#907821 (C++23) No.2444 一次変換と体積

• 問題: No.2444 一次変換と体積
• ユーザー: noya2
• 提出日時: 2023-08-25 22:11:26
• 言語: C++23 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 2 ms / 2,000 ms
• コード長: 24,126 bytes
• コンパイル時間: 3,061 ms
• コンパイル使用メモリ: 263,232 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-06-06 16:40:45
• 合計ジャッジ時間: 3,813 ms
• ジャッジサーバーID （参考情報）: judge4 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,248 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	2 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	2 ms; 5,376 KB
testcase_15	AC	2 ms; 5,376 KB
testcase_16	AC	2 ms; 5,376 KB
testcase_17	AC	2 ms; 5,376 KB
testcase_18	AC	2 ms; 5,376 KB
testcase_19	AC	2 ms; 5,376 KB

ソースコード

#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout.hpp"
namespace noya2 {

template<typename T> concept Scanable  = requires (ifstream &is, T &a){ is >> a; };
template<typename T> concept Printable = requires (ofstream &os, T &a){ os << a; };

template <typename Scanable> istream &operator>>(istream &is, vector<Scanable> &v);
template <typename Printable> ostream &operator<<(ostream &os, const vector<Printable> &v);

template <typename T, typename U>
requires Scanable<T> && Scanable<U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}
template <typename T, typename U>
requires Printable<T> && Printable<U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}

template <typename Scanable>
istream &operator>>(istream &is, vector<Scanable> &v){
    for (auto &x : v) is >> x;
    return is;
}
template <typename Printable>
ostream &operator<<(ostream &os, const vector<Printable> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}

void in() {}
template <typename Scanable, class... U>
void in(Scanable &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename Printable, class... U, char sep = ' '>
void out(const Printable &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}
template<typename Printable>
void out(const vector<vector<Printable>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"
namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(abs(a),abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(vector<T> &v){
    sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "c.cpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"

// AtCoderLibrary をそのままパクっている なにもわかっていない
// \( x _______ x) ~

#line 8 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"
#include <type_traits>
#line 10 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"

namespace noya2 {

constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

struct barrett {
    unsigned int _m;
    unsigned long long im;

    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    unsigned int umod() const { return _m; }

    unsigned int mul(unsigned int a, unsigned int b) const {
        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};

    long long s = b, t = a;
    long long m0 = 0, m1 = 1;

    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u; 

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

}  // namespace noya2

namespace noya2 {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 = typename std::conditional<std::is_same<T, __int128_t>::value || std::is_same<T, __int128>::value, std::true_type, std::false_type>::type;

template <class T>
using is_unsigned_int128 = typename std::conditional<std::is_same<T, __uint128_t>::value || std::is_same<T, unsigned __int128>::value, std::true_type, std::false_type>::type;

template <class T>
using make_unsigned_int128 = typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value || is_signed_int128<T>::value || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value && std::is_signed<T>::value) || is_signed_int128<T>::value, std::true_type, std::false_type>::type;

template <class T>
using is_unsigned_int = typename std::conditional<(is_integral<T>::value && std::is_unsigned<T>::value) || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int128<T>::value, make_unsigned_int128<T>, typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>, std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int = typename std::conditional<is_integral<T>::value && std::is_signed<T>::value, std::true_type, std::false_type>::type;

template <class T>
using is_unsigned_int = typename std::conditional<is_integral<T>::value && std::is_unsigned<T>::value, std::true_type, std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>, std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace noya2

namespace noya2 {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace noya2

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : noya2::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    static_modint() : _v(0) {}
    template <class T, noya2::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, noya2::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = noya2::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    friend std::ostream &operator<<(std::ostream &os, const mint& p) {
        return os << p.val();
    }
    friend std::istream &operator>>(std::istream &is, mint &a) {
        long long t; is >> t;
        a = mint(t);
        return (is);
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = noya2::is_prime<m>;
};

template <int id> struct dynamic_modint : noya2::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = noya2::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, noya2::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, noya2::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = noya2::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    friend std::ostream &operator<<(std::ostream &os, const mint& p) {
        return os << p.val();
    }
    friend std::istream &operator>>(std::istream &is, mint &a) {
        long long t; is >> t;
        a = mint(t);
        return (is);
    }

  private:
    unsigned int _v;
    static noya2::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> noya2::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace noya2 {

template <class T>
using is_static_modint = std::is_base_of<noya2::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace noya2
#line 4 "c.cpp"
using mint = modint;
#line 2 "/Users/noya2/Desktop/Noya2_library/math/matrix.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/math/matrix.hpp"

namespace noya2{

template<typename T> struct Matrix{
    int rows, cols;
    vector<vector<T>> m;
    Matrix (int h = 0, int w = -1, T init = T(0)) : m(h,vector<T>((w == -1 ? h : w),init)){
        rows = h, cols = (w == -1 ? h : w);
    } 
    Matrix (vector<vector<T>> _init) : m(_init), rows(_init.size()), cols(_init.at(0).size()){}
    vector<T>& operator[](const int i) const {return m[i];}
    vector<T>& operator[](const int i) {return m[i];}
    Matrix &operator+= (const Matrix &r){
        assert(this->rows == r.rows && this->cols == r.cols);
        for (int i = 0; i < r.rows; ++i){
            for (int j = 0; j < r.cols; ++j){
                m[i][j] += r.m[i][j];
            }
        }
        return *this;
    }
    Matrix &operator-= (const Matrix &r){
        assert(this->rows == r.rows && this->cols == r.cols);
        for (int i = 0; i < r.rows; ++i){
            for (int j = 0; j < r.cols; ++j){
                m[i][j] -= r.m[i][j];
            }
        }
        return *this;
    }
    Matrix &operator*= (const Matrix &r){
        assert(this->cols == r.rows);
        Matrix res(rows, r.cols);
        for (int i = 0; i < rows; ++i){
            for (int j = 0; j < r.cols; ++j){
                for (int k = 0; k < r.rows; ++k){
                    res[i][j] += m[i][k] * r.m[k][j];
                }
            }
        }
        return *this = res;
    }
    Matrix operator+ (const Matrix &r) const {return Matrix(*this) += r;}
    Matrix operator- (const Matrix &r) const {return Matrix(*this) -= r;}
    Matrix operator* (const Matrix &r) const {return Matrix(*this) *= r;}
    bool operator== (const Matrix &r){
        if (rows != r.rows || cols != r.cols) return false;
        for (int i = 0; i < r.rows; ++i){
            for (int j = 0; j < r.cols; ++j){
                if (m[i][j] != r.m[i][j]) return false;
            }
        }
        return true;
    }
    Matrix& operator+=(const T &r){
        for (int i = 0; i < rows; ++i){
            for (int j = 0; j < cols; ++j){
                m[i][j] += r;
            }
        }
        return *this;
    }
    Matrix& operator-=(const T &r){
        for (int i = 0; i < rows; ++i){
            for (int j = 0; j < cols; ++j){
                m[i][j] -= r;
            }
        }
        return *this;
    }
    Matrix& operator*=(const T &r){
        for (int i = 0; i < rows; ++i){
            for (int j = 0; j < cols; ++j){
                m[i][j] *= r;
            }
        }
        return *this;
    }
    Matrix& operator/=(const T &r){
        for (int i = 0; i < rows; ++i){
            for (int j = 0; j < cols; ++j){
                m[i][j] /= r;
            }
        }
        return *this;
    }
    Matrix operator+ (const T &r) const {return Matrix(*this) += r;}
    Matrix operator- (const T &r) const {return Matrix(*this) -= r;}
    Matrix operator* (const T &r) const {return Matrix(*this) *= r;}
    Matrix operator/ (const T &r) const {return Matrix(*this) /= r;}
    Matrix e(){
        assert(this->rows == this->cols);
        Matrix res(this->rows, this->rows);
        for (int i = 0; i < rows; ++i) res[i][i] = 1;
        return res;
    }
    Matrix pow(long long n){
        assert(this->rows == this->cols);
        if (n == 0) return e();
        Matrix f = pow(n / 2);
        Matrix ans = f * f;
        if (n % 2 == 1) ans *= *this;
        return ans;
    }
    // for T = int, long long, double, long double
    void show(){
        for (int i = 0; i < rows; ++i){
            for (int j = 0; j < cols; ++j){
                cout << m[i][j] << (j+1 == this->cols ? "\n" : " ");
            }
        }
    }
    T determinant() const {
        Matrix B(*this);
        assert(rows == cols);
        T ret = 1;
        for (int i = 0; i < rows; i++) {
            int idx = -1;
            for (int j = i; j < cols; j++) {
                if (B[j][i] != 0) {
                    idx = j;
                    break;
                }
            }
            if (idx == -1) return 0;
            if (i != idx) {
                ret *= T(-1);
                swap(B[i], B[idx]);
            }
            ret *= B[i][i];
            T inv = T(1) / B[i][i];
            for (int j = 0; j < cols; j++) {
                B[i][j] *= inv;
            }
            for (int j = i + 1; j < rows; j++) {
                T a = B[j][i];
                if (a == 0) continue;
                for (int k = i; k < cols; k++) {
                    B[j][k] -= B[i][k] * a;
                }
            }
        }
        return ret;
    }
};

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/misc/inversion.hpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/fenwick_tree.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/data_structure/fenwick_tree.hpp"

namespace noya2{

template <class T> struct fenwick_tree {
  public:
    fenwick_tree() : _n(0) {}
    explicit fenwick_tree(int n) : _n(n), data(n) {}

    void add(int p, T x) {
        assert(0 <= p && p < _n);
        p++;
        while (p <= _n) {
            data[p - 1] += x;
            p += p & -p;
        }
    }

    T sum(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        return sum(r) - sum(l);
    }

  private:
    int _n;
    vector<T> data;

    T sum(int r) {
        T s = 0;
        while (r > 0) {
            s += data[r - 1];
            r -= r & -r;
        }
        return s;
    }
};

} // namespace noya2
#line 5 "/Users/noya2/Desktop/Noya2_library/misc/inversion.hpp"

namespace noya2{

template<class T>
ll inversion(const vector<T> &a){
    auto b = a;
    uniq(b);
    fenwick_tree<T> fen(b.size());
    ll ans = 0;
    for (auto &x : a){
        int id = lower_bound(all(b),x) - b.begin();
        ans += fen.sum(id+1,b.size());
        fen.add(id,1);
    }
    return ans;
}

} // namespace noya2
#line 7 "c.cpp"

void solve(){
    int n, mo; in(n,mo);
    mint::set_mod(mo);
    Matrix<ll> mat(3);
    rep(i,3) rep(j,3){
        ll a; in(a);
        mat[i][j] = a;
    }
    ll ans = 0;
    vector<int> ids = {0,1,2};
    do {
        ll cur = (inversion(ids) % 2 == 0 ? 1 : -1);
        rep(i,3) cur *= mat[i][ids[i]];
        ans += cur;
    }while(next_permutation(all(ids)));
    ans = mint(abs(ans)).pow(n).val();
    out(ans);
}

int main(){
    int t = 1; //in(t);
    while (t--) { solve(); }
}