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<bits/stdc++.h>
#define ll long long
using namespace std;
int getint()
{
    ll i=0,f=1;char c;
    for(c=getchar();(c!='-')&&(c<'0'||c>'9');c=getchar());
    if(c=='-')c=getchar(),f=-1;
    for(;c>='0'&&c<='9';c=getchar())i=(i<<3)+(i<<1)+c-'0';
    return i*f;
}
const int N=200005,mod=924844033,g=5;
int n,tot,first[N],nxt[N<<1],to[N<<1],size[N];
ll fac[N],invfac[N],w[N],invw[N],a[N<<3],b[N<<3];
int pos[N<<3];
ll Pow(ll x,int y)
{
	int res=1;
	for(;y;y>>=1,x=x*x%mod)
		if(y&1)res=res*x%mod;
	return res;
}
void add(int x,int y)
{
	nxt[++tot]=first[x],first[x]=tot,to[tot]=y;
}
void dfs(int u,int fa)
{
	size[u]=1;
	for(int e=first[u];e;e=nxt[e])
	{
		int v=to[e];if(v==fa)continue;
		dfs(v,u),size[u]+=size[v];
		a[size[v]]--;
	}
	a[n]++,a[n-size[u]]--;
}
void NTT(ll *f,int len,int on)
{
	for(int i=1;i<len;i++)if(i<pos[i])swap(f[i],f[pos[i]]);
	for(int i=1,num=1;i<len;i<<=1,num++)
	{
		ll wi=on==1?w[num]:invw[num];
		for(int j=0;j<len;j+=(i<<1))
		{
			ll wn=1;
			for(int k=j;k<j+i;k++)
			{
				ll u=f[k],v=wn*f[k+i];
				f[k]=(u+v)%mod,f[k+i]=(u-v+mod)%mod;
				wn=wn*wi%mod;
			}
		}
	}
	if(on==-1)for(int i=0,inv=Pow(len,mod-2);i<len;i++)f[i]=f[i]*inv%mod;
}
int main()
{
	//freopen("tree.in","r",stdin);
	//freopen("tree.out","w",stdout);
	n=getint();
	fac[0]=1;for(int i=1;i<=n;i++)fac[i]=fac[i-1]*i%mod;
	invfac[n]=Pow(fac[n],mod-2);
	for(int i=n-1;i>=0;i--)invfac[i]=invfac[i+1]*(i+1)%mod;
	int len=1,num=0;
	while(len<=2*n)
	{
		len<<=1;
		w[++num]=Pow(g,(mod-1)/len);
		invw[num]=Pow(w[num],mod-2);
	}
	for(int i=1;i<len;i++)pos[i]=i&1?pos[i>>1]>>1|(len>>1):pos[i>>1]>>1;
	for(int i=1;i<n;i++)
	{
		int x=getint(),y=getint();
		add(x,y),add(y,x);
	}
	dfs(1,0);
	for(int i=0;i<=n;i++)a[i]=a[i]*fac[i]%mod;
	for(int i=0;i<=n;i++)b[i]=invfac[n-i];
	NTT(a,len,1),NTT(b,len,1);
	for(int i=0;i<len;i++)a[i]=a[i]*b[i]%mod;
	NTT(a,len,-1);
	for(int i=1;i<=n;i++)
		cout<<(a[i+n]*invfac[i]%mod+mod)%mod<<'\n';
}