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<cstring>
#include<algorithm>
using namespace std;
const int mxn=524288,md=924844033;
int power(int x,int p){
	int ret=1;
	for (;p;p>>=1,x=1ll*x*x%md)
		if (p&1) ret=1ll*ret*x%md;
	return ret;
}
bool check(int x){
	int num=md-1;
	for (int i=2;i*i<=num;++i)
		if (num%i==0){
			if (power(x,(md-1)/i)==1) return 0;
			for (;num%i==0;num/=i);
		}
	if (num>1&&power(x,(md-1)/num)==1) return 0;
	return 1;
}
int len,ln,invn,rev[mxn],w[21][mxn];
void NTT(int *a,int flg){
	for (int i=0;i<len;++i)
		if (i<rev[i]) swap(a[i],a[rev[i]]);
	for (int i=1,p=0;i<=len>>1;i<<=1,++p)
		for (int j=0,k,t,x,y;j<len;j+=i<<1)
			for (k=j,t=i;k<j+i;++k,t+=flg){
				x=a[k],y=1ll*w[p][t]*a[k+i]%md;
				a[k]=(x+y)%md,a[k+i]=(x-y)%md;
			}
	if (flg==-1)
		for (int i=0;i<len;++i)
			a[i]=1ll*a[i]*invn%md;
}
void NTT_init(int n){
	for (len=1,ln=0;len<n;len<<=1,++ln);
	for (int i=0;i<len;rev[i]=rev[i>>1]>>1|((i&1)<<(ln-1)),++i);
	invn=power(len,md-2);
}
void W_init(int n){
	NTT_init(n);
	for (int i=1,p=0;i<=len>>1;i<<=1,++p){
		w[p][i]=1;
		int x=power(5,(md-1)/(i<<1));
		for (int j=1;j<i;++j) w[p][i+j]=1ll*x*w[p][i+j-1]%md;
		x=power(x,md-2);
		for (int j=1;j<i;++j) w[p][i-j]=1ll*x*w[p][i-j+1]%md;
	}
}
int fct[mxn],ifc[mxn];
void init(int n){
	fct[0]=ifc[0]=1;
	for (int i=1;i<=n;++i) fct[i]=1ll*fct[i-1]*i%md;
	ifc[n]=power(fct[n],md-2);
	for (int i=n-1;i;--i) ifc[i]=ifc[i+1]*(i+1ll)%md;
}
int n,m,head[mxn],cnt[mxn],a[mxn],b[mxn];
struct ed{int to,nxt;}edge[mxn<<1];
void addedge(int u,int v){
	edge[++m]=(ed){v,head[u]},head[u]=m;
	edge[++m]=(ed){u,head[v]},head[v]=m;
}
int dfs(int u,int fa){
	int siz=1;
	for (int i=head[u],v;i;i=edge[i].nxt)
		if ((v=edge[i].to)!=fa) siz+=dfs(v,u);
	if (u>1) ++cnt[siz];
	++cnt[n-siz];
	return siz;
}
int main()
{
	scanf("%d",&n);
	init(n);
	W_init(n<<1);
	for (int i=1,x,y;i<n;++i)
		scanf("%d%d",&x,&y),addedge(x,y);
	dfs(1,0);
	for (int i=0;i<n;++i)
		a[i]=1ll*cnt[n-i]*fct[n-i]%md,b[i]=ifc[i];
	NTT(a,1),NTT(b,1);
	for (int i=0;i<len;++i)
		a[i]=1ll*a[i]*b[i]%md;
	NTT(a,-1);
	for (int i=1;i<=n;++i)
		printf("%lld\n",((1ll*fct[n]*ifc[n-i]%md*n%md-a[n-i])*ifc[i]%md+md)%md);
	return 0;
}