#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< struct Matrix{ ll h,w; vector> data; inline constexpr Matrix(ll h, ll w, bool identity = false) : h(h), w(w), data(h, vector(w)) { if(identity){ reserve(w, h); rep(h) data[i][i] = 1; } } inline constexpr Matrix(vector> data) : h(data.size()), w(data[0].size()), data(data) {} inline constexpr Matrix(Matrix &x) : h(x.h), w(x.w), data(x.data) {} inline constexpr Matrix reserve(ll _h, ll _w){ if(_h > h){ h = _h; data.resize(h); } if(_w > w){ w = _w; for(auto &i : data) i.resize(w); } return *this;} inline constexpr Matrix resize(ll _h, ll _w){ h = _h; w = _w; data.resize(h); for(auto &i : data) i.resize(w); return *this; } inline constexpr vector& operator[](ll x){ return data[x]; } inline constexpr const vector& operator[](ll x) const { return data[x]; } inline constexpr T& operator[](pll x){ return data[x.first][x.second]; } inline constexpr const T& operator[](pll x) const { return data[x.first][x.second]; } inline constexpr T& operator()(ll x, ll y){ return data[x][y]; } inline constexpr const T& operator()(ll x, ll y) const { return data[x][y]; } inline constexpr Matrix operator= (const Matrix &&x){ h = x.h; w = x.w; data = move(x.data); return *this; } inline constexpr Matrix operator= (const Matrix &x){ h = x.h; w = x.w; data = x.data; } inline constexpr Matrix operator+ (T x){ auto ans = *this; for(auto &i : ans.data) for(auto &j : i) j += x; return ans; } inline constexpr Matrix operator+ (const Matrix &x){ auto ans = *this; ans.reserve(x.h, x.w); rep(x.h) rep(j, x.w) ans[i][j] += x[i][j]; return ans; } inline constexpr Matrix operator+=(T x){ for(auto &i : data) for(auto &j : i) j += x; return *this; } inline constexpr Matrix operator+=(const Matrix &x){ reserve(x.h, x.w); rep(x.h) rep(j, x.w) data[i][j] += x[i][j]; return *this; } inline constexpr Matrix operator- (T x){ auto ans = *this; for(auto &i : ans.data) for(auto &j : i) j -= x; return ans; } inline constexpr Matrix operator- (const Matrix &x){ auto ans = *this; ans.reserve(x.h, x.w); rep(x.h) rep(j, x.w) ans[i][j] -= x[i][j]; return ans; } inline constexpr Matrix operator-=(T x){ for(auto &i : data) for(auto &j : i) j -= x; return *this; } inline constexpr Matrix operator-=(const Matrix &x){ reserve(x.h, x.w); rep(x.h) rep(j, x.w) data[i][j] -= x[i][j]; return *this; } inline constexpr Matrix operator* (T x){ auto ans = *this; for(auto &i : ans.data) for(auto &j : i) j *= x; return ans; } inline constexpr Matrix operator* (const Matrix &x){ Matrix ans(h, x.w); rep(ans.h) rep(j, ans.w) rep(k, min(w, x.h)) ans[i][j] += data[i][k] * x[k][j]; return ans; } inline constexpr Matrix operator*=(T x){ for(auto &i : data) for(auto &j : i) j *= x; return *this; } inline constexpr Matrix operator*=(const Matrix &x){ *this = *this * x; return *this; } inline constexpr Matrix pow(ll x){ reserve(w, h); ll i = 1; Matrix ans(h, w, true), cnt = *this; while(x){ if(x & i){ ans *= cnt; x ^= i; } cnt *= cnt; i *= 2; } return ans; } }; constexpr ll mod = MODD; inline constexpr ll extgcd(ll a, ll b, ll &x, ll &y){ ll g = a; x = 1; y = 0; if(b){ g = extgcd(b, a % b, y, x); y -= a / b * x; } return g; } inline constexpr ll invmod(ll a, ll m = mod){ ll x = 0, y = 0; extgcd(a, m, x, y); return (x + m) % m; } struct Modint{ ll _num; constexpr Modint() : _num() { _num = 0; } constexpr Modint(ll x) : _num() { _num = x % mod; if(_num < 0) _num += mod; } inline constexpr Modint operator= (int x){ _num = x % mod; if(_num<0) _num += mod; return *this; } inline constexpr Modint operator= (ll x){ _num = x % mod; if(_num<0) _num += mod; return *this; } inline constexpr Modint operator= (Modint x){ _num = x._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 >= 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 int main(){ LL(n,k); ll m=k*k*k; Matrixa(1,m),b(m,m); a(0,0)=1; auto at=[&k](ll a,ll b,ll c){return (a%k*k+b%k)*k+c%k;}; rep(x,k)rep(y,k)rep(z,k){ b[at(x,y,z)][at(x,y,z+1)]+=1; b[at(x,y,z)][at(x,y+z,z)]+=1; b[at(x,y,z)][at(x+y,y,z)]+=1; } a=a*b.pow(n); Modint ans=0; rep(k*k)ans+=a[0][i]; out(ans); }