#line 1 "main.cpp" #line 1 "main.cpp" #include using namespace std; #ifdef LOCAL #include #define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else #define debug(...) (static_cast(0)) #endif //#pragma GCC target("avx,avx2") //#pragma GCC optimize("O3") //#pragma GCC optimize("unroll-loops") using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair; using pii = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vul = vector; using vpii = vector; using vvpii = vector; using vpll = vector; using vs = vector; template using pq = priority_queue, greater>; #define overload4(_1, _2, _3, _4, name, ...) name #define overload3(a,b,c,name,...) name #define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER) #define rep2(i, n) for (ll i = 0; i < (n); ++i) #define rep3(i, a, b) for (ll i = (a); i < (b); ++i) #define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c)) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep1(n) for(ll i = (n) - 1;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) - (((b)-(a)-1) % (c) && (((b)-(a)-1) ^ c) < 0)) * (c);i >= (a);i -= c) #define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__) #define all1(i) begin(i) , end(i) #define all2(i,a) begin(i) , begin(i) + a #define all3(i,a,b) begin(i) + a , begin(i) + b #define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__) #define sum(...) accumulate(all(__VA_ARGS__),0LL) template bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; } template bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; } template auto min(const T& a){return *min_element(all(a));} template auto max(const T& a){return *max_element(all(a));} template void in(Ts&... t); #define INT(...) int __VA_ARGS__; in(__VA_ARGS__) #define LL(...) ll __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 LD(...) ld __VA_ARGS__; in(__VA_ARGS__) #define VEC(type, name, size) vector name(size); in(name) #define VV(type, name, h, w) vector> name(h, vector(w)); in(name) ll intpow(ll a, ll b){ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;} ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;if(a < 0) a += p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; } bool is_clamp(ll val,ll low,ll high) {return low <= val && val < high;} void Yes() {cout << "Yes\n";return;} void No() {cout << "No\n";return;} void YES() {cout << "YES\n";return;} void NO() {cout << "NO\n";return;} template U floor(U a, T b) {return a / b - (a % b && (a ^ b) < 0);} template U ceil(U x, T y) {return floor(x + y - 1, y);} template T bmod(U x, T y) {return x - y * floor(x, y);} template pair divmod(U x, T y) {U q = floor(x, y);return {q, x - q * y};} namespace IO{ #define VOID(a) decltype(void(a)) struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(15);}} setting; template struct P : P{}; template<> struct P<0>{}; template void i(T& t){ i(t, P<3>{}); } void i(vector::reference t, P<3>){ int a; i(a); t = a; } template auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; } template auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); } template void ituple(T& t, index_sequence){in(get(t)...);} template auto i(T& t, P<0>) -> VOID(tuple_size{}){ituple(t, make_index_sequence::value>{});} #undef VOID } #define unpack(a) (void)initializer_list{(a, 0)...} template void in(Ts&... t){ unpack(IO :: i(t)); } #undef unpack constexpr long double PI = 3.141592653589793238462643383279L; template struct REC { F f; REC(F &&f_) : f(forward(f_)) {} template auto operator()(Args &&...args) const { return f(*this, forward(args)...); }}; constexpr int mod = 998244353; //constexpr int mod = 1000000007; #line 2 "library/graph/graph-template.hpp" template struct Edge { int from, to; T cost; Edge() = default; Edge(int _to, T _cost) : from(-1), to(_to), cost(_cost) {} Edge(int _from, int _to, T _cost) : from(_from), to(_to), cost(_cost) {} bool operator < (const Edge &a) const { return cost < a.cost; } bool operator > (const Edge &a) const { return cost > a.cost; } Edge &operator = (const int &x) { to = x; return *this; } operator int() const { return to; } friend ostream operator<<(ostream &os, Edge &edge) { return os << edge.to; } }; template using Edges = vector>; template using Wgraph = vector>; using Ugraph = vector>; Ugraph uinput(int N, int M = -1, bool is_directed = false, int origin = 1) { Ugraph g(N); if (M == -1) M = N - 1; while(M--) { int a,b; cin >> a >> b; a -= origin, b -= origin; g[a].push_back(b); if(!is_directed) g[b].push_back(a); } return g; } template Wgraph winput(int N, int M = -1, bool is_directed = false,int origin = 1) { Wgraph g(N); if (M == -1) M = N - 1; while(M--) { int a,b; T c; cin >> a >> b >> c; a -= origin, b -= origin; g[a].emplace_back(b,c); if(!is_directed) g[b].emplace_back(a,c); } return g; } #line 3 "library/tree/HLD.hpp" template >> struct HLD { private: void dfs_sz(int cur) { size[cur] = 1; for (auto &dst:g[cur]) { if (dst == par[cur]) { if (g[cur].size() >= 2 && int(dst) == int(g[cur][0])) swap(g[cur][0],g[cur][1]); else continue; } depth[dst] = depth[cur] + 1; par[dst] = cur; dfs_sz(dst); size[cur] += size[dst]; if (size[dst] > size[g[cur][0]]) { swap(dst,g[cur][0]); } } } void dfs_hld(int cur) { ord[id] = cur; down[cur] = id++; for (auto dst:g[cur]) { if (dst == par[cur]) continue; nxt[dst] = (int(dst) == int(g[cur][0]) ? nxt[cur] : int(dst)); dfs_hld(dst); } up[cur] = id; } public: // [u, v) vector> ascend(int u,int v) const { vector> res; while (nxt[u] != nxt[v]) { res.emplace_back(down[u],down[nxt[u]]); u = par[nxt[u]]; } if (u != v) res.emplace_back(down[u],down[v] + 1); return res; } // (u, v] vector> descend(int u,int v) const { if (u == v) return {}; if (nxt[u] == nxt[v]) return {{down[u] + 1,down[v]}}; auto res = descend(u,par[nxt[v]]); res.emplace_back(down[nxt[v]],down[v]); return res; } G g; int id; vector size,depth,down,up,ord,nxt,par; HLD() = default; HLD(G& _g,int root = 0) : g(_g), id(0), size(g.size(),0), depth(g.size(),0), down(g.size(),-1), up(g.size(),-1), ord(g.size(),0), nxt(g.size(),root), par(g.size(),-1) { dfs_sz(root); dfs_hld(root); } void build(int root) { dfs_sz(root); dfs_hld(root); } pair idx(int i) const {return make_pair(down[i], up[i]);} template void path_query(int u,int v,bool vertex,const F& f) { int l = lca(u,v); for (auto &&[a,b] : ascend(u,l)) { int s = a + 1, t = b; s > t ? f(t,s) : f(s,t); } if (vertex) f(down[l], down[l] + 1); for (auto &&[a,b] : descend(l,v)) { int s = a,t = b + 1; s > t ? f(t,s) : f(s,t); } } template void path_noncommutative_query(int u,int v,bool vertex,const F& f) { int l = lca(u,v); for(auto &&[a,b]:ascend(u,l)) f(a + 1,b); if(vertex) f(down[l],down[l] + 1); for(auto &&[a,b]:descend(l,v)) f(a,b + 1); } template void subtree_query(int u,bool vertex,const F& f) { f(down[u] + int(!vertex), up[u]); } int lca(int a,int b) const { while (nxt[a] != nxt[b]) { if (down[a] < down[b]) swap(a, b); a = par[nxt[a]]; } return depth[a] < depth[b] ? a : b; } int dist(int a,int b) const {return depth[a] + depth[b] - depth[lca(a, b)] * 2;} int kth_ancestor(int u,int k) const { if(k < 0) return -1; while(u >= 0) { int h = nxt[u]; if(down[u] - k >= down[h]) return ord[down[u] - k]; k -= down[u] - down[h] + 1; u = par[h]; } return -1; } int next(int s,int t) const { assert(s != t && 0 <= s && s < g.size() && 0 <= t && t < g.size()); if(depth[s] >= depth[t]) return par[s]; int u = kth_ancestor(t,depth[t] - depth[s] - 1); return par[u] == s ? u : par[s]; } // s - t 間のパス上の頂点のうち s から距離 i の頂点 // (dist(s, t) < i のとき -1) int jump(int s,int t,int d) const { int lc = lca(s,t); int d1 = depth[s] - depth[lc]; if(d <= d1) return kth_ancestor(s,d); int d2 = d1 + depth[t] - depth[lc]; if(d <= d2) return kth_ancestor(t,d2 - d); return -1; } vector path(int s,int t) const { vector pre,suf; while (depth[s] > depth[t]) { pre.emplace_back(s); s = par[s]; } while (depth[s] < depth[t]) { suf.emplace_back(t); t = par[t]; } while(s != t) { pre.emplace_back(s); suf.emplace_back(t); s = par[s]; t = par[t]; } pre.push_back(s); reverse(begin(suf), end(suf)); copy(begin(suf), end(suf), back_inserter(pre)); return pre; } }; #line 2 "library/modint/Modint.hpp" template struct Modint{ int x; Modint():x(0) {} Modint(long long y): x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} Modint &operator += (const Modint &p) { if((x += p.x) >= mod) x -= mod; return *this;} Modint &operator -= (const Modint &p) { if ((x += mod - p.x) >= mod) x -= mod; return *this;} Modint &operator *= (const Modint &p) { x = (int)(1LL * x * p.x % mod); return *this;} Modint &operator /= (const Modint &p) { *this *= p.inverse(); return *this;} Modint operator -() const{return Modint(-x);} Modint operator +(const Modint &p) const {return Modint(*this) += p;} Modint operator -(const Modint &p) const {return Modint(*this) -= p;} Modint operator *(const Modint &p) const {return Modint(*this) *= p;} Modint operator /(const Modint &p) const {return Modint(*this) /= p;} Modint &operator ++() {if(x == mod - 1) x = 0; else x++; return *this;} Modint &operator --() {if(x == 0) x = mod - 1; else x--; return *this;} bool operator == (const Modint &p) const {return x == p.x;} bool operator != (const Modint &p) const {return x != p.x;} Modint inverse() const { int a = x, b = mod, u = 1, v = 0, t; while (b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return Modint(u);} Modint pow(long long n) const { Modint ret(1), mul(x); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret;} friend ostream &operator<<(ostream &os, const Modint &p) { return os << p.x; } friend istream &operator>>(istream &is, Modint &a) { long long t; is >> t; a = Modint(t); return (is); } int get() const { return x; } static constexpr int get_mod() {return mod;} }; #line 101 "main.cpp" using mint = Modint; using vm = vector; using vvm = vector; using vvvm = vector; #line 2 "library/ntt/ntt.hpp" template struct NTT{ static constexpr uint32_t get_pr() { uint32_t _mod = mint::get_mod(); using u64 = uint64_t; u64 ds[32] = {}; int idx = 0; u64 m = _mod - 1; for(u64 i = 2;i * i <= m; ++i) { if(m % i == 0) { ds[idx++] = i; while(m % i == 0) m /= i; } } if (m != 1) ds[idx++] = m; uint32_t _pr = 2; while(1) { int flg = 1; for(int i = 0;i < idx; ++i) { u64 a = _pr, b = (_mod - 1) / ds[i],r = 1; while(b) { if(b & 1) r = r * a % _mod; a = a * a % _mod; b >>= 1; } if(r == 1) { flg = 0; break; } } if (flg == 1) break; ++_pr; } return _pr; }; static constexpr uint32_t mod = mint::get_mod(); static constexpr uint32_t pr = get_pr(); static constexpr int level = __builtin_ctzll(mod - 1); mint dw[level], dy[level]; void setwy(int k) { mint w[level],y[level]; w[k - 1] = mint(pr).pow((mod - 1) / (1 << k)); y[k - 1] = w[k - 1].inverse(); for(int i = k - 2;i > 0; --i) w[i] = w[i+1] * w[i+1],y[i] = y[i+1] * y[i+1]; dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2]; for(int i = 3;i < k;++i) { dw[i] = dw[i-1] * y[i-2] * w[i]; dy[i] = dy[i-1] * w[i-2] * y[i]; } } NTT() {setwy(level);} void fft4(vector &a,int k) { if((int)a.size() <= 1) return; if(k == 1) { mint a1 = a[1]; a[1] = a[0] - a[1]; a[0] = a[0] + a1; return; } if (k & 1) { int v = 1 << (k - 1); for(int j = 0;j < v; ++j) { mint ajv = a[j + v]; a[j + v] = a[j] - ajv; a[j] += ajv; } } int u = 1 << (2 + (k & 1)); int v = 1 << (k - 2 - (k & 1)); mint one = mint(1); mint imag = dw[1]; while(v) { { int j0 = 0,j1 = v; int j2 = j1 + v; int j3 = j2 + v; for(;j0 < v; ++j0,++j1,++j2,++j3) { mint t0 = a[j0], t1 = a[j1],t2 = a[j2],t3 = a[j3]; mint t0p2 = t0 + t2,t1p3 = t1 + t3; mint t0m2 = t0 - t2,t1m3 = (t1 - t3) * imag; a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3; a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3; } } mint ww = one,xx = one * dw[2],wx = one; for(int jh = 4;jh < u;) { ww = xx * xx,wx = ww * xx; int j0 = jh * v; int je = j0 + v; int j2 = je + v; for(;j0 < je;++j0,++j2) { mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,t3 = a[j2 + v] * wx; mint t0p2 = t0 + t2,t1p3 = t1 + t3; mint t0m2 = t0 - t2,t1m3 = (t1 - t3) * imag; a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3; a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3; } xx *= dw[__builtin_ctzll((jh += 4))]; } u <<= 2; v >>= 2; } } void ifft4(vector &a,int k) { if((int)a.size() <= 1) return; if(k == 1) { mint a1 = a[1]; a[1] = a[0] - a[1]; a[0] = a[0] + a1; return; } int u = 1 << (k - 2); int v = 1; mint one = mint(1); mint imag = dy[1]; while(u) { { int j0 = 0,j1 = v; int j2 = j1 + v; int j3 = j2 + v; for(;j0 < v;++j0,++j1,++j2,++j3) { mint t0 = a[j0],t1 = a[j1],t2 = a[j2],t3 = a[j3]; mint t0p1 = t0 + t1, t2p3 = t2 + t3; mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag; a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3; a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3; } } mint ww = one,xx = one * dy[2],yy = one; u <<= 2; for(int jh = 4;jh < u;) { ww = xx * xx,yy = xx * imag; int j0 = jh * v; int je = j0 + v; int j2 = je + v; for(;j0 < je;++j0,++j2) { mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v]; mint t0p1 = t0 + t1, t2p3 = t2 + t3; mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy; a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww; a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww; } xx *= dy[__builtin_ctzll(jh += 4)]; } u >>= 4; v <<= 2; } if(k & 1) { u = 1 << (k - 1); for(int j = 0;j < u;++j) { mint ajv = a[j] - a[j+u]; a[j] += a[j+u]; a[j+u] = ajv; } } } void ntt(vector &a) { if((int)a.size() <= 1) return; fft4(a,__builtin_ctz(a.size())); } void intt(vector &a) { if((int)a.size() <= 1) return; ifft4(a,__builtin_ctz(a.size())); mint iv = mint(a.size()).inverse(); for(auto &x:a) x *= iv; } vector multiply(const vector &a,const vector &b) { int l = a.size() + b.size() - 1; if(min(a.size(),b.size()) <= 40) { vector s(l); for(int i = 0;i < (int)a.size();++i) for(int j = 0;j < (int)b.size();++j) s[i+j] += a[i] * b[j]; return s; } int k = 2, M = 4; while(M < l) M <<= 1, ++k; //setwy(k); vector s(M), t(M); for(int i = 0;i < (int)a.size();++i) s[i] = a[i]; for(int i = 0;i < (int)b.size();++i) t[i] = b[i]; fft4(s,k); fft4(t,k); for(int i = 0;i < M;++i) s[i] *= t[i]; ifft4(s,k); s.resize(l); mint invm = mint(M).inverse(); for(int i = 0;i < l;++i) s[i] *= invm; return s; } void ntt_doubling(vector &a) { int M = (int)a.size(); auto b = a; intt(b); mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1)); for(int i = 0;i < M;++i) b[i] *= r,r *= zeta; ntt(b); copy(begin(b),end(b),back_inserter(a)); } }; #line 106 "main.cpp" vector fact, fact_inv; void make_fact(int n){ fact.resize(n+1), fact_inv.resize(n+1); fact[0] = mint(1); rep(i,1,n+1) fact[i] = fact[i-1] * mint(i); fact_inv[n] = fact[n].inverse(); rrep(i,0,n) fact_inv[i] = fact_inv[i+1] * mint(i+1); } mint ncr(int n, int r){ if(n < 0 || r < 0 || n < r) return mint(0); return fact[n] * fact_inv[r] * fact_inv[n-r];} mint npr(int n, int r){ if(n < 0 || r < 0 || n < r) return mint(0); return fact[n] * fact_inv[n-r]; } void solve() { INT(n,s,t); s--,t--; vvi g(n); vi U(n-1),V(n-1); make_fact(n); rep(i,n-1) { INT(u,v); u--,v--; U[i] = u,V[i] = v; g[u].emplace_back(v); g[v].emplace_back(u); } HLD hld(g); int nears,neart; int D = 1e9; rep(i,2) { int x; if(i == 0) x = U[s]; else x = V[s]; rep(j,2) { int y; if(j == 0) y = U[t]; else y = V[t]; if(chmin(D,hld.dist(x,y))) { nears = x; neart = y; } } } auto path = hld.path(nears,neart); vvm C; rep(i,path.size()) { int c = g[path[i]].size() - 2; vm ctmp(c + 1); rep(j,c + 1) { ctmp[j] = npr(c,j); } C.emplace_back(ctmp); } debug(C,path); pq q; rep(i,C.size()) q.emplace(C[i].size(),i); NTT ntt; while(q.size() > 1) { auto [_,id1] = q.top(); q.pop(); auto [__,id2] = q.top(); q.pop(); C[id1] = ntt.multiply(C[id1],C[id2]); q.emplace(C[id1].size(),id1); C[id2].clear(); C[id2].shrink_to_fit(); } debug(C); vm ans(n); int id = q.top().second; int si = path.size(); debug(C[id]); rep(i,C[id].size()) { ans[si + i] = C[id][i]; } rep(i,n) cout << ans[i] << " \n"[i == n - 1]; } int main() { //INT(TT); int TT = 1; rep(i,TT) solve(); }