题解

#include<bits/stdc++.h>
using namespace std;
const int N=100007,P=1000000007;
int n,fa[N],size[N],num[N],ifac[N],ans[N];std::vector<int>e[N];std::set<int>root;
struct edge{int u,v,w;};std::vector<edge>vec;
int read(){int x=0,c=getchar();while(isspace(c))c=getchar();while(isdigit(c))(x*=10)+=c&15,c=getchar();return x;}
void inc(int&a,int b){a+=b-P,a+=a>>31&P;}
int mul(int a,int b){return 1ll*a*b%P;}
int pow(int a,int b){int r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(a,r);return r;}
int find(int x){return x==fa[x]? x:fa[x]=find(fa[x]);}
void dfs(int u,int fa,int dep,int root){for(int v:e[u])if(v^fa){if(e[v].size()==2)dfs(v,u,dep+1,root);else if(root<v)vec.push_back({root,v,dep+1});}}
int main()
{
    int n=read();
    for(int i=ans[0]=ifac[0]=1;i<=n;++i) ifac[i]=pow(ans[i]=mul(ans[i-1],i),P-2);
    for(int i=1,u,v;i<n;++i) u=read(),v=read(),e[u].push_back(v),e[v].push_back(u);
    for(int u=1;u<=n;++u) if(e[u].size()^2) num[fa[u]=u]=e[u].size(),dfs(u,0,1,u),size[u]=1,root.insert(u);
    sort(vec.begin(),vec.end(),[](edge a,edge b){return a.w>b.w;});
    for(int i=n-1;i;--i)
    {
	for(int u,v;vec.size()&&vec.back().w+i<n;vec.pop_back())
	    u=find(vec.back().u),v=find(vec.back().v),size[u]+=size[v]+vec.back().w-2,num[u]+=num[v]-2,root.erase(v),fa[v]=u;
	for(int x:root) ans[i]=mul(ans[i],ifac[i-n+size[x]+(n-i-1)*num[x]]);
    }
    for(int i=1;i<=n;++i) cout<<ans[i]<<'\n';
}