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

Solution (in CPP):

Solution:
/*Lucky_Glass*/
#include<vector>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

const int N=1e5;

int n,q;
long long m;
bool B1;

struct MERGESET{
	int Mfa[N+3],Msiz[N+3];
	void Init(int Nn){
		for(int i=1;i<=Nn;i++)
			Mfa[i]=i,Msiz[i]=1;
	}
	int FindFa(int u){
		if(u==Mfa[u]) return u;
		return Mfa[u]=FindFa(Mfa[u]);
	}
	bool Merge(int u,int v){
		int Fu=FindFa(u),Fv=FindFa(v);
		if(Fu==Fv) return false;
		Mfa[Fu]=Fv;
		Msiz[Fv]+=Msiz[Fu];
		Msiz[Fu]=0;
		return true;
	}
}Mset;

vector< pair<int,int> > Opt1;

int main(){
	scanf("%d%lld%d",&n,&m,&q);
	Mset.Init(n);
	for(int i=1;i<=q;i++){
		int u,v,tmp;
		scanf("%d%d%d",&u,&v,&tmp);
		u++;v++;
		if(tmp)
			Opt1.emplace_back(u,v),
			B1=true;
		else
			Mset.Merge(u,v);
	}
	for(auto it : Opt1){
		int u=it.first,v=it.second;
		int Fu=Mset.FindFa(u),Fv=Mset.FindFa(v);
		if(Fu==Fv){
			printf("No\n");
			return 0;
		}
	}
	long long Etot=0,Etre=0;
	for(int i=1;i<=n;i++)
		if(Mset.Msiz[i])
			Etot+=Mset.Msiz[i]-1,
			Etre++;
	if(B1){
		if(Etot+Etre<=m && m<=Etot+Etre*(Etre-1)/2)
			printf("Yes\n");
		else
			printf("No\n");
	}
	else{
		if(Etot+Etre-1<=m && m<=Etot+Etre*(Etre-1)/2)
			printf("Yes\n");
		else
			printf("No\n");
	}
	return 0;
}