#include #include using namespace std; using mint = atcoder::modint998244353; template struct csr { using itr = typename std::vector::iterator; struct Node { itr st, en; itr begin() { return st; } itr end() { return en; } int size() { return en - st; } T operator[](int p){ return st[p]; } }; const int N; std::vector start; std::vector E; std::vector> edge; csr(int n) : N(n), start(n + 1) {} void add_edge(int u, T v){ assert(0 <= u && u < N); start[u + 1]++; edge.emplace_back(u, v); } void build(){ E.resize(edge.size()); for(int i = 0; i < N; i++) start[i + 1] += start[i]; auto cnt = start; for(auto [u, v] : edge) E[cnt[u]++] = v; } Node operator[](int p) { return Node{E.begin() + start[p], E.begin() + start[p + 1]}; } }; int main() { ios::sync_with_stdio(false); cin.tie(0); int n, s, t, u, v, st, gl; cin >> n >> s >> t; s--, t--; csr> g(n); for(int i = 0; i + 1 < n; i++){ cin >> u >> v; u--, v--; g.add_edge(u, {v, i}); g.add_edge(v, {u, i}); if(i == s) st = u, gl = v; } g.build(); vector fact(n + 1), inv(n + 1); fact[0] = 1; for(int i = 1; i <= n; i++) fact[i] = mint::raw(i) * fact[i - 1]; inv[n] = fact[n].inv(); for(int i = n; i >= 1; i--) inv[i - 1] = mint::raw(i) * inv[i]; vector> tb; auto dfs = [&](auto dfs, int v, int p) -> bool { for(auto [u, ei] : g[v]){ if(u == p) continue; if(ei == t || dfs(dfs, u, v)){ int add = g[v].size() - 2; tb.emplace_back(vector(add + 1)); for(int i = 0; i <= add; i++){ tb.back()[i] = fact[add] * inv[add - i]; } return true; } } return false; }; if(!dfs(dfs, st, gl)){ dfs(dfs, gl, st); } queue que; u = 0; for(int i = 0; i < tb.size(); i++) que.emplace(i); while(que.size() >= 2){ u = que.front(); que.pop(); v = que.front(); que.pop(); tb[u] = atcoder::convolution(tb[u], tb[v]); que.emplace(u); } int mn = tb.size() + 1; for(int i = 1; i <= n; i++){ if(i < mn){ cout << '0'; }else if(i - mn < tb[u].size()){ cout << tb[u][i - mn].val(); }else{ cout << '0'; } cout << (i == n ? '\n' : ' '); } }