#include<bits/stdc++.h>
#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize("-fgcse")
#pragma GCC optimize("-fgcse-lm")
#pragma GCC optimize("-fipa-sra")
#pragma GCC optimize("-ftree-pre")
#pragma GCC optimize("-ftree-vrp")
#pragma GCC optimize("-fpeephole2")
#pragma GCC optimize("-ffast-math")
#pragma GCC optimize("-fsched-spec")
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize("-falign-jumps")
#pragma GCC optimize("-falign-loops")
#pragma GCC optimize("-falign-labels")
#pragma GCC optimize("-fdevirtualize")
#pragma GCC optimize("-fcaller-saves")
#pragma GCC optimize("-fcrossjumping")
#pragma GCC optimize("-fthread-jumps")
#pragma GCC optimize("-funroll-loops")
#pragma GCC optimize("-freorder-blocks")
#pragma GCC optimize("-fschedule-insns")
#pragma GCC optimize("inline-functions")
#pragma GCC optimize("-ftree-tail-merge")
#pragma GCC optimize("-fschedule-insns2")
#pragma GCC optimize("-fstrict-aliasing")
#pragma GCC optimize("-falign-functions")
#pragma GCC optimize("-fcse-follow-jumps")
#pragma GCC optimize("-fsched-interblock")
#pragma GCC optimize("-fpartial-inlining")
#pragma GCC optimize("no-stack-protector")
#pragma GCC optimize("-freorder-functions")
#pragma GCC optimize("-findirect-inlining")
#pragma GCC optimize("-fhoist-adjacent-loads")
#pragma GCC optimize("-frerun-cse-after-loop")
#pragma GCC optimize("inline-small-functions")
#pragma GCC optimize("-finline-small-functions")
#pragma GCC optimize("-ftree-switch-conversion")
#pragma GCC optimize("-foptimize-sibling-calls")
#pragma GCC optimize("-fexpensive-optimizations")
#pragma GCC optimize("inline-functions-called-once")
#pragma GCC optimize("-fdelete-null-pointer-checks")
#define ll long long
#define mod 998244353
#define N 3005
#define M 10005
using namespace std;
vector<ll> op[M];
ll n,m,x,y,i,jc[M],inv[M],ans,f[N][N],son[M];
namespace lglr{
	ll f1[M],f2[M],tot,p1[M],p2[M];
	inline ll solve(ll x){
		if(x<=tot) return f2[x];
		p1[0] = 1,p2[tot+1] = 1;
		for(ll i=1;i<=tot;i++) p1[i]=p1[i-1]*(x-i)%mod;
		for(ll i=tot;i>=1;i--) p2[i]=p2[i+1]*(x-i)%mod;
		ll ans = 0;
		for(ll i=1;i<=tot;i++){
			if((tot-i)%2==0) ans = (ans+p1[i-1]*p2[i+1]%mod*f2[i]%mod*inv[i-1]%mod*inv[tot-i])%mod;
			else ans = (ans-p1[i-1]*p2[i+1]%mod*f2[i]%mod*inv[i-1]%mod*inv[tot-i])%mod;
		}
		return (ans%mod+mod)%mod;
	}
}
inline ll qmi(ll a,ll b,ll p){
	ll res = 1%p,t = a;
	while(b){
		if(b&1) res=res*t%p;
		t=t*t%p;
		b>>=1;
	}
	return res;
}
namespace poly{
	ll n,m,len,res[M],G,invG,invn,nn,qm[M],qm2[M],temp[M],tempa[M],tempb[M],temp2[M],c[M],TF7[M];
	inline void init(ll n){
		for(ll i=0;i<n;i++){
			res[i]=((res[i>>1])>>1);
			if(i&1) res[i]+=(n>>1);
		}
		for(ll i=0;i<13;i++){
			ll w1=qmi(G,(mod-1)/(1<<(i+1)),mod);
			ll w2=qmi(invG,(mod-1)/(1<<(i+1)),mod);
			for(ll j=0,now=1,now2=1;j<(1<<i);j++,now=now*w1%mod,now2=now2*w2%mod) qm[(1<<i)+j]=now,qm2[(1<<i)+j]=now2;
		}
	}
	inline void ntt(ll *f,ll n,ll type){
		static unsigned long long tmp[M];
		ll u = __builtin_ctz((1ll<<13)/n);
		for(ll i=0;i<n;i++) tmp[i]=f[res[i]>>u];
		for(ll i=1;i<n;i<<=1){
			for(ll r=(i<<1),j=0;j<n;j+=r){
				for(ll k=0;k<i;k++){
					ll y = (type==1?qm[i|k]:qm2[i|k])*tmp[j|k|i]%mod;
					tmp[j|k|i] = (tmp[j|k]+mod-y),tmp[j|k]+=y;
				}
			}
		}
		for(ll i=0;i<n;i++) f[i]=tmp[i]%mod;
	}
	inline void times(ll *a,ll *b,ll *cp,ll n,ll m,ll tim){
		if(n+m<=150){
			for(ll i=0;i<n+m-1;i++) c[i]=0;
			for(ll i=0;i<n;i++){
				for(ll j=0;j<m;j++) c[i+j]=(c[i+j]+a[i]*b[j])%mod;
			}
			for(ll i=0;i<n+m-1;i++) cp[i]=c[i];
			return ;
		}
		ll nn = n,mm = m,op = 1;
		while(op<=n+m) op*=2;
		n=op;
		if(tim==0){
			for(ll i=0;i<n;i++) tempa[i]=(i>=nn?0:a[i]);
			for(ll i=0;i<n;i++) tempb[i]=(i>=mm?0:b[i]);
			ntt(tempa,n,1),ntt(tempb,n,1);
			for(ll i=0;i<n;i++) c[i]=tempa[i]*tempb[i]%mod;
			ntt(c,n,-1);
			ll invn = qmi(n,mod-2,mod);
			for(ll i=0;i<nn+mm;i++) cp[i]=c[i]*invn%mod;
		}
		else{
			for(ll i=0;i<n;i++) tempa[i]=(i>=nn?0:a[i]);
			ntt(tempa,n,1);
			for(ll i=0;i<n;i++) c[i]=tempa[i]*b[i]%mod;
			ntt(c,n,-1);
			ll invn = qmi(n,mod-2,mod);
			for(ll i=0;i<nn+mm;i++) cp[i]=c[i]*invn%mod;
		}
	}
}
ll f1[M],f2[M],f3[M],f4[M],f5[M],f6[M],f7[M],f8[M],ls=1,rs=0,now=1;
inline void dfs(ll x,ll fa){
	son[x] = 1;
	for(ll i=0;i<op[x].size();i++){
		if(op[x][i]==fa) continue;
		dfs(op[x][i],x);
	}
	ll p=0;
	f1[0]=1;
	for(ll i=1;i<=n+2;i++) f1[i]=0;
	for(ll i=0;i<op[x].size();i++){
		if(op[x][i]==fa) continue;
		if(p==0){
			for(ll j=0;j<=n+2;j++) f1[j]=f[op[x][i]][j];
			son[x]+=son[op[x][i]];
			p=1;
			continue;
		}
		for(ll j=0;j<=n+2;j++) f2[j]=f[op[x][i]][j];
//		cout<<"begin "<<x<<" "<<op[x][i]<<endl;
//		for(ll j=0;j<=n+2;j++) cout<<f1[j]<<" ";
//		cout<<endl;
//		for(ll j=0;j<=n+2;j++) cout<<f2[j]<<" ";
//		cout<<endl;
		son[x]+=son[op[x][i]];
		poly::times(f1,f2,f1,n+3,n+3,0);
//		for(ll j=0;j<=n+2;j++) cout<<f1[j]<<" ";
//		cout<<endl;
//		cout<<"end "<<x<<" "<<op[x][i]<<endl;
	}
//	for(ll i=0;i<=n+2;i++) cout<<f1[i]<<" ";
//	cout<<endl;
	for(ll i=1;i<=n+2;i++){
		f4[i]=(f4[i-1]+f1[i])%mod;
		f5[i]=f4[i]*inv[i-1]%mod*inv[n+2-i]%mod;
		if((n+2-i)%2==1) f5[i]=(mod-f5[i])%mod;
	}
	for(ll i=1;i<=n+2;i++) f6[i]=f5[i];
	if((n+3)+2*(n+2)+1<=200) poly::times(f6,f8,f6,n+3,2*(n+2)+1,0);
	else poly::times(f6,f7,f6,n+3,2*(n+2)+1,1);
	for(ll i=1;i<=n+2;i++) f3[i]=f6[2*(n+2)-i];
	ls=1,rs=0;
	for(ll i=1;i<=n+2;i++){
		if(m-i<=n+2) f3[i]=f4[m-i];
		else{
			if(ls==1&&rs==0){
				now=1;
				for(ll j=m-i-(n+2);j<=m-i-1;j++) now=now*j%mod;
				ls=1,rs=1;
			}
			else now=now*(m-i-(n+2))%mod*qmi(m-(i-1)-1,mod-2,mod)%mod;
			f3[i]=f3[i]*now%mod;
		}
		f3[i]=(f3[i]+f1[0])%mod;
	}
	lglr::tot = n+2;
	for(ll i=1;i<=n+2;i++) lglr::f1[i]=i,lglr::f2[i]=(lglr::f2[i-1]+f3[i])%mod;
	f3[0] = (qmi(m,son[x],mod)-lglr::solve(m)+mod)%mod;
	for(ll i=0;i<=n+2;i++) f[x][i]=f3[i];
//	cout<<"! "<<x<<endl;
//	for(ll i=0;i<=n+2;i++) cout<<f3[i]<<" ";
//	cout<<endl;
	lglr::tot = n+2;
	for(ll i=1;i<=n+2;i++) lglr::f1[i]=i,lglr::f2[i]=(lglr::f2[i-1]+f[x][i]*i)%mod;
	ans = (ans+lglr::solve(m)*qmi(m,n-son[x],mod))%mod;
//	cout<<"! "<<ans<<endl;
} 
int main(){
//	freopen("1.in","r",stdin);
	poly::G=3,poly::invG=qmi(poly::G,mod-2,mod),poly::init(1<<13);
	ios::sync_with_stdio(false);
	cin>>n>>m;
	jc[0]=1;
	for(i=1;i<=5000;i++) jc[i]=jc[i-1]*i%mod;
	inv[5000]=qmi(jc[5000],mod-2,mod);
	for(i=5000;i>=1;i--) inv[i-1]=inv[i]*i%mod;
	for(i=1;i<n;i++) cin>>x>>y,op[x].push_back(y),op[y].push_back(x);
	for(ll i=0;i<=2*(n+2);i++) f7[2*(n+2)-i]=qmi((m-i+mod)%mod,mod-2,mod)%mod,f8[2*(n+2)-i]=f7[2*(n+2)-i];
	ll op = 1,kl = (n+3)+2*(n+2)+1;
	while(op<=kl) op*=2;
	poly::ntt(f7,op,1);
	dfs(1,-1);
	cout<<ans<<endl;
	return 0;
}
/*
2 4
1 2

50

3 2
1 2
1 3
*/