For this Question: You are given an undirected unweighted connected graph consisting of N vertices (numbered 1 to N) and N edges. Let d(u, v) denote the shortest distance between nodes u and v in the graph. You need to find the sum of d(u, v)<sup>K</sup> over all pairs (u, v) such that 1 ≤ u < v ≤ N. Since this sum can be large, you need to print it modulo 998244353.

Note: There can be self-edges in the graph.The first line contains two space-separated integers N and K.
Then N lines follow, each containing two space-separated integers u and v, denoting an edge between vertices u and v.

<b> Constraints: </b>
1 ≤ N ≤ 2×10<sup>5</sup>
1 ≤ K ≤ 10<sup>9</sup>
1 ≤ u, v ≤ NPrint a single integer, the summation of d(u, v)<sup>K</sup> modulo 998244353.Sample Input 1:
3 1
1 2
2 3
3 1

Sample Output 1:
3

Sample Explanation 1:
Answer = d(1,2) + d(1,3) + d(2,3) = 1 + 1 + 1 = 3

Sample Input 2:
4 2
1 2
1 3
1 4
1 1

Sample Output 2:
15

Sample Explanation 2:
Answer = d(1,2)<sup>2</sup> + d(1,3)<sup>2</sup> + d(1,4)<sup>2</sup> +  d(2,3)<sup>2</sup> + d(2,4)<sup>2</sup> + d(3,4)<sup>2</sup> = 1<sup>2</sup> + 1<sup>2</sup> + 1<sup>2</sup> + 2<sup>2</sup> + 2<sup>2</sup> + 2<sup>2</sup> = 15, I have written this Solution Code: #include<cstdio>
#include<algorithm>
#include<cstring>
#include<vector>
#include<ctime>
using namespace std;
typedef long long ll;
typedef vector<int> Poly;
const int MAXN=1e5+5,mod=998244353,G=3,invG=(mod+1)/3;
int n,K,ed[MAXN][2],m,pre[MAXN],lp[MAXN],tl[MAXN],m2;
Poly ans;
int fnd(int x){
	if(x!=pre[x]) pre[x]=fnd(pre[x]);
	return pre[x];
}
int cnte,h[MAXN],to[MAXN<<1],nx[MAXN<<1];
inline void adde(int u,int v){
	cnte++;
	nx[cnte]=h[u];
	to[cnte]=v;
	h[u]=cnte;
}
ll Fstpw(ll a,int b){
	ll res=1;
	while(b){
		if(b&1) res=res*a%mod;
		b>>=1;
		a=a*a%mod;
	}
	return res;
}
void ntt(int *a,int n,int tp){
	int bit=0;
	while(1<<bit<n) bit++;
	static int rev[MAXN<<2];
	for(int i=1; i<n; i++){
		rev[i]=rev[i>>1]>>1|((i&1)<<bit-1);
		if(i<rev[i]) swap(a[i],a[rev[i]]);
	}
	for(int mid=1; mid<n; mid<<=1){
		ll w=1,w1=Fstpw(tp==1?G:invG,(mod-1)/mid/2);
		for(int j=0; j<mid; j++,w=w*w1%mod)
			for(int i=0; i<n; i+=mid*2){
				int x=a[i+j],y=w*a[i+j+mid]%mod;
				a[i+j]=(x+y)%mod;
				a[i+j+mid]=(x-y+mod)%mod;
			}
	}
	if(tp==-1){
		ll t=Fstpw(n,mod-2);
		for(int i=0; i<n; i++)
			a[i]=a[i]*t%mod;
	}
	return ;
}
Poly operator +(Poly a,Poly b){
	if(a.size()<b.size()) swap(a,b);
	for(int i=0; i<b.size(); i++)
		a[i]=(a[i]+b[i])%mod;
	return a;
}
Poly operator -(Poly a,Poly b){
	if(a.size()<b.size()) a.resize(b.size());
	for(int i=0; i<b.size(); i++)
		a[i]=(a[i]-b[i]+mod)%mod;
	return a;
}
//long clk;
Poly operator *(Poly a,Poly b){
	//clk-=clock();
	if(a.empty()||b.empty()) return Poly{};
	int n=a.size()-1,m=b.size()-1,siz=1;
	while(siz<=n+m) siz<<=1;
	static int f[MAXN<<2],g[MAXN<<2];
	for(int i=0; i<siz; i++){
		f[i]=i<=n?a[i]:0;
		g[i]=i<=m?b[i]:0;
	}
	ntt(f,siz,1);
	ntt(g,siz,1);
	for(int i=0; i<siz; i++)
		f[i]=1ll*f[i]*g[i]%mod;
	ntt(f,siz,-1);
	//clk+=clock();
	return Poly(f,f+n+m+1);
}
inline void ad(Poly &c,Poly &a,Poly &b,int s){
	Poly t(a*b);
	if(c.size()<t.size()+s) c.resize(t.size()+s);
	for(int i=0; i<t.size(); i++)
		c[i+s]=(c[i+s]+t[i])%mod;
	return ;
}
inline void ad(Poly &c,Poly &a,int s){
	if(c.size()<a.size()+s) c.resize(a.size()+s);
	for(int i=0; i<a.size(); i++)
		c[i+s]=(c[i+s]+a[i])%mod;
	return ;
}
int fa[MAXN],dep[MAXN],siz[MAXN];
Poly a[MAXN];
void Dfs1(int u){
	for(int i=h[u]; i; i=nx[i]){
		int v=to[i];
		if(v==fa[u]) continue;
		fa[v]=u;
		dep[v]=dep[u]+1;
		Dfs1(v);
	}
	return ;
}
int cen;
bool vis[MAXN];
int getrt(int u,int s){
	siz[u]=1;
	int mx=0;
	for(int i=h[u]; i; i=nx[i]){
		int v=to[i];
		if(vis[v]||v==fa[u]) continue;
		fa[v]=u;
		getrt(v,s);
		mx=max(mx,siz[v]);
		siz[u]+=siz[v];
	}
	mx=max(mx,s-siz[u]);
	if(mx<=s/2) cen=u;
	return cen;
}
Poly cnt;
void Add(int co){
	cnt=cnt*cnt;
	if(cnt.size()>n) cnt.resize(n);
	for(int i=1; i<cnt.size(); i++)
		ans[i]=(ans[i]+1ll*cnt[i]*co+mod)%mod;
	cnt.clear();
	return ;
}
void Dfs2(int u){
	siz[u]=1;
	if(dep[u]<cnt.size()) cnt[dep[u]]++;
	else cnt.push_back(1);
	for(int i=h[u]; i; i=nx[i]){
		int v=to[i];
		if(vis[v]||v==fa[u]) continue;
		fa[v]=u;
		dep[v]=dep[u]+1;
		Dfs2(v);
		siz[u]+=siz[v];
	}
	return ;
}
void Divide(int u){
	vis[u]=1;
	fa[u]=0;
	dep[u]=0;
	Dfs2(u);
	Add(1);
	for(int i=h[u]; i; i=nx[i]){
		int v=to[i];
		if(vis[v]) continue;
		cnt.push_back(0);
		Dfs2(v);
		Add(-1);
		v=getrt(v,siz[v]);
		Divide(v);
	}
	return ;
}
Poly f[MAXN<<2],g[MAXN<<2];
#define lc k<<1
#define rc k<<1|1
#define ls lc,l,mid
#define rs rc,mid+1,r
#define Clear() f[lc].clear(),f[rc].clear(),g[lc].clear(),g[rc].clear()
void Dfs3(int k,int l,int r){
	//for(int i=l; i<=r; i++) for(int j=i+1; j<=r; j++) ans=ans+Shift(a[i]*a[j],j-i); return ;
	if(l==r){
		f[k]=g[k]=a[l];
		return ;
	}
	int mid=l+r>>1;
	Dfs3(ls);
	Dfs3(rs);
	ad(ans,g[lc],f[rc],1);
	swap(f[k],f[lc]);
	ad(f[k],f[rc],mid-l+1);
	swap(g[k],g[rc]);
	ad(g[k],g[lc],r-mid);
	Clear();
	return ;
}
void Dfs4(int k,int l,int r){
	//for(int i=1; i<=m2; i++) for(int j=i+1; j<=m2; j++) ans=ans+Shift(a[i+m2]*a[j],i+m2-j); return ;
	if(l==r){
		f[k]=a[l+m2];
		g[k]=a[l];
		return ;
	}
	int mid=l+r>>1;
	Dfs4(ls);
	Dfs4(rs);
	ad(ans,f[lc],g[rc],l+m2-r);
	swap(f[k],f[lc]);
	ad(f[k],f[rc],mid-l+1);
	swap(g[k],g[rc]);
	ad(g[k],g[lc],r-mid);
	Clear();
	return ;
}
void Dfs5(int k,int l,int r){
	//for(int i=1; i<=m2; i++) for(int j=i+1; j<=m2; j++) ans=ans+Shift(a[i]*a[j+m2],i+m-j-m2); return ;
	if(l==r){
		f[k]=a[l];
		g[k]=a[l+m2];
		return ;
	}
	int mid=l+r>>1;
	Dfs5(ls);
	Dfs5(rs);
	ad(ans,f[lc],g[rc],l+m-r-m2);
	swap(f[k],f[lc]);
	ad(f[k],f[rc],mid-l+1);
	swap(g[k],g[rc]);
	ad(g[k],g[lc],r-mid);
	Clear();
	return ;
}
int main(){
	//freopen("sub16.in","r",stdin);
	//freopen("b.out","w",stdout);
	scanf("%d%d",&n,&K);
	ans.resize(n+1);
	for(int i=1; i<=n; i++)
		pre[i]=i;
	for(int i=1; i<=n; i++){
		int &u=ed[i][0],&v=ed[i][1];
		scanf("%d%d",&u,&v);
		int x=fnd(u),y=fnd(v);
		if(x==y) ed[0][0]=u,ed[0][1]=v;
		else pre[x]=y,adde(u,v),adde(v,u);
	}
	Dfs1(ed[0][0]);
	int p=ed[0][1];
	while(p!=ed[0][0]){
		lp[++m]=p;
		p=fa[p];
	}
	lp[++m]=ed[0][0];
	for(int i=1; i<=m; i++)
		tl[lp[i]]=i,vis[lp[i]]=1;
	for(int i=1; i<=n; i++){
		int u=i;
		while(!tl[u]) u=fa[u];
		int t=tl[u];
		u=i;
		while(!tl[u]){
			tl[u]=t;
			u=fa[u];
		}
		int d=dep[i]-dep[lp[t]];
		if(d>=a[t].size()) a[t].resize(d+1);
		a[t][d]++;
	}
	//printf("%.2f\n",(double)(clock())/CLOCKS_PER_SEC);
	for(int i=1; i<=m; i++)
		Divide(lp[i]);
	//printf("%.2f\n",(double)(clock())/CLOCKS_PER_SEC);
	for(int i=1; i<=n; i++)
		ans[i]=ans[i]*(mod+1ll)/2%mod;
	if(m>1){
		//for(int i=1; i<=m; i++) for(int j=i+1; j<=m; j++) ans=ans+Shift(a[i]*a[j],min(j-i,i+m-j));
		m2=m/2;
		for(int i=1; i<=m2; i++)
			ad(ans,a[i],a[i+m2],m2);
		//printf("%.2f\n",(double)(clock())/CLOCKS_PER_SEC);
		Dfs3(1,1,m2);
		//printf("3 %.2f\n",(double)(clock())/CLOCKS_PER_SEC);
		Dfs3(1,m2+1,m2*2);
		//printf("3 %.2f\n",(double)(clock())/CLOCKS_PER_SEC);
		Dfs4(1,1,m2);
		//printf("4 %.2f\n",(double)(clock())/CLOCKS_PER_SEC);
		Dfs5(1,1,m2);
		//printf("5 %.2f\n",(double)(clock())/CLOCKS_PER_SEC);
		if(m&1){
			Poly t(n);
			for(int i=1; i<=m2; i++){
				for(int j=0; j<a[i].size(); j++)
					t[i+j]=(t[i+j]+a[i][j])%mod;
				for(int j=0; j<a[i+m2].size(); j++)
					t[m-i-m2+j]=(t[m-i-m2+j]+a[i+m2][j])%mod;
			}
			ad(ans,t,a[m],0);
		}
		//printf("odd %.2f\n",(double)(clock())/CLOCKS_PER_SEC);
	}
	int as=0;
	for(int i=1; i<n; i++)
		as=(as+Fstpw(i,K)*ans[i])%mod;
	as=as%mod;
	printf("%d\n",as);
	//printf("%.2f\n",(double)(clock())/CLOCKS_PER_SEC);
	//printf("ntt %.2f\n",(double)(clk)/CLOCKS_PER_SEC);
	return 0;
}
, In this Programming Language: C++, Now tell me if this Code is compilable or not?