#include<bits/stdc++.h>
using namespace std;
using ll=long long;
struct DSU{
	int n;
	vector<int> par,siz;
	DSU(int n):n(n){
		par.resize(n);
		siz.resize(n,1);
		for(int i=0;i<n;i++){
			par[i]=i;
		}
	}	
	int find(int x){
		if(par[x]==x){
			return x;
		}
		return par[x]=find(par[x]);
	}
	void unite(int u,int v){
		u=find(u),v=find(v);
		if(u==v){
			return;
		}
		if(siz[u]<siz[v]){
			swap(u,v);
		}
		siz[u]+=siz[v];
		par[v]=u;
	}
};
int main(){
	ll n,m,q;cin>>n>>m>>q;
	vector<int> a(q),b(q),c(q);
	DSU uf(n);
	for(int i=0;i<q;i++){
		cin>>a[i]>>b[i]>>c[i];
		if(c[i]==0){
			uf.unite(a[i],b[i]);
		}
	}
	ll s=0;
	for(int i=0;i<n;i++){
		if(uf.find(i)!=i){
			continue;
		}
		s++;
		m-=uf.siz[i]-1;
	}
	set<int> st;
	for(int i=0;i<q;i++){
		if(c[i]==1){
			if(uf.find(a[i])==uf.find(b[i])){
				cout<<"No"<<endl;
				return 0;
			}
			st.insert(uf.find(a[i]));
			st.insert(uf.find(b[i]));
		}
	}
	ll lb=st.size(),ub=s*(s-1LL)/2LL;
	//cout<<lb<<" "<<m<<" "<<ub<<endl;
	if(lb<=m&&m<=ub){
		cout<<"Yes"<<endl;
	}else{
		cout<<"No"<<endl;
	}
}

### Prompt

Generate a CPP solution to the following problem:

Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.

One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 \leq i \leq Q-1) is represented as integers A_i,B_i,C_i and means the following:

* If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
* If C_i=1: there were two or more simple paths from Vertex A_i to B_i.



Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.

Constraints

* 2 \leq N \leq 10^5
* N-1 \leq M \leq N \times (N-1)/2
* 1 \leq Q \leq 10^5
* 0 \leq A_i,B_i \leq N-1
* A_i \neq B_i
* 0 \leq C_i \leq 1
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M Q
A_0 B_0 C_0
A_1 B_1 C_1
\vdots
A_{Q-1} B_{Q-1} C_{Q-1}


Output

If there exists a graph that matches Snuke's memory, print `Yes`; otherwise, print `No`.

Examples

Input

5 5 3
0 1 0
1 2 1
2 3 0


Output

Yes


Input

4 4 3
0 1 0
1 2 1
2 3 0


Output

No


Input

10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0


Output

No

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
using ll=long long;
struct DSU{
	int n;
	vector<int> par,siz;
	DSU(int n):n(n){
		par.resize(n);
		siz.resize(n,1);
		for(int i=0;i<n;i++){
			par[i]=i;
		}
	}	
	int find(int x){
		if(par[x]==x){
			return x;
		}
		return par[x]=find(par[x]);
	}
	void unite(int u,int v){
		u=find(u),v=find(v);
		if(u==v){
			return;
		}
		if(siz[u]<siz[v]){
			swap(u,v);
		}
		siz[u]+=siz[v];
		par[v]=u;
	}
};
int main(){
	ll n,m,q;cin>>n>>m>>q;
	vector<int> a(q),b(q),c(q);
	DSU uf(n);
	for(int i=0;i<q;i++){
		cin>>a[i]>>b[i]>>c[i];
		if(c[i]==0){
			uf.unite(a[i],b[i]);
		}
	}
	ll s=0;
	for(int i=0;i<n;i++){
		if(uf.find(i)!=i){
			continue;
		}
		s++;
		m-=uf.siz[i]-1;
	}
	set<int> st;
	for(int i=0;i<q;i++){
		if(c[i]==1){
			if(uf.find(a[i])==uf.find(b[i])){
				cout<<"No"<<endl;
				return 0;
			}
			st.insert(uf.find(a[i]));
			st.insert(uf.find(b[i]));
		}
	}
	ll lb=st.size(),ub=s*(s-1LL)/2LL;
	//cout<<lb<<" "<<m<<" "<<ub<<endl;
	if(lb<=m&&m<=ub){
		cout<<"Yes"<<endl;
	}else{
		cout<<"No"<<endl;
	}
}

```