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<algorithm>
using namespace std;
#define MAXN 200010
#define MO 924844033
#define G 5
#define LL long long
LL fac[MAXN],inv[MAXN],f[MAXN];
int n;
LL PowMod(LL a,int b)
{
	LL ret=1;
	while(b)
	{
		if(b&1) ret=ret*a%MO;
		a=a*a%MO;
		b>>=1;
	}
	return ret;
}
void Pre()
{
	fac[0]=1;
	for(int i=1;i<=n;i++)
		fac[i]=fac[i-1]*i%MO;
	inv[n]=PowMod(fac[n],MO-2);
	for(int i=n-1;i>=0;i--)
		inv[i]=inv[i+1]*(i+1)%MO;
}
int Adj[MAXN],V[MAXN*2],nxt[MAXN*2],c,siz[MAXN];
void AddEdge(int u,int v)
{
	c++;V[c]=v,nxt[c]=Adj[u];Adj[u]=c;
}
void dfs(int u,int p)
{
	siz[u]=1;
	for(int i=Adj[u];i;i=nxt[i])
		if(V[i]!=p)
		{
			dfs(V[i],u);
			siz[u]+=siz[V[i]];
		}
	f[siz[u]]--;
	f[n-siz[u]]--;
}
void NTT(LL A[],int N,int typ)
{
	for(int i=1,j=0;i<N-1;i++)
	{
		for(int s=N;j^=s>>=1,~j&s;);
		if(i<j) swap(A[i],A[j]);
	}
	for(int i=1;i<N;i<<=1)
	{
		LL w1=PowMod(G,(MO-1)/(i<<1)),w=1;
		if(typ==-1)
			w1=PowMod(w1,MO-2);
		for(int j=0;j<i;j++,w=w*w1%MO)
			for(int l=j,r=l+i;l<N;l+=(i<<1),r=l+i)
			{
				int tmp=A[r]*w%MO;
				A[r]=(A[l]-tmp+MO)%MO;
				A[l]=(A[l]+tmp)%MO;
			}
	}
	if(typ==-1)
	{
		int Inv=PowMod(N,MO-2);
		for(int i=0;i<N;i++)
			A[i]=A[i]*Inv%MO;
	}
}
LL a[MAXN*4],b[MAXN*4];
int main()
{
	scanf("%d",&n);
	Pre();
	int u,v;
	for(int i=1;i<n;i++)
	{
		scanf("%d%d",&u,&v);
		AddEdge(u,v);
		AddEdge(v,u);
	}
	dfs(1,0);
	f[n]=n;
	int len=1;
	for(;len<=2*n;len<<=1);
	for(int i=0;i<=n;i++)
	{
		a[i]=f[i]*fac[i]%MO;
		b[i]=inv[n-i];
	}
	NTT(a,len,1);
	NTT(b,len,1);
	for(int i=0;i<=len;i++)
		a[i]=a[i]*b[i]%MO;
	NTT(a,len,-1);
	for(int i=1;i<=n;i++)
	{
		LL ans=a[i+n]*inv[i]%MO;
		printf("%lld\n",(ans%MO+MO)%MO);
	}
}