傳送門

題解：
把 $({\sum }_i{x}_i{)}^k$

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;

const int RLEN=1<<18|1;
inline char nc() {
	static char ibuf[RLEN],*ib,*ob;
	(ib==ob) && (ob=(ib=ibuf)+fread(ibuf,1,RLEN,stdin));
	return (ib==ob) ? -1 : *ib++;
}
inline int rd() {
	char ch=nc(); int i=0,f=1;
	while(!isdigit(ch)) {if(ch=='-')f=-1; ch=nc();}
	while(isdigit(ch)) {i=(i<<1)+(i<<3)+ch-'0'; ch=nc();}
	return i*f;
}

const int N=1e5+50, mod=3e5+50;
inline int add(int x,int y) {return (x+y>=mod) ? (x+y-mod) : (x+y);}
inline int dec(int x,int y) {return (x-y<0) ? (x-y+mod) : (x-y);}
inline int mul(int x,int y) {return (long long)x*y%mod;}
inline int power(int a,int b,int rs=1) {for(;b;b>>=1,a=mul(a,a)) if(b&1) rs=mul(rs,a); return rs;}

int n,m,k,ans,s[4][4];
vector <int> edge[N];
inline void init() {
	n=rd(), m=rd(), k=rd(); ans=0;
	for(int i=1;i<=n;i++) edge[i].clear();
	for(int i=1;i<=m;i++) {
		int x=rd(), y=rd();
		edge[x].push_back(y);
		edge[y].push_back(x);
	}
}
vector <int> g[N];
int vis[N],vs;
inline LL calc_ring() {
	for(int i=1;i<=n;i++) g[i].clear();
	for(int i=1;i<=n;i++)
		for(auto v:edge[i]) {
			if(edge[i].size()>edge[v].size()) continue;
			else if(edge[i].size()<edge[v].size()) g[i].push_back(v);
			else if(i<v) g[i].push_back(v);
		}
	LL cnt=0;
	for(int i=1;i<=n;i++) {
		++vs;
		for(auto v:g[i]) vis[v]=vs;
		for(auto v:g[i]) for(auto u:g[v])
			if(vis[u]==vs) ++cnt;
	} return cnt;
}
inline void solve() {
	init();
	ans=mul(s[k][1],mul(m,power(2,n-2)));
	if(k>=2 && m>=2) {
		LL cnt=0;
		for(int i=1;i<=n;i++)
			for(auto v:edge[i])
				cnt+=edge[v].size()-1;
		cnt/=2;
		if(cnt) ans=add(ans,mul(mul(s[k][2],2),mul(cnt%mod,power(2,n-3))));
		cnt=(LL)m*(m-1)/2-cnt;
		if(cnt) ans=add(ans,mul(mul(s[k][2],2),mul(cnt%mod,power(2,n-4))));
	}
	if(k>=3 && m>=3) {
		LL c34=0, c35=0, c33=0, c36=0;
		
		
		c33=calc_ring();
		if(c33) ans=add(ans,mul(mul(s[k][3],6),mul(c33%mod,power(2,n-3))));
		
		for(int i=1;i<=n;i++) 
			for(auto v:edge[i])
				c34+=(LL)(edge[i].size()-1)*(edge[v].size()-1);
		c34/=2;
		for(int i=1;i<=n;i++) {
			int t=edge[i].size();
			c34+=(LL)t*(t-1)*(t-2)/6;
		}
		c34-=c33*3;
		if(c34) ans=add(ans,mul(mul(s[k][3],6),mul(c34%mod,power(2,n-4))));
		
		for(int i=1;i<=n;i++) {
			LL ban_edge=0;
			for(int j=0;j<edge[i].size();++j) {
				int v=edge[i][j];
				c35+=j*(m-edge[i].size()-edge[v].size()+1)-ban_edge;
				ban_edge+=edge[v].size()-1; 
			}
		}
		c35+=c33*3;
		if(c35) ans=add(ans,mul(mul(s[k][3],6),mul(c35%mod,power(2,n-5))));
		
		c36=(LL)m*(m-1)*(m-2)/6-c33-c34-c35;
		if(c36) ans=add(ans,mul(mul(s[k][3],6),mul(c36%mod,power(2,n-6))));
	} cout<<ans<<'\n';
}
int main() {
	s[0][0]=s[1][1]=1; 
	s[2][1]=s[2][2]=1;
	s[3][1]=s[3][3]=1; s[3][2]=3;
	for(int T=rd();T;T--) solve();
}