#include using namespace std; using ll=long long; using ld=long double; using ull=unsigned long long; using uint=unsigned int; using pcc=pair; using pii=pair; using pll=pair; using pdd=pair; using tuplis=pair; using tuplis2=pair; template using pq=priority_queue,greater>; const ll LINF=0x1fffffffffffffff; const int INF=0x3fffffff; const ll MOD=1000000007; const ll MODD=998244353; const ld DINF=numeric_limits::infinity(); const ld EPS=1e-9; const vectorfour{0,1,0,-1,0}; #define _overload4(_1,_2,_3,_4,name,...) name #define _overload3(_1,_2,_3,name,...) name #define _rep1(n) for(ll i=0;i=0;i--) #define _rrep2(i,n) for(ll i=n-1;i>=0;i--) #define _rrep3(i,a,b) for(ll i=b-1;i>=a;i--) #define _rrep4(i,a,b,c) for(ll i=a+(b-a-1)/c*c;i>=a;i-=c) #define rrep(...) _overload4(__VA_ARGS__,_rrep4,_rrep3,_rrep2,_rrep1)(__VA_ARGS__) #define each(i,a) for(auto &i:a) #define sum(...) accumulate(range(__VA_ARGS__),0LL) #define dsum(...) accumulate(range(__VA_ARGS__),double(0)) #define _range(i) (i).begin(),(i).end() #define _range2(i,k) (i).begin(),(i).begin()+k #define _range3(i,a,b) (i).begin()+a,(i).begin()+b #define range(...) _overload3(__VA_ARGS__,_range3,_range2,_range)(__VA_ARGS__) #define _rrange(i) (i).rbegin(),(i).rend() #define _rrange2(i,k) (i).rbegin(),(i).rbegin()+k #define _rrange3(i,a,b) (i).rbegin()+a,(i).rbegin()+b #define rrange(...) _overload3(__VA_ARGS__,_rrange3,_rrange2,_rrange)(__VA_ARGS__) #define elif else if #define unless(a) if(!(a)) #define mp make_pair #define mt make_tuple #define INT(...) int __VA_ARGS__;in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;in(__VA_ARGS__) #define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__) #define STR(...) string __VA_ARGS__;in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;in(__VA_ARGS__) #define vec(type,name,...) vector name(__VA_ARGS__) #define VEC(type,name,size) vector name(size);in(name) #define vv(type,name,h,...) vector>name(h,vector(__VA_ARGS__)) #define VV(type,name,h,...) vector>name(h,vector(__VA_ARGS__));in(name) #define vvv(type,name,h,w,...) vector>>name(h,vector>(w,vector(__VA_ARGS__))) inline constexpr ll gcd(ll a,ll b){if(!a||!b)return 0;while(b){ll c=b;b=a%b;a=c;}return a;} inline constexpr ll lcm(ll a,ll b){if(!a||!b)return 0;return a*b/gcd(a,b);} template inline constexpr T min(vector &v){return *min_element(range(v));} inline char min(string &v){return *min_element(range(v));} template inline constexpr T max(vector &v){return *max_element(range(v));} inline char max(string &v){return *max_element(range(v));} inline constexpr ll intpow(ll a,ll b){ll ans=1;for(ll i=1;b;i*=2){if(b&i){b^=i;ans*=a;}a*=a;}return ans;} inline constexpr ll modpow(ll a,ll b,ll mod = MOD){ll ans=1;for(ll i=1;b;i*=2){if(b&i){b^=i;ans*=a;ans%=mod;}a*=a;a%=mod;}return ans;} template inline constexpr bool chmin(T &mn,const T &cnt){if(mn>cnt){mn=cnt;return 1;}else return 0;} template inline constexpr bool chmax(T &mx,const T &cnt){if(mx> a; } inline void scan(float &a){ scanf("%f", &a); } inline void scan(double &a){ scanf("%lf", &a); } inline void scan(long double &a){ scanf("%Lf", &a); } inline void scan(vector &vec){ for(unsigned i = 0; i < vec.size(); i++) { int a; scan(a); vec[i] = a; } } inline void scan(string &a){ cin >> a; } template inline void scan(vector &vec); template inline void scan(array &vec); template inline void scan(pair &p); template inline void scan(T (&vec)[size]); template inline void scan(vector &vec){ for(auto &i : vec) scan(i); } template inline void scan(array &vec){ for(auto &i : vec) scan(i); } template inline void scan(pair &p){ scan(p.first); scan(p.second); } template inline void scan(T (&vec)[size]){ for(auto &i : vec) scan(i); } template inline void scan(T &a){ cin>>a; } inline void in(){} template inline void in(Head &head, Tail&... tail){ scan(head); in(tail...); } inline void print(){ putchar('\n'); } inline void print(const bool &a){ printf("%d", a); } inline void print(const int &a){ printf("%d", a); } inline void print(const unsigned &a){ printf("%u", a); } inline void print(const long &a){ printf("%ld", a); } inline void print(const long long &a){ printf("%lld", a); } inline void print(const unsigned long long &a){ printf("%llu", a); } inline void print(const char &a){ printf("%c", a); } inline void print(const char a[]){ printf("%s", a); } inline void print(const float &a){ printf("%.10f", a); } inline void print(const double &a){ printf("%.10f", a); } inline void print(const long double &a){ printf("%.10Lf", a); } template void print(const vector &vec); template void print(const array &vec); template void print(const pair &p); template inline void print(const T (&vec)[size]); template void print(const vector &vec){ print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } } template void print(const array &vec){ print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } } template void print(const pair &p){ print(p.first); putchar(' '); print(p.second); } template inline void print(const T (&vec)[size]){ print(vec[0]); for(auto i = vec; ++i != end(vec); ){ putchar(' '); print(*i); } } template inline void print(const T &a){ cout << a; } inline int out(){ putchar('\n'); return 0; } template inline int out(const T &t){ print(t); putchar('\n'); return 0; } template inline int out(const Head &head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; } template inline void err(T t){cerr<= mod) a -= mod; return Modint{a}; } inline constexpr Modint operator+=(int x){ _num += x; _num %= mod; if(_num < 0) _num += mod; return *this; } inline constexpr Modint operator+=(ll x){ _num += x; _num %= mod; if(_num < 0) _num += mod; return *this; } inline constexpr Modint operator+=(Modint x){ _num += x._num; if(_num >= mod) _num -= mod; return *this; } inline constexpr Modint operator++(){ if(_num == mod - 1) _num = 0; else _num++; return *this; } inline constexpr Modint operator- (int x){ return Modint(_num - x); } inline constexpr Modint operator- (ll x){ return Modint(_num - x); } inline constexpr Modint operator- (Modint x){ ll a = _num - x._num; if(a < 0) a += mod; return Modint{a}; } inline constexpr Modint operator-=(int x){ _num -= x; _num %= mod; if(_num < 0) _num += mod; return *this; } inline constexpr Modint operator-=(ll x){ _num -= x; _num %= mod; if(_num < 0) _num += mod; return *this; } inline constexpr Modint operator-=(Modint x){ _num -= x._num; if(_num < 0) _num += mod; return *this; } inline constexpr Modint operator--(){ if(_num == 0) _num = mod - 1; else _num--; return *this; } inline constexpr Modint operator* (int x){ return Modint(_num * (x % mod)); } inline constexpr Modint operator* (ll x){ return Modint(_num * (x % mod)); } inline constexpr Modint operator* (Modint x){ return Modint{_num * x._num % mod}; } inline constexpr Modint operator*=(int x){ _num *= Modint(x); _num %= mod; return *this; } inline constexpr Modint operator*=(ll x){ _num *= Modint(x); _num %= mod; return *this; } inline constexpr Modint operator*=(Modint x){ _num *= x._num; _num %= mod; return *this; } inline constexpr Modint operator/ (int x){ return Modint(_num * invmod(Modint(x), mod)); } inline constexpr Modint operator/ (ll x){ return Modint(_num * invmod(Modint(x), mod)); } inline constexpr Modint operator/ (Modint x){ return Modint{_num * invmod(x._num, mod) % mod}; } inline constexpr Modint operator/=(int x){ _num *= invmod(Modint(x), mod); _num %= mod; return *this; } inline constexpr Modint operator/=(ll x){ _num *= invmod(Modint(x), mod); _num %= mod; return *this; } inline constexpr Modint operator/=(Modint x){ _num *= invmod(x._num, mod); _num %= mod; return *this; } inline constexpr Modint pow(ll x){ ll i = 1; Modint ans = 1, cnt = *this; while(i <= x){ if(x & i){ ans *= cnt; x ^= i; } cnt *= cnt; i *= 2; } return ans; } inline constexpr operator ll() const { return _num; } }; vector fac(1, 1), inv(1, 1); inline void reserve(ll a){ if(fac.size() >= a) return; if(a < fac.size() * 2) a = fac.size() * 2; if(a >= mod) a = mod; while(fac.size() < a) fac.push_back(fac.back() * ll(fac.size())); inv.resize(fac.size()); inv.back() = Modint(1) / fac.back(); for(ll i = inv.size() - 1; !inv[i - 1]; i--) inv[i - 1] = inv[i] * i; } inline Modint fact(ll n){ if(n < 0) return 0; reserve(n + 1); return fac[n]; } inline Modint perm(ll n, ll r){ if(r < 0 || n < r) return 0; reserve(n + 1); return fac[n] * inv[n - r]; } inline Modint comb(ll n, ll r){ if(r < 0 || n < r) return 0; reserve(n + 1); return fac[n] * inv[r] * inv[n - r]; } inline Modint Mcomb(ll n, ll r){ return comb(n + r - 1, n - 1); } // r個をn部屋に分ける typedef Modint number; typedef vector Array; typedef vector matrix; // O( n ) matrix identity(int n) { matrix A(n, Array(n)); for (int i = 0; i < n; ++i) A[i][i] = 1; return A; } // O( n ) number inner_product(const Array &a, const Array &b) { number ans = 0; for (int i = 0; i < a.size(); ++i) ans += a[i] * b[i]; return ans; } // O( n^2 ) Array mul(const matrix &A, const Array &x) { Array y(A.size()); for (int i = 0; i < A.size(); ++i) for (int j = 0; j < A[0].size(); ++j) y[i] = A[i][j] * x[j]; return y; } // O( n^3 ) matrix mul(const matrix &A, const matrix &B) { matrix C(A.size(), Array(B[0].size())); for (int i = 0; i < C.size(); ++i) for (int j = 0; j < C[i].size(); ++j) for (int k = 0; k < A[i].size(); ++k) C[i][j] += A[i][k] * B[k][j]; return C; } // O( n^3 log e ) matrix pow(const matrix &A, int e) { return e == 0 ? identity(A.size()) : e % 2 == 0 ? pow(mul(A, A), e/2) : mul(A, pow(A, e-1)); } int main(){ LL(n,k); vv(Modint,a,k*k*k,k*k*k); vv(Modint,b,k*k*k,k*k*k); a[0][0]=1; auto at=[k](ll a,ll b,ll c){return a%k*k*k+b%k*k+c%k;}; rep(i1,k)rep(i2,k)rep(i3,k){ ++b[at(i1,i2,i3)][at(i1,i2,i3+1)]; ++b[at(i1,i2,i3)][at(i1,i2+i3,i3)]; ++b[at(i1,i2,i3)][at(i1+i2,i2,i3)]; } b=pow(b,n); a=mul(a,b); rep(i,1,k*k)a[0][0]+=a[0][i]; out(a[0][0]); }