Problem: One day, Takahashi was given the following problem from Aoki:

* You are given a tree with N vertices and an integer K. The vertices are numbered 1 through N. The edges are represented by pairs of integers (a_i, b_i).
* For a set S of vertices in the tree, let f(S) be the minimum number of the vertices in a subtree of the given tree that contains all vertices in S.
* There are <image> ways to choose K vertices from the trees. For each of them, let S be the set of the chosen vertices, and find the sum of f(S) over all <image> ways.
* Since the answer may be extremely large, print it modulo 924844033(prime).



Since it was too easy for him, he decided to solve this problem for all K = 1,2,...,N.

Constraints

* 2 ≦ N ≦ 200,000
* 1 ≦ a_i, b_i ≦ N
* The given graph is a tree.

Input

The input is given from Standard Input in the following format:


N
a_1 b_1
a_2 b_2
:
a_{N-1} b_{N-1}


Output

Print N lines. The i-th line should contain the answer to the problem where K=i, modulo 924844033.

Examples

Input

3
1 2
2 3


Output

3
7
3


Input

4
1 2
1 3
1 4


Output

4
15
13
4


Input

7
1 2
2 3
2 4
4 5
4 6
6 7


Output

7
67
150
179
122
45
7

Solution (in CPP):

Solution:
#include<cstdio>
#include<cmath>
#include<algorithm>
#include<vector>
#define SF scanf
#define PF printf
#define MAXN 524388
#define MOD 924844033
using namespace std;
typedef long long ll;
struct node{
	int x;
	node *nxt;	
}edge[MAXN*2];
node *head[MAXN],*ncnt=edge;
void add_edge(int x,int y){
	ncnt++;
	ncnt->x=y;
	ncnt->nxt=head[x];
	head[x]=ncnt;	
}
ll f[MAXN],g[MAXN];
ll G=5;
int u,v;
ll fsp(ll x,int y){
	ll res=1;
	while(y){
		if(y&1)
			res=res*x%MOD;
		x=x*x%MOD;
		y>>=1;
	}
	return res;
}
void ntt(ll a[],int N,int flag){
	int i,j,k;
	for(i=1,j=0;i<N;i++){
		for(int d=N;j^=d>>=1,~j&d;);
		if(i<j)
			swap(a[i],a[j]);	
	}
	for(i=1;i<N;i<<=1){
		ll wn=fsp(G,(MOD-1)/(i<<1));
		if(flag==0)
			wn=fsp(wn,MOD-2);
		for(j=0;j<N;j+=i<<1){
			ll w=1;
			for(k=0;k<i;k++,w=w*wn%MOD){
				ll x=a[j+k],y=w*a[i+j+k]%MOD;
				a[j+k]=(x+y)%MOD;
				a[i+j+k]=(x-y+MOD)%MOD;
			}
		}
	}
	if(flag==0){
		ll inv=fsp(N,MOD-2);
		for(i=0;i<N;i++)
			a[i]=a[i]*inv%MOD;
	}
}
int siz[MAXN];
int cnt[MAXN];
int n;
void dfs(int x,int f){
	siz[x]=1;
	for(node *v=head[x];v!=NULL;v=v->nxt){
		int u=v->x;
		if(u==f)
			continue;
		dfs(u,x);
		cnt[siz[u]]++;
		cnt[n-siz[u]]++;
		siz[x]+=siz[u];
	}
}
ll fac[MAXN],ifac[MAXN];
int main(){
	SF("%d",&n);
	for(int i=1;i<n;i++){
		SF("%d%d",&u,&v);
		add_edge(u,v);
		add_edge(v,u);
	}
	dfs(1,0);
	for(int i=1;i<n;i++)
		cnt[i]=MOD-cnt[i];
	cnt[n]=n;
	fac[0]=1;
	for(int i=1;i<=n;i++)
		fac[i]=fac[i-1]*i%MOD;
	ifac[n]=fsp(fac[n],MOD-2);
	for(int i=n;i>=1;i--)
		ifac[i-1]=ifac[i]*i%MOD;
		
	for(int i=1;i<=n;i++)
		f[n-i]=cnt[i]*fac[i]%MOD;
	for(int i=0;i<=n;i++)
		g[i]=ifac[i];
	int len=1;
	while(len<=n*2)
		len<<=1;
	/*for(int i=0;i<n;i++){
		ll res=0;
		for(int j=0;j<=i;j++)
			res=(res+f[j]*g[i-j])%MOD;
	}*/
	ntt(g,len,1);
	ntt(f,len,1);
	for(int i=0;i<len;i++)
		g[i]=g[i]*f[i]%MOD;
	ntt(g,len,0);
	for(int i=1;i<=n;i++)
		PF("%lld\n",g[n-i]*ifac[i]%MOD);
}