#include<iostream>
#include<cstdio>
#include<vector>
#define N 2001
#define K 12
#define M 4096
#define g 3
#define mod 998244353
using namespace std;
int read()
{
	char c=0;
	int sum=0;
	while (c<'0'||c>'9') c=getchar();
	while ('0'<=c&&c<='9') sum=sum*10+c-'0',c=getchar();
	return sum;
}
int fast_pow(int a,int b)
{
	int res=1,mul=a;
	while (b)
	{
		if (b&1) res=1ll*res*mul%mod;
		mul=1ll*mul*mul%mod,b>>=1;
	}
	return res;
}
void Adder(int &x,int d)
{
	x=x+d>=mod?x+d-mod:x+d;
	return;
}
void Adder2(int &x,int d)
{
	x=x+d<0?x+d+mod:x+d;
	return;
}
int MD(int x)
{
	return x>=mod?x-mod:x;
}
int MD2(int x)
{
	return x<0?x+mod:x;
}
int n,m,ans,length,sz[N+1],szt[N+1],A[N+1],B[N+1],rev[M+1],tA[M+1],tB[M+1],wn[K+1][M+1],wn2[K+1][M+1],num[M+1],delta[N+1],delta2[N+1],fac[N+1],invfac[N+1],inv[N+1],pw[N+1],F[N+1],dp[N+1][N+1];
bool used[N+1];
vector<int>E[N+1];
void add(int x,int y)
{
	E[x].push_back(y),E[y].push_back(x);
	return;
}
int calc(int x)
{
	int res=0;
	for (int i=0;i<=szt[x];++i) Adder(res,1ll*dp[x][i]*delta[i]%mod);
	return res;
}
int calc2(int x)
{
	int res=0;
	for (int i=0;i<=szt[x];++i) Adder(res,1ll*dp[x][i]*delta2[i]%mod);
	return res;
}
void NTT(int limit,int *s,int type)
{
	int s1,s2;
	for (int i=1;i<limit;++i) rev[i]=(rev[i>>1]>>1)|((i&1)?limit>>1:0);
	for (int i=0;i<limit;++i)
		if (rev[i]>i)
			swap(s[i],s[rev[i]]);
	if (type==1)
	{
		for (int i=2;i<=limit;i<<=1)
			for (int j=0;j+i-1<limit;j+=i)
				for (int k=j;k<j+(i>>1);++k)
					s1=s[k],s2=1ll*s[k+(i>>1)]*wn[num[i]][k-j]%mod,s[k]=MD(s1+s2),s[k+(i>>1)]=MD2(s1-s2);
	}
	else
	{
		for (int i=2;i<=limit;i<<=1)
			for (int j=0;j+i-1<limit;j+=i)
				for (int k=j;k<j+(i>>1);++k)
					s1=s[k],s2=1ll*s[k+(i>>1)]*wn2[num[i]][k-j]%mod,s[k]=MD(s1+s2),s[k+(i>>1)]=MD2(s1-s2);
		s1=fast_pow(limit,mod-2);
		for (int i=0;i<=limit;++i) s[i]=1ll*s[i]*s1%mod;
	}
	return;
}
void dfs(int x)
{
	int limit=1;
	used[x]=1,sz[x]=1,szt[x]=0,dp[x][0]=1;
	for (int i=0;i<E[x].size();++i)
		if (!used[E[x][i]])
		{
			dfs(E[x][i]),sz[x]+=sz[E[x][i]];
			for (int j=0;j<=szt[x]+szt[E[x][i]];++j) F[j]=0;
			for (int j=0;j<=szt[x];++j)
				for (int k=0;k<=szt[E[x][i]];++k)
					Adder(F[j+k],1ll*dp[x][j]*dp[E[x][i]][k]%mod);
			szt[x]+=szt[E[x][i]];
			for (int j=0;j<=szt[x];++j) dp[x][j]=F[j];
		}
    szt[x]++;
	for (int i=szt[x];i>=1;--i) dp[x][i]=dp[x][i-1];
	dp[x][0]=0;
	while (limit<=(szt[x]<<1)) limit<<=1;
	for (int i=0;i<=limit;++i) tA[i]=tB[i]=0;
	for (int i=0;i<=szt[x];++i) tA[i]=1ll*dp[x][i]*A[i]%mod,tB[szt[x]-i]=invfac[i];
	NTT(limit,tA,1),NTT(limit,tB,1);
	for (int i=0;i<=limit;++i) tA[i]=1ll*tA[i]*tB[i]%mod;
	NTT(limit,tA,-1);
	for (int i=0;i<=szt[x];++i) dp[x][i]=(i&1)?1ll*tA[szt[x]+i]*B[i]%mod:MD2(-1ll*tA[szt[x]+i]*B[i]%mod);
	Adder(dp[x][0],MD2(pw[sz[x]]-calc(x))),Adder(ans,1ll*calc2(x)*pw[n-sz[x]]%mod);
	return;
}
int main()
{
	int x,y;
	fac[0]=1;
	for (int i=1;i<=N;++i) fac[i]=1ll*fac[i-1]*i%mod;
	invfac[N]=fast_pow(fac[N],mod-2);
	for (int i=N-1;i>=0;--i) invfac[i]=1ll*invfac[i+1]*(i+1)%mod;
	for (int i=1;i<=N;++i) inv[i]=1ll*fac[i-1]*invfac[i]%mod;
	for (int i=2,w;i<=M;i<<=1)
	{
		num[i]=++length,w=fast_pow(g,(mod-1)/i);
		for (int j=0,res=1;j<(i>>1);++j,res=1ll*res*w%mod) wn[num[i]][j]=res;
		w=fast_pow(g,(mod-1)/i*(i-1));
		for (int j=0,res=1;j<(i>>1);++j,res=1ll*res*w%mod) wn2[num[i]][j]=res;
	}
	n=read(),m=read(),pw[0]=A[0]=B[0]=1;
	for (int i=1;i<=n;++i) A[i]=1ll*A[i-1]*(m+i)%mod,B[i]=1ll*B[i-1]*fast_pow(m+i,mod-2)%mod;
	for (int i=0;i<=n;++i) delta[i]=1ll*A[i]*invfac[i]%mod,delta2[i]=1ll*A[i]*m%mod*invfac[i+1]%mod*i%mod;
	for (int i=1;i<=n;++i) pw[i]=1ll*pw[i-1]*m%mod;
	for (int i=1;i<=n-1;++i) x=read(),y=read(),add(x,y);
	dfs(1),printf("%d\n",ans);
	return 0;
}