CF921 D. Good Trip

题面

代码

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#include<bits/stdc++.h>
using namespace std;
#define IOS ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define rep(i,a,n) for(int i=a;i<=n;i++)
#define per(i,a,n) for(int i=n;i>=a;i--)
#define first fi
#define seconf se 
#define push_back pb
#define endl "\n"
#define O(x) cout<<#x<<":"<<x<<endl;
using ll=long long;
using pii=pair<int,int>;
using pll=pair<ll,ll>;
#define N 200100
#define MOD int(1e9+7)
ll f[N],g[N];
ll ksm(ll a,ll b,ll mod=MOD){
	if(b==0) return 1;
	if(b==1) return a%mod;
	ll mid=ksm(a,b>>1,mod);
	if(b&1) return mid*mid%mod*a%mod;
	else return mid*mid%mod;
}
ll inv(ll a,ll mod=MOD){
	return ksm(a,mod-2,mod);
}
ll om(ll a,ll mod=MOD){
	return (a%mod+mod)%mod;
}
void Init(){
	f[0]=1;
	rep(i,1,200000) f[i]=om(f[i-1]*i);
	//rep(i,1,100) O(f[i])
	g[200000]=inv(f[200000]);
	per(i,0,199999) g[i]=om(g[i+1]*(i+1));
	//O(g[1])
}
ll C(ll n,ll m){
	if(n<m) return 0;
	return om(om(f[n]*g[m])*g[n-m]);
}
void solve()
{
	int n,m,k; ll ans1=0;
	cin>>n>>m>>k;
	vector<ll> f1(m+1);
	rep(i,1,m){
		int a,b;
		cin>>a>>b>>f1[i];
		ans1=om(ans1+f1[i]);
	}
	//O(ans1)
	ans1=om(ans1*k),ans1=om(ans1*inv(C(n,2)));
	//O(ans1)
	ll ans2=0;
	rep(i,0,k){
		ll v1=C(k,i);
		ll d=C(n,2);
		ll v2=ksm(inv(d),i);
		ll v3=ksm(om(1-inv(d)),k-i);
		ll v4=om(om(1ll*i*(i-1))*inv(2));
		ans2=om(ans2+om(om(om(v1*v2)*v3)*v4));
	}
	cout<<om(ans1+om(1ll*m*ans2))<<endl;
}
int main()
{
	IOS
	Init();
	int t=1;cin>>t;
	while(t--) {
		solve();
	//O(t)	
	}
	return 0;
}