;
class Nimber {
using u64= unsigned long long;
using u32= unsigned;
using u16= unsigned short;
static inline std::array<u16, 65536> pw, ln;
template <u16 h= 3> static inline u16 half(u16 A) { return A ? pw[(ln[A] + h) % 65535] : 0; }
template <u16 h= 0> static inline u16 mul(u16 A, u16 B) { return A && B ? pw[(ln[A] + ln[B] + h) % 65535] : 0; }
template <u16 h= 0> static inline u16 mul(u16 A, u16 B, u16 C) { return A && B && C ? pw[(ln[A] + ln[B] + ln[C] + h) % 65535] : 0; }
static inline u16 inv(u16 A) { return assert(A), pw[65535 - ln[A]]; }
static inline u16 sqrt(u16 A) { return A ? pw[u16((65537 * u32(ln[A])) >> 1)] : 0; }
static inline u64 mul(u64 A, u64 B) {
u16 a0= u16(A), a1= u16(A >> 16), a2= u16(A >> 32), a3= A >> 48, b0= u16(B), b1= u16(B >> 16), b2= u16(B >> 32), b3= B >> 48, x0= a1 ^ a0, x1= a3 ^ a2, y0= b1 ^ b0, y1= b3 ^ b2, c0= mul(a0, b0), c1= mul(x0, y0) ^ c0, c2= mul<0>(a2 ^ a0, b2 ^ b0), c3= mul<0>(x0 ^ x1, y0 ^ y1) ^ c2 ^ c1;
return c2^= (c0^= mul<3>(a1, b1)) ^ mul<3>(u16(a3 ^ a1), u16(b3 ^ b1)), c1^= mul<6>(a3, b3) ^ mul<3>(x1, y1), c0^= mul<6>(a2, b2) ^ mul<6>(x1, y1), (u64(c3) << 48) | (u64(c2) << 32) | (u32(c1) << 16) | c0;
}
static inline u64 inv(u64 A) {
u16 a0= u16(A), a1= u16(A >> 16), a2= u16(A >> 32), a3= A >> 48, x= a2 ^ a3, y= a1 ^ a3, w= a0 ^ a2, v= a0 ^ a1, b3= mul(a1, a2, a1 ^ x), b2= mul(a0, a2, a0 ^ x), b1= mul(a0, a1, a0 ^ y), b0= mul(a0, v, w), t= mul<3>(w, x, x);
return b0^= b1 ^ b2, b1^= b3, b2^= b3, b0^= b3^= mul(a0, a0, a3), b1^= t ^ mul<3>(a1, y, y), b0^= t ^ mul<3>(v, y, y), b3^= t= mul<3>(a1, a3, y) ^ mul<3>(a2, x, x), b2^= t ^ mul<3>(a0, a3, a3) ^ mul<3>(a1, a1, a2), b3^= mul<6>(a3, a3, x), b2^= mul<6>(a3, x, x), b1^= mul<6>(a3, a3, y ^ w), b0^= mul<6>(y, x, x), b2^= mul<9>(a3, a3, a3), b0^= mul<9>(a3, a3, y), t= mul<6>(x, b3) ^ mul<6>(a3, b2) ^ mul<3>(a1, b1) ^ mul(a0, b0), t= inv(t), (u64(mul(b3, t)) << 48) | (u64(mul(b2, t)) << 32) | (u32(mul(b1, t)) << 16) | mul(b0, t);
}
static inline u64 square(u64 A) {
u16 a0= u16(A), a1= u16(A >> 16), a2= u16(A >> 32), a3= A >> 48;
return a3= mul(a3, a3), a2= mul(a2, a2), a1= mul(a1, a1), a0= mul(a0, a0), a0^= half(a1) ^ half<6>(a3), a2^= half(a3), a1^= half(a3 ^ a2), (u64(a3) << 48) | (u64(a2) << 32) | (u32(a1) << 16) | a0;
}
static inline u64 pow(u64 A, u64 k) {
for (u64 ret= 1;; A= square(A))
if (k & 1 ? ret= mul(ret, A) : 0; !(k>>= 1)) return ret;
}
template <int mod> static inline int mdif(int a, int b) { return a+= mod & -((a-= b) < 0); }
template <int mod> static inline int mmul(int a, int b) { return u64(a) * b % mod; }
static inline int log16(u16 A, u16 B) {
int a= ln[A], b= ln[B], x= 1;
if (a == 0) return b == 0 ? 1 : -1;
for (int q, z, u, y= 0, t= 65535; t;) z= x, u= a, x= y, y= z - y * (q= a / t), a= t, t= u - t * q;
return b % a ? -1 : u32(b / a) * (x < 0 ? 65535 + x : x) % 65535;
}
template <int period, int size> static inline int bsgs(u64 x, u64 y) {
static constexpr int mask= size - 1;
std::pair<u64, int> vs[size];
int os[size + 1]= {};
u64 so[size], big= 1;
for (int i= 0; i < size; ++i, big= mul(big, x)) ++os[(so[i]= big) & mask];
for (int i= 0; i < size; ++i) os[i + 1]+= os[i];
for (int i= 0; i < size; ++i) vs[--os[so[i] & mask]]= {so[i], i};
for (int t= 0; t < period; t+= size, y= mul(y, big))
for (int m= (y & mask), i= os[m], ret; i < os[m + 1]; ++i)
if (y == vs[i].first) return (ret= vs[i].second - t) < 0 ? ret + period : ret;
return -1;
}
static inline u64 log(u64 A, u64 B) {
if (B == 1) return 0;
if (!A && !B) return 1;
if (!A || !B) return u64(-1);
static constexpr int P0= 641, P1= 65535, P2= 65537, P3= 6700417, iv10= 40691, iv21= 32768, iv20= 45242, iv32= 3317441, iv31= 3350208, iv30= 3883315;
int a0= bsgs<P0, 16>(pow(A, 0x663d80ff99c27f), pow(B, 0x663d80ff99c27f));
if (a0 == -1) return u64(-1);
int a1= log16(pow(A, 0x1000100010001), pow(B, 0x1000100010001));
if (a1 == -1) return u64(-1);
int a2= bsgs<P2, 256>(pow(A, 0xffff0000ffff), pow(B, 0xffff0000ffff));
if (a2 == -1) return u64(-1);
int a3= bsgs<P3, 2048>(pow(A, 0x280fffffd7f), pow(B, 0x280fffffd7f));
if (a3 == -1) return u64(-1);
int x1= mmul<P1>(mdif<P1>(a1, a0), iv10), x2= mdif<P2>(mmul<P2>(mdif<P2>(a2, a0), iv20), mmul<P2>(x1, iv21)), x3= mdif<P3>(mdif<P3>(mmul<P3>(mdif<P3>(a3, a0), iv30), mmul<P3>(x1, iv31)), mmul<P3>(x2, iv32));
return u64(P0) * (u64(P1) * (u64(P2) * x3 + x2) + x1) + a0;
}
u64 x;
public:
static inline void init(u32 x= 0, u32 y= 0) {
constexpr u16 f2n[16]= {0x0001u, 0x2827u, 0x392bu, 0x8000u, 0x20fdu, 0x4d1du, 0xde4au, 0x0a17u, 0x3464u, 0xe3a9u, 0x6d8du, 0x34bcu, 0xa921u, 0xa173u, 0x0ebcu, 0x0e69u};
for (int i= pw[0]= pw[65535]= 1; i < 65535; ++i) pw[i]= (pw[i - 1] << 1) ^ (0x1681fu & (-(pw[i - 1] >= 0x8000u)));
for (int i= 1; i < 65535; ln[pw[i]= y]= i, i++)
for (x= pw[i], y= 0; x; x&= x - 1) y^= f2n[__builtin_ctz(x)];
}
Nimber(u64 x_= 0): x(x_) {}
Nimber &operator+=(const Nimber &r) { return x^= r.x, *this; }
Nimber &operator-=(const Nimber &r) { return x^= r.x, *this; }
Nimber &operator*=(const Nimber &r) { return x= mul(x, r.x), *this; }
Nimber &operator/=(const Nimber &r) { return x= mul(x, inv(r.x)), *this; }
Nimber operator+(const Nimber &r) const { return Nimber(x ^ r.x); }
Nimber operator-(const Nimber &r) const { return Nimber(x ^ r.x); }
Nimber operator*(const Nimber &r) const { return Nimber(mul(x, r.x)); }
Nimber operator/(const Nimber &r) const { return Nimber(mul(x, inv(r.x))); }
Nimber operator-() const { return *this; }
Nimber inv() const { return Nimber(inv(x)); }
Nimber square() const { return Nimber(square(x)); }
Nimber sqrt() const {
u16 a0= u16(x), a1= u16(x >> 16), a2= u16(x >> 32), a3= x >> 48;
return a1^= half(a3 ^ a2), a2^= half(a3), a0^= half(a1) ^ half<6>(a3), Nimber((u64(sqrt(a3)) << 48) | (u64(sqrt(a2)) << 32) | (u32(sqrt(a1)) << 16) | sqrt(a0));
}
u64 val() const { return x; }
Nimber pow(u64 k) const { return Nimber(pow(x, k)); }
u64 log(const Nimber &r) const { return log(x, r.x); }
bool operator==(const Nimber &r) const { return x == r.x; }
bool operator!=(const Nimber &r) const { return x != r.x; }
bool operator<(const Nimber &r) const { return x < r.x; }
bool operator>(const Nimber &r) const { return x > r.x; }
bool operator<=(const Nimber &r) const { return x <= r.x; }
bool operator>=(const Nimber &r) const { return x >= r.x; }
friend std::ostream &operator<<(std::ostream &os, const Nimber &r) { return os << r.x; }
friend std::istream &operator>>(std::istream &is, Nimber &r) { return is >> r.x, is; }
};
namespace _la_internal {
using namespace std;
template <class R> struct Vector {
valarray<R> dat;
Vector()= default;
Vector(size_t n): dat(n) {}
Vector(size_t n, const R &v): dat(v, n) {}
Vector(const initializer_list<R> &v): dat(v) {}
R &operator[](int i) { return dat[i]; }
const R &operator[](int i) const { return dat[i]; }
bool operator==(const Vector &r) const {
if (dat.size() != r.dat.size()) return false;
for (int i= dat.size(); i--;)
if (dat[i] != r.dat[i]) return false;
return true;
}
bool operator!=(const Vector &r) const { return !(*this == r); }
explicit operator bool() const { return dat.size(); }
Vector operator-() const { return Vector(dat.size())-= *this; }
Vector &operator+=(const Vector &r) { return dat+= r.dat, *this; }
Vector &operator-=(const Vector &r) { return dat-= r.dat, *this; }
Vector &operator*=(const R &r) { return dat*= r, *this; }
Vector operator+(const Vector &r) const { return Vector(*this)+= r; }
Vector operator-(const Vector &r) const { return Vector(*this)-= r; }
Vector operator*(const R &r) const { return Vector(*this)*= r; }
size_t size() const { return dat.size(); }
friend R dot(const Vector<R> &a, const Vector<R> &b) { return assert(a.size() == b.size()), (a.dat * b.dat).sum(); }
};
using u128= __uint128_t;
using u64= uint64_t;
using u8= uint8_t;
class Ref {
u128 *ref;
u8 i;
public:
Ref(u128 *ref, u8 i): ref(ref), i(i) {}
Ref &operator=(const Ref &r) { return *this= bool(r); }
Ref &operator=(bool b) { return *ref&= ~(u128(1) << i), *ref|= u128(b) << i, *this; }
Ref &operator|=(bool b) { return *ref|= u128(b) << i, *this; }
Ref &operator&=(bool b) { return *ref&= ~(u128(!b) << i), *this; }
Ref &operator^=(bool b) { return *ref^= u128(b) << i, *this; }
operator bool() const { return (*ref >> i) & 1; }
};
template <> class Vector<bool> {
size_t n;
public:
valarray<u128> dat;
Vector(): n(0) {}
Vector(size_t n): n(n), dat((n + 127) >> 7) {}
Vector(size_t n, bool b): n(n), dat(-u128(b), (n + 127) >> 7) {
if (int k= n & 127; k) dat[dat.size() - 1]&= (u128(1) << k) - 1;
}
Vector(const initializer_list<bool> &v): n(v.size()), dat((n + 127) >> 7) {
int i= 0;
for (bool b: v) dat[i >> 7]|= u128(b) << (i & 127), ++i;
}
Ref operator[](int i) { return {begin(dat) + (i >> 7), u8(i & 127)}; }
bool operator[](int i) const { return (dat[i >> 7] >> (i & 127)) & 1; }
bool operator==(const Vector &r) const {
if (dat.size() != r.dat.size()) return false;
for (int i= dat.size(); i--;)
if (dat[i] != r.dat[i]) return false;
return true;
}
bool operator!=(const Vector &r) const { return !(*this == r); }
explicit operator bool() const { return n; }
Vector operator-() const { return Vector(*this); }
Vector &operator+=(const Vector &r) { return dat^= r.dat, *this; }
Vector &operator-=(const Vector &r) { return dat^= r.dat, *this; }
Vector &operator*=(bool b) { return dat*= b, *this; }
Vector operator+(const Vector &r) const { return Vector(*this)+= r; }
Vector operator-(const Vector &r) const { return Vector(*this)-= r; }
Vector operator*(bool b) const { return Vector(*this)*= b; }
size_t size() const { return n; }
friend bool dot(const Vector<bool> &a, const Vector<bool> &b) {
assert(a.size() == b.size());
u128 v= 0;
for (int i= a.dat.size(); i--;) v^= a.dat[i] & b.dat[i];
return __builtin_parityll(v >> 64) ^ __builtin_parityll(u64(v));
}
};
template <class R> Vector<R> operator*(const R &r, const Vector<R> &v) { return v * r; }
template <class R> ostream &operator<<(ostream &os, const Vector<R> &v) {
os << '[';
for (int _= 0, __= v.size(); _ < __; ++_) os << (_ ? ", " : "") << v[_];
return os << ']';
}
}
using _la_internal::Vector;
namespace _la_internal {
template <class R, class D> struct Mat {
Mat(): W(0) {}
Mat(size_t h, size_t w): W(w), dat(h * w) {}
Mat(size_t h, size_t w, R v): W(w), dat(v, h * w) {}
Mat(initializer_list<initializer_list<R>> v): W(v.size() ? v.begin()->size() : 0), dat(v.size() * W) {
auto it= begin(dat);
for (const auto &r: v) {
assert(r.size() == W);
for (R x: r) *it++= x;
}
}
size_t width() const { return W; }
size_t height() const { return W ? dat.size() / W : 0; }
auto operator[](int i) { return begin(dat) + i * W; }
auto operator[](int i) const { return begin(dat) + i * W; }
protected:
size_t W;
valarray<R> dat;
void add(const Mat &r) { assert(dat.size() == r.dat.size()), assert(W == r.W), dat+= r.dat; }
D mul(const Mat &r) const {
const size_t h= height(), w= r.W, l= W;
assert(l == r.height());
D ret(h, w);
auto a= begin(dat);
auto c= begin(ret.dat);
for (int i= h; i--; c+= w) {
auto b= begin(r.dat);
for (int k= l; k--; ++a) {
auto d= c;
auto v= *a;
for (int j= w; j--; ++b, ++d) *d+= v * *b;
}
}
return ret;
}
Vector<R> mul(const Vector<R> &r) const {
assert(W == r.size());
const size_t h= height();
Vector<R> ret(h);
auto a= begin(dat);
for (size_t i= 0; i < h; ++i)
for (size_t k= 0; k < W; ++k, ++a) ret[i]+= *a * r[k];
return ret;
}
};
template <class D> struct Mat<bool, D> {
struct Array {
u128 *bg;
Array(u128 *it): bg(it) {}
Ref operator[](int i) { return Ref{bg + (i >> 7), u8(i & 127)}; }
bool operator[](int i) const { return (bg[i >> 7] >> (i & 127)) & 1; }
};
struct ConstArray {
const u128 *bg;
ConstArray(const u128 *it): bg(it) {}
bool operator[](int i) const { return (bg[i >> 7] >> (i & 127)) & 1; }
};
Mat(): H(0), W(0), m(0) {}
Mat(size_t h, size_t w): H(h), W(w), m((w + 127) >> 7), dat(h * m) {}
Mat(size_t h, size_t w, bool b): H(h), W(w), m((w + 127) >> 7), dat(-u128(b), h * m) {
if (size_t i= h, k= w & 127; k)
for (u128 s= (u128(1) << k) - 1; i--;) dat[i * m]&= s;
}
Mat(const initializer_list<initializer_list<bool>> &v): H(v.size()), W(H ? v.begin()->size() : 0), m((W + 127) >> 7), dat(H * m) {
auto it= begin(dat);
for (const auto &r: v) {
assert(r.size() == W);
int i= 0;
for (bool b: r) it[i >> 7]|= u128(b) << (i & 127), ++i;
it+= m;
}
}
size_t width() const { return W; }
size_t height() const { return H; }
Array operator[](int i) { return {begin(dat) + i * m}; }
ConstArray operator[](int i) const { return {begin(dat) + i * m}; }
ConstArray get(int i) const { return {begin(dat) + i * m}; }
protected:
size_t H, W, m;
valarray<u128> dat;
void add(const Mat &r) { assert(H == r.H), assert(W == r.W), dat^= r.dat; }
D mul(const Mat &r) const {
assert(W == r.H);
D ret(H, r.W);
valarray<u128> tmp(r.m << 8);
auto y= begin(r.dat);
for (size_t l= 0; l < W; l+= 8) {
auto t= begin(tmp) + r.m;
for (int i= 0, n= min<size_t>(8, W - l); i < n; ++i, y+= r.m) {
auto u= begin(tmp);
for (int s= 1 << i; s--;) {
auto z= y;
for (int j= r.m; j--; ++u, ++t, ++z) *t= *u ^ *z;
}
}
auto a= begin(dat) + (l >> 7);
auto c= begin(ret.dat);
for (int i= H; i--; a+= m) {
auto u= begin(tmp) + ((*a >> (l & 127)) & 255) * r.m;
for (int j= r.m; j--; ++c, ++u) *c^= *u;
}
}
return ret;
}
Vector<bool> mul(const Vector<bool> &r) const {
assert(W == r.size());
Vector<bool> ret(H);
auto a= begin(dat);
for (size_t i= 0; i < H; ++i) {
u128 v= 0;
for (size_t j= 0; j < m; ++j, ++a) v^= *a & r.dat[j];
ret[i]= __builtin_parityll(v >> 64) ^ __builtin_parityll(u64(v));
}
return ret;
}
};
template <class R> struct Matrix: public Mat<R, Matrix<R>> {
using Mat<R, Matrix<R>>::Mat;
explicit operator bool() const { return this->W; }
static Matrix identity(int n) {
Matrix ret(n, n);
for (; n--;) ret[n][n]= R(true);
return ret;
}
Matrix submatrix(const vector<int> &rows, const vector<int> &cols) const {
Matrix ret(rows.size(), cols.size());
for (int i= rows.size(); i--;)
for (int j= cols.size(); j--;) ret[i][j]= (*this)[rows[i]][cols[j]];
return ret;
}
Matrix submatrix_rm(vector<int> rows, vector<int> cols) const {
sort(begin(rows), end(rows)), sort(begin(cols), end(cols)), rows.erase(unique(begin(rows), end(rows)), end(rows)), cols.erase(unique(begin(cols), end(cols)), end(cols));
const int H= this->height(), W= this->width(), n= rows.size(), m= cols.size();
vector<int> rs(H - n), cs(W - m);
for (int i= 0, j= 0, k= 0; i < H; ++i)
if (j < n && rows[j] == i) ++j;
else rs[k++]= i;
for (int i= 0, j= 0, k= 0; i < W; ++i)
if (j < m && cols[j] == i) ++j;
else cs[k++]= i;
return submatrix(rs, cs);
}
bool operator==(const Matrix &r) const {
if (this->width() != r.width() || this->height() != r.height()) return false;
for (int i= this->dat.size(); i--;)
if (this->dat[i] != r.dat[i]) return false;
return true;
}
bool operator!=(const Matrix &r) const { return !(*this == r); }
Matrix &operator*=(const Matrix &r) { return *this= this->mul(r); }
Matrix operator*(const Matrix &r) const { return this->mul(r); }
Matrix &operator*=(R r) { return this->dat*= r, *this; }
template <class T> Matrix operator*(T r) const {
static_assert(is_convertible_v<T, R>);
return Matrix(*this)*= r;
}
Matrix &operator+=(const Matrix &r) { return this->add(r), *this; }
Matrix operator+(const Matrix &r) const { return Matrix(*this)+= r; }
Vector<R> operator*(const Vector<R> &r) const { return this->mul(r); }
Vector<R> operator()(const Vector<R> &r) const { return this->mul(r); }
Matrix pow(uint64_t k) const {
size_t W= this->width();
assert(W == this->height());
for (Matrix ret= identity(W), b= *this;; b*= b)
if (k & 1 ? ret*= b, !(k>>= 1) : !(k>>= 1)) return ret;
}
};
template <class R, class T> Matrix<R> operator*(const T &r, const Matrix<R> &m) { return m * r; }
template <class R> ostream &operator<<(ostream &os, const Matrix<R> &m) {
os << "\n[";
for (int i= 0, h= m.height(); i < h; os << ']', ++i) {
if (i) os << "\n ";
os << '[';
for (int j= 0, w= m.width(); j < w; ++j) os << (j ? ", " : "") << m[i][j];
}
return os << ']';
}
template <class K> static bool is_zero(K x) {
if constexpr (is_floating_point_v<K>) return abs(x) < 1e-8;
else return x == K();
}
}
using _la_internal::Matrix;
namespace _la_internal {
template <class K> class LU_Decomposition {
Matrix<K> dat;
vector<size_t> perm, piv;
bool sgn;
size_t psz;
public:
LU_Decomposition(const Matrix<K> &A): dat(A), perm(A.height()), sgn(false), psz(0) {
const size_t h= A.height(), w= A.width();
iota(perm.begin(), perm.end(), 0), piv.resize(min(w, h));
for (size_t c= 0, pos; c < w && psz < h; ++c) {
pos= psz;
if constexpr (is_floating_point_v<K>) {
for (size_t r= psz + 1; r < h; ++r)
if (abs(dat[perm[pos]][c]) < abs(dat[perm[r]][c])) pos= r;
} else if (is_zero(dat[perm[pos]][c]))
for (size_t r= psz + 1; r < h; ++r)
if (!is_zero(dat[perm[r]][c])) pos= r, r= h;
if (is_zero(dat[perm[pos]][c])) continue;
if (pos != psz) sgn= !sgn, swap(perm[pos], perm[psz]);
const auto b= dat[perm[psz]];
for (size_t r= psz + 1, i; r < h; ++r) {
auto a= dat[perm[r]];
K m= a[c] / b[c];
for (a[c]= K(), a[psz]= m, i= c + 1; i < w; ++i) a[i]-= b[i] * m;
}
piv[psz++]= c;
}
}
size_t rank() const { return psz; }
bool is_regular() const { return rank() == dat.height() && rank() == dat.width(); }
K det() const {
assert(dat.height() == dat.width());
K ret= sgn ? -1 : 1;
for (size_t i= dat.width(); i--;) ret*= dat[perm[i]][i];
return ret;
}
vector<Vector<K>> kernel() const {
const size_t w= dat.width(), n= rank();
vector ker(w - n, Vector<K>(w));
for (size_t c= 0, i= 0; c < w; ++c) {
if (i < n && piv[i] == c) ++i;
else {
auto &a= ker[c - i];
a[c]= 1;
for (size_t r= i; r--;) a[r]= -dat[perm[r]][c];
for (size_t j= i, k, r; j--;) {
K x= a[j] / dat[perm[j]][k= piv[j]];
for (a[j]= 0, a[k]= x, r= j; r--;) a[r]-= dat[perm[r]][k] * x;
}
}
}
return ker;
}
Vector<K> linear_equations(const Vector<K> &b) const {
const size_t h= dat.height(), w= dat.width(), n= rank();
assert(h == b.size());
Vector<K> y(h), x(w);
for (size_t c= 0; c < h; ++c)
if (y[c]+= b[perm[c]]; c < w)
for (size_t r= c + 1; r < h; ++r) y[r]-= y[c] * dat[perm[r]][c];
for (size_t i= n; i < h; ++i)
if (!is_zero(y[i])) return Vector<K>(); // no solution
for (size_t i= n, r; i--;)
for (x[piv[i]]= y[i] / dat[perm[i]][piv[i]], r= i; r--;) y[r]-= x[piv[i]] * dat[perm[r]][piv[i]];
return x;
}
Matrix<K> inverse_matrix() const {
if (!is_regular()) return Matrix<K>(); // no solution
const size_t n= dat.width();
Matrix<K> ret(n, n);
for (size_t i= 0; i < n; ++i) {
Vector<K> y(n);
for (size_t c= 0; c < n; ++c)
if (y[c]+= perm[c] == i; !is_zero(y[c]))
for (size_t r= c + 1; r < n; ++r) y[r]-= y[c] * dat[perm[r]][c];
for (size_t j= n; j--;) {
K m= ret[j][i]= y[j] / dat[perm[j]][j];
for (size_t r= j; r--;) y[r]-= m * dat[perm[r]][j];
}
}
return ret;
}
};
void add_upper(u128 *a, const u128 *b, size_t bg, size_t ed) { //[bg,ed)
if (bg >= ed) return;
size_t s= bg >> 7;
a[s]^= b[s] & -(u128(1) << (bg & 127));
for (size_t i= (ed + 127) >> 7; --i > s;) a[i]^= b[i];
}
void add_lower(u128 *a, const u128 *b, size_t ed) { //[0,ed)
size_t s= ed >> 7;
for (a[s]^= b[s] & ((u128(1) << (ed & 127)) - 1); s--;) a[s]^= b[s];
}
void subst_lower(u128 *a, const u128 *b, size_t ed) { //[0,ed)
size_t s= ed >> 7;
for (a[s]= b[s] & ((u128(1) << (ed & 127)) - 1); s--;) a[s]= b[s];
}
bool any1_upper(const u128 *a, size_t bg, size_t ed) { //[bg,ed)
if (bg >= ed) return false;
size_t s= bg >> 7;
if (a[s] & -(u128(1) << (bg & 127))) return true;
for (size_t i= (ed + 127) >> 7; --i > s;)
if (a[i]) return true;
return false;
}
template <> class LU_Decomposition<bool> {
Matrix<bool> dat;
vector<size_t> perm, piv;
size_t psz;
public:
LU_Decomposition(Matrix<bool> A): dat(A.width(), A.height()), perm(A.height()), psz(0) {
const size_t h= A.height(), w= A.width();
iota(perm.begin(), perm.end(), 0), piv.resize(min(w, h));
for (size_t c= 0, pos; c < w && psz < h; ++c) {
for (pos= psz; pos < h; ++pos)
if (A.get(perm[pos])[c]) break;
if (pos == h) continue;
if (pos != psz) swap(perm[pos], perm[psz]);
auto b= A.get(perm[psz]);
for (size_t r= psz + 1; r < h; ++r) {
auto a= A[perm[r]];
if (bool m= a[c]; m) add_upper(a.bg, b.bg, c, w), a[psz]= 1;
}
piv[psz++]= c;
}
for (size_t j= w; j--;)
for (size_t i= h; i--;) dat[j][i]= A.get(perm[i])[j];
}
size_t rank() const { return psz; }
bool is_regular() const { return rank() == dat.height() && rank() == dat.width(); }
bool det() const { return is_regular(); }
vector<Vector<bool>> kernel() const {
const size_t w= dat.height(), n= rank();
vector ker(w - rank(), Vector<bool>(w));
for (size_t c= 0, i= 0; c < w; ++c) {
if (i < n && piv[i] == c) ++i;
else {
auto &a= ker[c - i];
subst_lower(begin(a.dat), dat[c].bg, i), a[c]= 1;
for (size_t j= i, k; j--;) {
bool x= a[j];
if (a[j]= 0, a[k= piv[j]]= x; x) add_lower(begin(a.dat), dat[k].bg, j);
}
}
}
return ker;
}
Vector<bool> linear_equations(const Vector<bool> &b) const {
const size_t h= dat.width(), w= dat.height(), n= rank();
assert(h == b.size());
Vector<bool> y(h), x(w);
for (size_t c= 0; c < h; ++c)
if (y[c]^= b[perm[c]]; c < w && y[c]) add_upper(begin(y.dat), dat[c].bg, c + 1, h);
if (any1_upper(begin(y.dat), n, h)) return Vector<bool>(); // no solution
for (size_t i= n; i--;)
if ((x[piv[i]]= y[i])) add_lower(begin(y.dat), dat[piv[i]].bg, i);
return x;
}
Matrix<bool> inverse_matrix() const {
if (!is_regular()) return Matrix<bool>(); // no solution
const size_t n= dat.width();
Matrix<bool> ret(n, n);
for (size_t i= 0; i < n; ++i) {
Vector<bool> y(n);
for (size_t c= 0; c < n; ++c)
if (y[c]^= perm[c] == i; y[c]) add_upper(begin(y.dat), dat[c].bg, c + 1, n);
for (size_t j= n; j--;)
if ((ret[j][i]= y[j])) add_lower(begin(y.dat), dat[j].bg, j);
}
return ret;
}
};
}
using _la_internal::LU_Decomposition;
using namespace std;
signed main() {
cin.tie(0);
ios::sync_with_stdio(0);
using Mint= ModInt<998244353>;
Nimber::init();
int N, T;
cin >> N >> T;
Matrix<Nimber> H(T, N);
for (int i= 0; i < T; ++i)
for (int j= 0; j < N; ++j) {
long long x;
cin >> x;
H[i][j]= x - 1;
}
Mint ans= 0, pw= Mint(2).pow(64);
for (long long s= 1ll << N; s--;) {
vector<int> rm;
int n= 0;
for (int i= N; i--;)
if ((s >> i) & 1) rm.push_back(i);
else ++n;
Mint x= pw.pow(n - LU_Decomposition(H.submatrix_rm({}, rm)).rank());
if ((N - n) & 1) ans-= x;
else ans+= x;
}
cout << ans << '\n';
return 0;
}