// what is matter? never mind. 
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,sse4,popcnt,abm,mmx,avx,avx2") 
#include<bits/stdc++.h>
#define For(i,a,b) for(int i=(a);i<=(b);++i)
#define Rep(i,a,b) for(int i=(a);i>=(b);--i)
#define ll long long
#define ull unsigned long long
#define int long long
#define i128 __int128
using namespace std;
inline int read()
{
	char c=getchar();int x=0;bool f=0;
	for(;!isdigit(c);c=getchar())f^=!(c^45);
	for(;isdigit(c);c=getchar())x=(x<<1)+(x<<3)+(c^48);
	if(f)x=-x;return x;
}
 
#define mod 998244353
struct modint{
	int x;
	modint(int o=0){x=o;}
	modint &operator = (int o){return x=o,*this;}
	modint &operator +=(modint o){return x=x+o.x>=mod?x+o.x-mod:x+o.x,*this;}
	modint &operator -=(modint o){return x=x-o.x<0?x-o.x+mod:x-o.x,*this;}
	modint &operator *=(modint o){return x=1ll*x*o.x%mod,*this;}
	modint &operator ^=(int b){
		modint a=*this,c=1;
		for(;b;b>>=1,a*=a)if(b&1)c*=a;
		return x=c.x,*this;
	}
	modint &operator /=(modint o){return *this *=o^=mod-2;}
	friend modint operator +(modint a,modint b){return a+=b;}
	friend modint operator -(modint a,modint b){return a-=b;}
	friend modint operator *(modint a,modint b){return a*=b;}
	friend modint operator /(modint a,modint b){return a/=b;}
	friend modint operator ^(modint a,int b){return a^=b;}
	friend bool operator ==(modint a,modint b){return a.x==b.x;}
	friend bool operator !=(modint a,modint b){return a.x!=b.x;}
	bool operator ! () {return !x;}
	modint operator - () {return x?mod-x:0;}
	bool operator <(const modint&b)const{return x<b.x;}
};
inline modint qpow(modint x,int y){return x^y;}

vector<modint> fac,ifac,iv;
inline void initC(int n)
{
	if(iv.empty())fac=ifac=iv=vector<modint>(2,1);
	int m=iv.size(); ++n;
	if(m>=n)return;
	iv.resize(n),fac.resize(n),ifac.resize(n);
	For(i,m,n-1){
		iv[i]=iv[mod%i]*(mod-mod/i);
		fac[i]=fac[i-1]*i,ifac[i]=ifac[i-1]*iv[i];
	}
}
inline modint C(int n,int m){
	if(m<0||n<m)return 0;
	return initC(n),fac[n]*ifac[m]*ifac[n-m];
}
inline modint sign(int n){return (n&1)?(mod-1):(1);}

#define fi first
#define se second
#define pb push_back
#define mkp make_pair
typedef pair<int,int>pii;
typedef vector<int>vi;

#define maxn 500005
#define inf 0x3f3f3f3f

int n,c;
vi e[maxn];

int rt;
modint out=0;
ll ans;

int t[maxn],m,val[maxn],pos[maxn];

int fa[maxn];
int s[maxn],sz[maxn],ssz[maxn];
void dfs1(int u,int pa){
	fa[u]=pa;
	sz[u]=1;
	ssz[u]=0;
	for(int v:e[u]) 
		if(v!=pa){
			dfs1(v,u),sz[u]+=sz[v];
			ans+=ssz[u]*ssz[v]*2;
			ssz[u]+=ssz[v];
		} 
	ssz[u]+=sz[u];
	if(pa && e[u].size()==1){
		t[++m]=u;
	}
}

void dfs2(int u,int pa){
	for(int v:e[u])if(v!=pa){
		s[v]=s[u];
		s[v]-=sz[v],s[v]+=n-sz[v];
		dfs2(v,u);
	}
}

int seq[10000007];

pii tr[maxn<<2];
int leaf[maxn];
void up(int p){
	tr[p]=min(tr[p<<1],tr[p<<1|1]);
}
void build(int p,int l,int r){
	if(l==r)return leaf[l]=p,tr[p]=mkp(val[l],l),void();
	int mid=l+r>>1;
	build(p<<1,l,mid),build(p<<1|1,mid+1,r),up(p);
}
void upd(int u){
	int p=leaf[u];
	tr[p]=mkp(val[u],u);
	while(p>>=1) up(p);
}

modint S3(modint x){
	return x*x*x;
}
int pres[maxn];

void work()
{
	n=read(),c=read();
	For(i,1,n)e[i].clear(),sz[i]=s[i]=fa[i]=0; 
	ans=0,out=0,m=0;
	
	For(i,2,n){
		int u=read(),v=read();
		e[u].pb(v),e[v].pb(u);
	}
	
	rt=1;
	For(i,1,n)if(e[i].size()>1){
		rt=i;
		break;
	}
	dfs1(rt,0);
	For(i,1,n) if(i!=rt) s[rt]+=sz[i];
	dfs2(rt,0);
	For(i,1,m) {
	//	cout<<"t,st "<<t[i]<<" "<<s[t[i]]-(n-1)<<"\n";
		pos[i]=1;
		int u=i;
		val[u]=(s[t[u]]-(n-1))*2+(n-1)*(pos[u]*2+1)-(pos[u]-1)*2;
	}
	build(1,1,m);
	
//	int s2=0;
//	For(i,1,n) s2+=sz[i];
	For(i,1,n) if(i!=rt) ans+=(n-sz[i])*sz[i],ans+=(n-sz[i])*(ssz[i]-sz[i])*2;
	
//	cout<<ans<<"\n";
//	ans=15;

//	cout<<ans<<"\n";
	out+=S3(ans%mod);
	
	int V=n*3+inf;
	For(i,1,c-(n-1)){
		int u=tr[1].se;
		if(i>V){
			u=seq[i%m];
		}
		
		ans+=val[u];
		ans+=(i-1)*2;
		++pos[u];
	//	val[u]+=(n-1)*2;
		val[u]=(s[t[u]]-(n-1))*2+(n-1)*(pos[u]*2+1)-(pos[u]-1)*2;
//		if(i>n*4) {
//		//	if(!pres[u]) exit(233);
//			cout<<u<<" "<<i-pres[u]<<" "<<seq[i%m]<<"\n";
//		}
		
		pres[u]=i;
	//	For(u,1,m) cout<<t[u]<<" "<<pos[u]<<"\n";
		
	//	cout<<ans<<"\n";
		out+=S3(ans%mod);
		
		if(i<=V){
			upd(u);
		//	seq[i%m]=u;
		}
	}
	cout<<out.x<<"\n";
}

signed main()
{
//	freopen("data.in","r",stdin);
//	freopen("my.out","w",stdout);
	int T=read();
	while(T--)work();
	return 0;
}
/*

1
5 10
1 4
1 3
1 2
5 4

1 2 3
*/