#include<bits/stdc++.h>
#define Gc() getchar()
#define Me(x,y) memset(x,y,sizeof(x))
#define Mc(x,y) memcpy(x,y,sizeof(x))
#define d(x,y) ((m)*(x-1)+(y))
#define R(n) (rnd()%(n)+1)
#define Pc(x) putchar(x)
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define eb emplace_back
#define all(x) x.begin(),x.end()
using namespace std;using ll=long long;using db=double;using lb=long db;using ui=unsigned;using ull=unsigned long long;using pii=pair<int,int>;
const int N=2000+5,M=N*4+5,K=1e7+5,mod=998244353,Mod=mod-1;const db eps=1e-9;const int INF=1e9+7;mt19937 rnd(263082);
#define Tp template<typename T>
#define Ts template<typename T,typename... Ar>
namespace Debug{
	Tp void _debug(char* f,T t){cerr<<f<<'='<<t<<endl;}
	Ts void _debug(char* f,T x,Ar... y){while(*f!=',') cerr<<*f++;cerr<<'='<<x<<",";_debug(f+1,y...);}
	#ifdef LOCAL
	#define gdb(...) _debug((char*)#__VA_ARGS__,__VA_ARGS__)
	#else 
	#define gdb(...) void()
	#endif
}using namespace Debug;

using poly=vector<ll>;
ll mpow(ll x,int y=mod-2){ll ans=1;while(y) y&1&&(ans=ans*x%mod),y>>=1,x=x*x%mod;return ans;}
ll sgn(int x){return x&1?mod-1:1;}
namespace Poly{
	const int N=1<<21,g=3;
	int tr[N],k,a[N],b[N];ll pw[N];
	void init(int n){
		for(k=2;k<=n;k<<=1);
		for(int i=0;i<k;i++) tr[i]=(tr[i>>1]>>1)|(i&1?k/2:0);
		pw[k/2]=1;pw[k/2+1]=mpow(g,(mod-1)/k);
		for(int i=k/2+2;i<k;i++) pw[i]=pw[i-1]*pw[k/2+1]%mod;
		for(int i=k/2-1;i;i--) pw[i]=pw[i<<1];
	}
	void ntt(int *A,int k,int flag){
		static ull a[N];for(int i=0;i<k;i++) a[tr[i]]=A[i];
		for(int i=2;i<=k;i<<=1){
			ll *e=pw+i/2;
			for(int j=0;j<k;j+=i){
				for(int h=j;h<j+i/2;h++){
					int x=a[h+i/2]*e[h-j]%mod;
					a[h+i/2]=a[h]+mod-x;a[h]+=x;
				}
			}
			if(i==(1<<18)){
				for(int j=0;j<k;j++) a[j]%=mod;
			}
		}
		for(int i=0;i<k;i++) A[i]=a[i]%mod;
		if(flag) return;
		reverse(A+1,A+k);
		ll iv=mpow(k);for(int i=0;i<k;i++) A[i]=A[i]*iv%mod;
	}
	namespace Public{
		poly operator *(const poly &A,const poly &B){
			int n=A.size(),m=B.size(),lim=n+m-1;
			init(lim);
			copy(A.begin(),A.end(),a);fill(a+n,a+k,0);
			copy(B.begin(),B.end(),b);fill(b+m,b+k,0);
			ntt(a,k,1);ntt(b,k,1);
			for(int i=0;i<k;i++) a[i]=1ll*a[i]*b[i]%mod;
			ntt(a,k,0);
			poly c(lim);copy(a,a+lim,c.begin());
			return c;
		}
		poly& operator *=(poly &A,const poly &B){
			return A=A*B;
		}
		poly operator *(const poly &A,const int B){
			poly C=A;for(int i=0;i<C.size();i++) C[i]=1ll*C[i]*B%mod;
			return C;
		}
		poly& operator *=(poly &A,const int &B){
			return A=A*B;
		}
		poly operator +(const poly &A,const poly &B){
			poly C(max(A.size(),B.size()));
			for(int i=0;i<A.size();i++) C[i]=A[i];
			for(int i=0;i<B.size();i++) C[i]=(B[i]+C[i])%mod;
			return C;
		}
		poly& operator +=(poly &A,const poly &B){
			return A=A+B;
		}
		poly operator -(const poly &A,const poly &B){
			poly C(max(A.size(),B.size()));
			for(int i=0;i<A.size();i++) C[i]=A[i];
			for(int i=0;i<B.size();i++) C[i]=(C[i]+mod-B[i])%mod;
			return C;
		}
		poly& operator -=(poly &A,const poly &B){
			return A=A-B;
		}
		poly operator %(const poly &A,const int &B){
			poly C=A;
			if(C.size()>B) C.resize(B);
			return C;
		}
		poly& operator %=(poly &A,const int B){
			return A=A%B;
		}
		poly inve(poly A,int n=-1){
			if(n==-1) n=A.size();
			if(n==1) return poly({(int)mpow(A[0])});
			poly A0=inve(A%(n+1>>1),n+1>>1);
			return A0*(poly({2})-A*A0%n)%n;
		}
		poly sqrt(poly A,int n=-1){
			if(n==-1) n=A.size();
			if(n==1) return poly({1});
			poly A0=sqrt(A%(n+1>>1),n+1>>1);
			return (A0*A0%n+A)*inve(A0,n)%n*(mod+1>>1);
		}
		poly der(poly A){
			poly B(A.size()-1);
			for(int i=1;i<A.size();i++) B[i-1]=1ll*A[i]*i%mod;
			return B;
		}
		poly integ(poly A){
			poly B(A.size()+1);
			static ll inv[N];inv[1]=1;for(int i=2;i<=A.size();i++) inv[i]=(mod-inv[mod%i])*(mod/i)%mod;
			for(int i=0;i<A.size();i++) B[i+1]=inv[i+1]*A[i]%mod;
			return B;
		}
		poly ln(poly A,int n=-1){
			if(n==-1) n=A.size();
			return integ(der(A)*inve(A,n)%n)%n;
		}
		poly exp(poly A,int n=-1){
			if(n==-1) n=A.size();
			if(n==1) return poly({1});
			poly A0=exp(A%(n+1>>1),n+1>>1);
			return A0*(poly({1})-ln(A0,n)+A)%n;
		}
		poly mpow(poly A,int n,ll k){gdb(n,k);
			auto p=find_if(A.begin(),A.end(),[](ll x){return x;})-A.begin();
			if(p==A.size()) return A;
			poly B(A.size()-p);for(int i=p;i<A.size();i++) B[i-p]=A[i];
			ll v=::mpow(B[0],k%Mod),iv=::mpow(B[0]);
			for(ll &i:B) i=i*iv%mod;B=ln(B,n);
			for(ll &i:B) i=k%mod*i%mod;B=exp(B,n);
			for(ll &i:B) i=i*v%mod;
			for(int i=n-1;~i;i--) B[i]=(i>=1ll*k*p?B[i-k*p]:0);
			return B;
		}
	}
}using namespace Poly::Public;



int n,m;
vector<int> S[N];
ll ans;
ll dp[N][N],f[N],g[N],inv[N],frv[N],pw[N];
int siz[N],sum[N];
ll LGLR(ll *f,int len,int x){
	static ll pre[N],suf[N];
	pre[0]=1;for(int i=1;i<=len;i++) pre[i]=pre[i-1]*(x+mod-i)%mod;
	suf[len+1]=1;for(int i=len;i;i--) suf[i]=suf[i+1]*(x+mod-i)%mod;
	ll tot=0;
	for(int i=1;i<=len;i++) tot+=pre[i-1]*suf[i+1]%mod*f[i]%mod*frv[i-1]%mod*sgn(len-i)%mod*frv[len-i]%mod;
	return tot%mod;
}
void LGLRS(ll *f,int len,ll *dp,int k){
	if(!k) return;
	// for(int i=1;i<=k;i++) dp[i]=LGLR(f,len,m-i);
	poly F(f+1,f+len+1);
	for(int i=1;i<=len;i++) F[i-1]=F[i-1]*frv[i-1]%mod*sgn(len-i)%mod*frv[len-i]%mod;

	static ll frc[N*2],inv[N*2],frv[N*2];
	for(int i=frc[0]=1;i<=len+k;i++) frc[i]=frc[i-1]*(m-k-len+(i-1)+mod)%mod;
	for(int i=frv[0]=1;i<=len+k;i++) inv[i]=mpow(m-k-len+(i-1)+mod),frv[i]=frv[i-1]*inv[i]%mod;
	poly G(inv+1,inv+len+k);
	reverse(G.begin(),G.end());
	reverse(all(F));
	F*=G;
	for(int i=1;i<=k;i++) dp[i]=F[i+len-2]*frc[len+k-i]%mod*frv[k-i]%mod,gdb(dp[i]);
	/*for(int i=1;i<=k;i++){
		dp[i]=0;
		for(int j=1;j<=len;j++) (dp[i]+=F[j-1]*inv[len+k-i-j+1])%=mod;
		dp[i]=dp[i]*frc[len+k-i]%mod*frv[k-i]%mod;
		gdb(dp[i],f[1],f[2],len,LGLR(f,len,m-i));
	}*/
}
void dfs(int x,int La){
	for(int i:S[x]) if(i^La) dfs(i,x);
	siz[x]=sum[x]=1;dp[x][0]=1;
	for(int i:S[x]) if(i^La){
		copy(dp[x],dp[x]+siz[x]+1,f);
		copy(dp[i],dp[i]+siz[i]+1,g);
		for(int j=siz[x]+1;j<=siz[x]+siz[i];j++) f[j]=LGLR(f,siz[x],j);
		for(int j=siz[i]+1;j<=siz[x]+siz[i];j++) g[j]=LGLR(g,siz[i],j);
		fill(dp[x],dp[x]+siz[x]+1,0);
		poly F(f,f+siz[x]+siz[i]+1),G(g,g+siz[x]+siz[i]+1);
		F*=G;
		for(int j=0;j<=siz[x]+siz[i];j++) dp[x][j]=F[j];
		// for(int j=0;j<=siz[x]+siz[i];j++) for(int h=0;j+h<=siz[x]+siz[i];h++) (dp[x][j+h]+=f[j]*g[h])%=mod;
		siz[x]+=siz[i];
		if(siz[x]>m) fill(dp[x]+m+1,dp[x]+siz[x]+1,0),siz[x]=m;
		sum[x]+=sum[i];
	}
	copy(dp[x],dp[x]+siz[x]+1,f);
	for(int i=1;i<=siz[x];i++) (f[i]+=f[i-1])%=mod;
	int k=siz[x]+2;
	while(k>m) dp[x][k]=0,k--;
	while(k&&m-k<=siz[x]) dp[x][k]=f[m-k],k--;
	LGLRS(f,siz[x],dp[x],k);
	// for(int i=1;i<=siz[x]+2;i++) dp[x][i]=(i>m?0:(i==m?f[0]:LGLR(f,siz[x],m-i)));
	copy(dp[x]+1,dp[x]+siz[x]+2,f+1);
	for(int i=2;i<=siz[x]+1;i++) (f[i]+=f[i-1])%=mod;
	dp[x][0]=(pw[sum[x]]+mod-LGLR(f,siz[x]+1,m))%mod;
	copy(dp[x],dp[x]+siz[x]+3,f);
	for(int i=0;i<=siz[x]+2;i++) (f[i]*=i)%=mod;
	for(int i=1;i<=siz[x]+2;i++) (f[i]+=f[i-1])%=mod;
	ans+=LGLR(f,siz[x]+2,m)*pw[n-sum[x]]%mod;
}
void Solve(){
	scanf("%d%d",&n,&m);
	inv[1]=1;for(int i=2;i<=n+2;i++) inv[i]=(mod-inv[mod%i])*(mod/i)%mod;
	for(int i=frv[0]=1;i<=n+2;i++) frv[i]=frv[i-1]*inv[i]%mod;
	for(int i=pw[0]=1;i<=n;i++) pw[i]=pw[i-1]*m%mod;
	for(int i=1;i<n;i++){
		int x,y;scanf("%d%d",&x,&y);
		S[x].push_back(y);S[y].push_back(x);
	}
	dfs(1,0);
	printf("%lld\n",ans%mod);
}
int main(){
	int t=1;
	// scanf("%d",&t);
	while(t--) Solve();
	cerr<<clock()*1.0/CLOCKS_PER_SEC<<'\n';
}