#define ATCODER #define _USE_MATH_DEFINES #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ld = long double; using pll = pair; using pdd = pair; //template using pq = priority_queue, greater>; #define FOR(i, a, b) for(ll i=(a); i<(b);i++) #define REP(i, n) for(ll i=0; i<(n);i++) #define ROF(i, a, b) for(ll i=(b-1); i>=(a);i--) #define PER(i, n) for(ll i=n-1; i>=0;i--) #define REPREP(i,j,a,b) for(ll i=0;i > #define VV2(type,n,m,val) vector< vector > val;val.resize(n);for(ll i;i #define VEC(type,n,val) vector val;val.resize(n) #define VL vector #define VVL vector< vector > #define VP vector< pair > #define SZ size() #define all(i) begin(i),end(i) #define SORT(i) sort(all(i)) #define BITI(i) (1<>i) & 1) != 0) #define ALLBIT(n) (ll(1)<v?v:n #define MP(a,b) make_pair(a,b) #define DET2(x1,y1,x2,y2) x1*y2-x2*y1 #define DET3(x1,y1,z1,x2,y2,z2,x3,y3,z3) x1*y2*z3+x2*y3*z1+x3*y1*z2-z1*y2*x3-z2*y3*x1-z3*y1*x2 #define INC(a) for(auto& v:a)v++; #define DEC(a) for(auto& v:a)v--; #define SQU(x) (x)*(x) #define L0 ll(0) #ifdef ATCODER #include using namespace atcoder; using mint = modint1000000007; using mint2 = modint998244353; #endif template vector read(size_t n) { vector ts(n); for (size_t i = 0; i < n; i++) cin >> ts[i]; return ts; } template void read_tuple_impl(TV&) {} template void read_tuple_impl(TV& ts) { get(ts).emplace_back(*(istream_iterator(cin))); read_tuple_impl(ts); } template decltype(auto) read_tuple(size_t n) { tuple...> ts; for (size_t i = 0; i < n; i++) read_tuple_impl(ts); return ts; } using val = ll; using func = ll; val op(val a, val b) { return min(a, b); } val e() { return 1e18; } val mp(func f, val a) { if (f == -1) return a; return f; } func comp(func f, func g) { if (f == -1) return g; return f; } func id() { return -1; } ll di[4] = { 1,0,-1,0 }; ll dj[4] = { 0,1,0,-1 }; //ll di[4] = { -1,-1,1,1 }; //ll dj[4] = { -1,1,-1,1 }; ll di8[8] = { 0,-1,-1,-1,0,1,1,1 }; ll dj8[8] = { -1,-1,0,1,1,1,0,-1 }; template void Factorical(ll siz, vector& out) { out.resize(siz + 1); out[0] = T(1); for (ll i = 0; i < siz; i++) { out[i + 1] = out[i] * (i + 1); } } template T Combi(ll a, ll b, vector& fact) { if (a < 0 || b < 0 || a < b) return 0; return fact[a] / (fact[b] * fact[a - b]); } void solve() { ll n, m; cin >> n >> m; vector fact; Factorical(m + 1, fact); vector ans(3); REP(w0, m+1) { REP(w1, m + 1) { ll w2 = m - w0 - w1; if (w2 < 0) break; vector g(3); ll gw = (w1 * 2 + w2) % 3; g[gw] = fact[m] / (fact[w0] * fact[w1] * fact[w2]); vector f(3); f[0] = w0; f[1] = w1; f[2] = w2; ll bn = n; auto mf = f; while (bn) { if (bn % 2) { g = convolution(g, mf); while (g.size() > 3) { g[(g.size() - 1) % 3] += g.back(); g.pop_back(); } } mf = convolution(mf, mf); while (mf.size() > 3) { mf[(mf.size() - 1) % 3] += mf.back(); mf.pop_back(); } bn /= 2; } REP(i, 3) { ans[i] += g[i]; } } } mint2 div = mint2(1) / 3; div = div.pow(m); cout << ((ans[0] - ans[1]) * div).val(); return; } int main() { ll t = 1; //cin >> t; while (t--) { solve(); } return 0; }