#line 1 ".lib/template.hpp"


#include <iostream>
#include <string>
#include <vector>
#include <array>
#include <tuple>
#include <stack>
#include <queue>
#include <deque>
#include <algorithm>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <bitset>
#include <cmath>
#include <functional>
#include <cassert>
#include <climits>
#include <iomanip>
#include <numeric>
#include <memory>
#include <random>
#include <thread>
#include <chrono>
#define allof(obj) (obj).begin(), (obj).end()
#define range(i, l, r) for(int i=l;i<r;i++)
#define bit_subset(i, S) for(int i=S, zero_cnt=0;(zero_cnt+=i==S)<2;i=(i-1)&S)
#define bit_kpop(i, n, k) for(int i=(1<<k)-1,x_bit,y_bit;i<(1<<n);x_bit=(i&-i),y_bit=i+x_bit,i=(!i?(1<<n):((i&~y_bit)/x_bit>>1)|y_bit))
#define bit_kth(i, k) ((i >> k)&1)
#define bit_highest(i) (i?63-__builtin_clzll(i):-1)
#define bit_lowest(i) (i?__builtin_ctzll(i):-1)
#define sleepms(t) std::this_thread::sleep_for(std::chrono::milliseconds(t))
using ll = long long;
using ld = long double;
using ul = uint64_t;
using pi = std::pair<int, int>;
using pl = std::pair<ll, ll>;
using namespace std;

template<typename F, typename S>
std::ostream &operator<<(std::ostream &dest, const std::pair<F, S> &p){
  dest << p.first << ' ' << p.second;
  return dest;
}
template<typename T>
std::ostream &operator<<(std::ostream &dest, const std::vector<std::vector<T>> &v){
  int sz = v.size();
  if(sz==0) return dest;
  for(int i=0;i<sz;i++){
    int m = v[i].size();
    for(int j=0;j<m;j++) dest << v[i][j] << (i!=sz-1&&j==m-1?'\n':' ');
  }
  return dest;
}
template<typename T>
std::ostream &operator<<(std::ostream &dest, const std::vector<T> &v){
  int sz = v.size();
  if(sz==0) return dest;
  for(int i=0;i<sz-1;i++) dest << v[i] << ' ';
  dest << v[sz-1];
  return dest;
}
template<typename T, size_t sz>
std::ostream &operator<<(std::ostream &dest, const std::array<T, sz> &v){
  if(sz==0) return dest;
  for(int i=0;i<sz-1;i++) dest << v[i] << ' ';
  dest << v[sz-1];
  return dest;
}
template<typename T>
std::ostream &operator<<(std::ostream &dest, const std::set<T> &v){
  for(auto itr=v.begin();itr!=v.end();){
    dest << *itr;
    itr++;
    if(itr!=v.end()) dest << ' ';
  }
  return dest;
}
template<typename T, typename E>
std::ostream &operator<<(std::ostream &dest, const std::map<T, E> &v){
  for(auto itr=v.begin();itr!=v.end();){
    dest << '(' << itr->first << ", " << itr->second << ')';
    itr++;
    if(itr!=v.end()) dest << '\n';
  }
  return dest;
}
template<typename T>
vector<T> make_vec(size_t sz, T val){return std::vector<T>(sz, val);}
template<typename T, typename... Tail>
auto make_vec(size_t sz, Tail ...tail){
  return std::vector<decltype(make_vec<T>(tail...))>(sz, make_vec<T>(tail...));
}
template<typename T>
vector<T> read_vec(size_t sz){
  std::vector<T> v(sz);
  for(int i=0;i<(int)sz;i++) std::cin >> v[i];
  return v;
}
template<typename T, typename... Tail>
auto read_vec(size_t sz, Tail ...tail){
  auto v = std::vector<decltype(read_vec<T>(tail...))>(sz);
  for(int i=0;i<(int)sz;i++) v[i] = read_vec<T>(tail...);
  return v;
}
void io_init(){
  std::cin.tie(nullptr);
  std::ios::sync_with_stdio(false);
}

#line 1 ".lib/math/mod.hpp"


#line 6 ".lib/math/mod.hpp"
#include <type_traits>
#line 8 ".lib/math/mod.hpp"
#include <ostream>
#line 1 ".lib/math/minior/mod_base.hpp"


#line 4 ".lib/math/minior/mod_base.hpp"
// @param m `1 <= m`
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 long long y = x * _m;
    return (unsigned int)(z - y + (z < y ? _m : 0));
  }
};
// @param n `0 <= n`
// @param m `1 <= m`
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);

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);

int ceil_pow2(int n){
  int x = 0;
  while ((1U << x) < (unsigned int)(n)) x++;
  return x;
}
int bsf(unsigned int n){
  return __builtin_ctz(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};
}


#line 13 ".lib/math/mod.hpp"

template<int m>
long long modpow(long long a, long long b){
  assert(0 <= b);
  assert(0 < m);
  a = safe_mod(a, m);
  long long ret = 1;
  while(b){
    if(b & 1) ret = (ret * a) % m;
    a = (a * a) % m;
    b >>= 1;
  }
  return ret;
}
// @param 0 <= b, 0 < m
long long modpow(long long a, long long b, int m){
  assert(0 <= b);
  assert(0 < m);
  a = safe_mod(a, m);
  long long ret = 1;
  while(b){
    if(b & 1) ret = (ret * a) % m;
    a = (a * a) % m;
    b >>= 1;
  }
  return ret;
}

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

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : 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>
  static_modint(T v){
    long long x = v % (long long)umod();
    if (x < 0) x += umod();
    _v = x;
  }
  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 = 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;}
private:
  unsigned int _v;
  static constexpr unsigned int umod(){return m;}
  static constexpr bool prime = is_prime<m>;
};

template<int id> 
struct dynamic_modint : modint_base{
  using mint = dynamic_modint;
public:
  static int mod(){return (int)(bt.umod());}
  static void set_mod(int m){
    assert(1 <= m);
    bt = barrett(m);
  }
  static mint raw(int v){
    mint x;
    x._v = v;
    return x;
  }
  dynamic_modint(): _v(0){}
  template <class T>
  dynamic_modint(T v){
    long long x = v % (long long)(mod());
    if (x < 0) x += mod();
    _v = x;
  }
  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 = 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;}
private:
  unsigned int _v;
  static barrett bt;
  static unsigned int umod(){return bt.umod();}
};
template <int id>
barrett dynamic_modint<id>::bt(998244353);
using modint = dynamic_modint<-1>;

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
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>;
template <class T>
using is_static_modint = std::is_base_of<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>;
template<int m>
std::ostream &operator<<(std::ostream &dest, const static_modint<m> &a){
  dest << a.val();
  return dest;
}
template<int id>
std::ostream &operator<<(std::ostream &dest, const dynamic_modint<id> &a){
  dest << a.val();
  return dest;
}

// 0 <= n < m <= int_max
// 前処理 O(n + log(m))
// 各種計算 O(1)
// 変数 <= n
template<typename mint, is_modint<mint>* = nullptr>
struct modcomb{
private:
  int n;
  std::vector<mint> f, i, fi;
  void init(int _n){
    assert(0 <= _n && _n < mint::mod());
    if(_n < f.size()) return;
    n = _n;
    f.resize(n + 1), i.resize(n + 1), fi.resize(n + 1);
    f[0] = fi[0] = mint(1);
    if(n) f[1] = fi[1] = i[1] = mint(1);
    for(int j = 2; j <= n; j++) f[j] = f[j - 1] * j;
    fi[n] = f[n].inv();
    for(int j = n; j >= 2; j--){
      fi[j - 1] = fi[j] * j;
      i[j] = f[j - 1] * fi[j];
    }
  }
public:
  modcomb(): n(-1){}
  modcomb(int _n){
    init(_n);
  }
  void recalc(int _n){
    init(std::min(mint::mod() - 1, 1 << ceil_pow2(_n)));
  }
  mint comb(int a, int b){
    if((a < 0) || (b < 0) || (a < b)) return 0;
    return f[a] * fi[a - b] * fi[b];
  }
  mint perm(int a, int b){
    if((a < 0) || (b < 0) || (a < b)) return 0;
    return f[a] * fi[a - b];
  }
  mint fac(int x){
    assert(0 <= x && x <= n);
    return f[x];
  }
  mint inv(int x){
    assert(0 < x && x <= n);
    return i[x];
  }
  mint finv(int x){
    assert(0 <= x && x <= n);
    return fi[x];
  }
};
template<typename mint, is_modint<mint>* = nullptr>
struct modpow_table{
  std::vector<mint> v;
  // x^maxkまで計算できる
  modpow_table(){}
  void init(int x, int maxk){
    v.resize(maxk + 1);
    v[0] = 1;
    for(int i = 1; i <= maxk; i++) v[i] = v[i - 1] * x;
  }
  mint pow(int k){
    assert(0 <= k && k < v.size());
    return v[k];
  }
};

#line 1 ".lib/math/matrix/matrix_mod.hpp"


#line 5 ".lib/math/matrix/matrix_mod.hpp"

template<typename mint>
struct matrix_mod{
  int n, m;
  using _mint = mint;
private:
  using vec = std::vector<mint>;
  using matrix = matrix_mod<mint>;
  // n × k 行列と k × m 行列の積(n × m行列)
  // K == 0だと壊れる
  static matrix __mul_mat(const matrix &vl, const matrix &vr){
    int N = vl.n, K = vl.m, M = vr.m;
    assert(K == vr.n);
    assert(K);
    if(N == 0) return matrix(0, M);
    if(M == 0) return matrix(N, 0);
    auto vr_t = vr.t();
    matrix ret(N, M, 0);
    for(int i = 0; i < N; i++){
      for(int j = 0; j < M; j++){
        __int128_t S = 0;
        for(int k = 0; k < K; k++){
          S += (long long)vl.val[i][k].val() * vr_t[j][k].val();
        }
        ret[i][j] = S % mint::mod();
      }
    }
    return ret;
  }
  // n × m 行列と n × m 行列の和(n × m行列)
  static void __add_mat_inplace(matrix &vl, const matrix &vr){
    assert(vl.n == vr.n && vl.m == vr.m);
    int N = vl.n, M = vl.m;
    for(int i = 0; i < N; i++){
      for(int j = 0; j < M; j++){
        vl[i][j] += vr[i][j];
      }
    }
  }
  // n × m 行列と n × m 行列の差(n × m行列)
  static void __sub_mat_inplace(matrix &vl, const matrix &vr){
    assert(vl.n == vr.n && vl.m == vr.m);
    int N = vl.n, M = vl.m;
    for(int i = 0; i < N; i++){
      for(int j = 0; j < M; j++){
        vl[i][j] -= vr[i][j];
      }
    }
  }
  static void __mul_val_inplace(matrix &vl, mint vr){
    int N = vl.n, M = vl.m;
    for(int i = 0; i < N; i++){
      for(int j = 0; j < M; j++){
        vl[i][j] *= vr;
      }
    }
  }
  static void __add_val_inplace(matrix &vl, mint vr){
    int N = vl.n, M = vl.m;
    for(int i = 0; i < N; i++){
      for(int j = 0; j < M; j++){
        vl[i][j] += vr;
      }
    }
  }
  static void __sub_val_inplace(matrix &vl, mint vr){
    int N = vl.n, M = vl.m;
    for(int i = 0; i < N; i++){
      for(int j = 0; j < M; j++){
        vl[i][j] -= vr;
      }
    }
  }
  std::vector<vec> val;
public:
  matrix_mod(): n(0), m(0){}
  matrix_mod(int _n, int _m, mint x = mint(0)) : n(_n), m(_m), val(_n, vec(_m, x)){}
  matrix_mod(const matrix_mod &v) : n(v.n), m(v.m), val(v.val){}
  matrix_mod(const vec &v): n(1), m(v.size()), val(1, vec(v.size())){val[0] = v;}
  matrix_mod(const std::vector<vec> &v): n(v.size()), m(v[0].size()), val(v){}

  matrix_mod operator +  (const matrix_mod &vr){matrix_mod tmp(*this); return tmp += vr;}
  matrix_mod operator -  (const matrix_mod &vr){matrix_mod tmp(*this); return tmp -= vr;}
  matrix_mod operator *  (const matrix_mod &vr){return __mul_mat(*this, vr);}
  matrix_mod operator ^  (const long long vr){return pow(vr);}
  matrix_mod operator *  (const mint vr){matrix_mod tmp(*this); return tmp *= vr;}
  matrix_mod operator += (const matrix_mod &vr){__add_mat_inplace(*this, vr); return *this;}
  matrix_mod operator -= (const matrix_mod &vr){__sub_mat_inplace(*this, vr); return *this;}
  matrix_mod operator *= (const matrix_mod &vr){return (*this) = __mul_mat(*this, vr);}
  matrix_mod operator ^= (const long long vr){return (*this) = pow(vr);}
  matrix_mod operator *= (const mint vr){__mul_val_inplace(*this, vr); return *this;}
  vec& operator [] (const int i){return val[i];}

  // n次の単位行列
  static matrix_mod eye(int n){
    matrix_mod ret(n, n, 0);
    for(int i = 0; i < n; i++) ret[i][i] = mint(1);
    return ret;
  }
  void print()const{
    for(int i = 0; i < n; i++){
      for(int j = 0; j < m; j++){
        std::cout << val[i][j] << (j == m - 1 ? '\n' : ' ');
      }
    }
  }
  matrix_mod pow(long long k){
    assert(n && m && n == m); // 正方行列でなければならない
    matrix_mod ret = eye(n); // k == 0の場合単位行列を返す
    matrix_mod m(*this);
    while(k){
      if(k & 1) ret *= m;
      m *= m;
      k >>= 1;
    }
    return ret;
  }
  // 転置
  matrix_mod t()const{
    matrix_mod ret(m, n, 0);
    for(int i = 0; i < n; i++){
      for(int j = 0; j < m; j++){
        ret[j][i] = val[i][j];
      }
    }
    return ret;
  }
  //掃き出し法で上三角行列を作る, {変形後の行列、行のスワップ回数}を返す O(NM^2)
  std::pair<matrix_mod, int> gaussian_elimination(){
    matrix_mod v(*this);
    int row = 0;//確定していない行
    int swp = 0;
    for(int i = 0; i < m && row < n; i++){
      //i列目が0でない行を探す
      int r = -1;
      for(int j = row; j < n; j++){
        if(v[j][i].val()){
          r = j;
          break;
        }
      }
      if(r == -1) continue;
      if(r != row){
        swp++;
        std::swap(v[r], v[row]);
      }
      //i列目が0でない行の処理
      for(int j = row + 1; j < n; j++){
        if(v[j][i].val() == 0) continue;
        mint x = v[j][i] / v[row][i];
        for(int k = i; k < m; k++){
          v[j][k] -= x * v[row][k];
        }
      }
      row++;
    }
    return {v, swp};
  }
  //掃き出し法で上三角行列を作る, {変形後の行列、行のスワップ回数}を返す O(NM^2 * log mod)
  std::pair<matrix_mod, int> gaussian_elimination_arbitrary_mod(){
    matrix_mod v(*this);
    int row = 0;//確定していない行
    int swp = 0;
    for(int i = 0; i < m && row < n; i++){
      //i列目が0でない行を探す
      int r = -1;
      for(int j = row; j < n; j++){
        if(v[j][i].val()){
          r = j;
          break;
        }
      }
      if(r == -1) continue;
      if(r != row){
        swp++;
        std::swap(v[r], v[row]);
      }
      //i列目が0でない行の処理
      for(int j = row + 1; j < n; j++){
        while(v[j][i].val() != 0){
          if(v[row][i].val() > v[j][i].val()){
            swp++;
            std::swap(v[row], v[j]);
          }
          int x = v[j][i].val() / v[row][i].val();
          for(int k = i; k < m; k++){
            v[j][k] -= x * v[row][k];
          }
        }
      }
      row++;
    }
    return {v, swp};
  }
  //すでに上三角行列になっていることが前提
  int rank(){
    int cnt = 0;
    for(int i = 0; i < n; i++, cnt++){
      bool f = false;
      for(int j = i; j < m; j++){
        if(val[i][j].val()){
          f = true;
          break;
        }
      }
      if(!f) break;
    }
    return cnt;
  }
  // 行列式 O(N^3)
  mint det(){
    assert(n == m); // 正方行列のみ
    auto [tmp, swp] = gaussian_elimination();
    mint res(1);
    for(int i = 0; i < n; i++) res *= tmp[i][i];
    return swp & 1 ? -res : res;
  }
  // 行列式 O(N^3 * log mod)
  mint det_arbitrary_mod(){
    assert(n == m); // 正方行列のみ
    auto [tmp, swp] = gaussian_elimination_arbitrary_mod();
    mint res(1);
    for(int i = 0; i < n; i++) res *= tmp[i][i];
    return swp & 1 ? -res : res;
  }
  // (n, m) + (n, l) -> (n, m + l)　横に結合
  matrix_mod concat_horizontal(matrix_mod vr){
    assert(n == vr.n);
    matrix_mod res(*this);
    for(int i = 0; i < n; i++){
      res[i].insert(res[i].end(), vr[i].begin(), vr[i].end());
    }
    res.m += vr.m;
    return res;
  }
  // (n, m) + (l, m) -> (n + l, m) 縦に結合
  matrix_mod concat_vertical(matrix_mod vr){
    assert(m == vr.m);
    matrix_mod res(*this);
    for(int i = 0; i < vr.n; i++) res.val.push_back(vr[i]);
    res.n += vr.n;
    return res;
  }
  // (n, m) -> (n, k), (n, m - k)
  std::pair<matrix_mod, matrix_mod> split_horizontal(int k){
    assert(0 <= k && k <= m);
    matrix_mod a(n, k), b(n, m - k);
    for(int i = 0; i < n; i++){
      for(int j = 0; j < k; j++){
        a[i][j] = val[i][j];
      }
    }
    for(int i = 0; i < n; i++){
      for(int j = 0; j < m - k; j++){
        b[i][j] = val[i][j + k];
      }
    }
    return {a, b};
  }
  // (n, m) -> (k, m), (n - k, m)
  std::pair<matrix_mod, matrix_mod> split_vertical(int k){
    assert(0 <= k && k <= n);
    matrix_mod a(k, m), b(n - k, m);
    for(int i = 0; i < k; i++){
      for(int j = 0; j < m; j++){
        a[i][j] = val[i][j];
      }
    }
    for(int i = 0; i < n - k; i++){
      for(int j = 0; j < m; j++){
        b[i][j] = val[k + i][j];
      }
    }
    return {a, b};
  }
  matrix_mod inv(){
    assert(n == m);
    auto [tmp, swp] = concat_horizontal(eye(n)).gaussian_elimination();
    for(int i = 0; i < n; i++){
      mint x = tmp[i][i];
      if(!x.val()) return matrix_mod{};// 存在しない
      x = x.inv();
      for(int j = 0; j < 2 * n; j++) tmp[i][j] *= x;
    }
    for(int i = n - 1; i >= 0; i--){
      for(int j = i + 1; j < n; j++){
        if(!tmp[i][j].val()) continue;
        mint c = tmp[i][j];
        for(int k = j; k < 2 * n; k++){
          tmp[i][k] -= c * tmp[j][k];
        }
      }
    }
    return tmp.split_horizontal(n).second;
  }
  // https://ja.wikipedia.org/wiki/LU%E5%88%86%E8%A7%A3
  // キャッシュのためにuを転置して実装
  std::pair<matrix_mod, matrix_mod> lu_decomposition(){
    matrix_mod l = eye(n), u(n, n);
    for(int i = 0; i < n; i++){
      // u[i][i]を決定
      u[i][i] = val[i][i];
      for(int j = 0; j < i; j++) u[i][i] -= l[i][j] * u[i][j];
      if(u[i][i].val() == 0) return {matrix_mod{}, matrix_mod{}}; // 不可能
      mint iuii = u[i][i].inv();
      // l[0, n)[i]を決定
      for(int j = i + 1; j < n; j++){
        l[j][i] = val[j][i];
        for(int k = 0; k < i; k++) l[j][i] -= l[j][k] * u[i][k];
        l[j][i] *= iuii;
      }
      // u[i][0, n)を決定
      for(int j = i + 1; j < n; j++){
        u[j][i] = val[i][j];
        for(int k = 0; k < i; k++) u[j][i] -= l[i][k] * u[j][k];
      }
    }
    u = u.t();
    return {l, u};
  }
  // Ax = b
  // (n, m) * (m, 1) -> (n, 1)
  // を満たす連立方程式を解く, 解空間の次元、(rank*変数)の基底を返す
  // 解空間の基底は任意のt_iについてA * (v1t1 + v2t2 ...) = 0を満たす
  // つまり plus + res[0]t_0 + res[1]t_1 + res[2]t_2...は全て解を満たす
  // 解が存在しない場合解空間の次元として-1を返す
  std::tuple<int, matrix_mod, vec> system_of_linear_equations(const vec &vr){
    assert(vr.size() == n);
    matrix_mod tmp = concat_horizontal(matrix_mod(vr).t()).gaussian_elimination().first;
    //解空間の次元 = 変数の数 - 階数
    int r = tmp.rank();
    std::vector<int> fc(r, -1);//各行に初めて非零要素が現れる列
    for(int i = 0; i < r; i++){
      mint tmp_inv;
      bool f = false;
      for(int j = i; j < tmp.m; j++){
        if(tmp[i][j].val() == 0) continue;
        if(j == tmp.m - 1 && !f){
          return {-1, matrix_mod{}, vec{}}; // 解なし
        }
        if(!f){
          tmp_inv = tmp[i][j].inv();
          fc[i] = j;
          f = true;
        }
        tmp[i][j] = tmp[i][j] * tmp_inv;
      }
    }
    int d = tmp.m - 1 - r, v = tmp.m - 1;
    vec plus(v, 0);
    for(int i = r - 1; i >= 0; i--){
      int idx = fc[i];
      assert(idx != -1);
      plus[idx] = tmp[i][v];
      for(int j = idx + 1; j < v; j++){
        plus[idx] -= plus[j] * tmp[i][j];
      }
    }
    matrix_mod res(d, v, 0);
    std::vector<bool> not_fc(v, true);
    for(int i = 0; i < r; i++) not_fc[fc[i]] = false;
    for(int i = 0, j = 0; i < v; i++) if(not_fc[i]) res[j++][i] = 1;
    for(int i = r - 1; i >= 0; i--){ //各行に1つまだ確定していない変数が現れる
      int col = fc[i];
      assert(col != -1);
      assert(tmp[i][col].val() == 1);
      for(int k = 0; k < d; k++){ // 次元
        for(int j = col + 1; j < v; j++){ // すでに確定した要素
          res[k][col] -= res[k][j] * tmp[i][j];
        }
      }
    }
    return {d, res, plus};
  }
};

#line 4 "a.cpp"
using mint = dynamic_modint<0>;
using M = matrix_mod<mint>;

int main(){
  io_init();
  int n, b;
  std::cin >> n >> b;
  mint::set_mod(b);
  M m(3, 3);
  range(i, 0, 3){
    range(j, 0, 3){
      int t;
      std::cin >> t;
      m[i][j] = t;
    }
  }
  m = m.pow(n).gaussian_elimination_arbitrary_mod().first;
  std::cout << m.pow(n).det_arbitrary_mod() << '\n';
}