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:
#include <cstdio>
#define Maxn 200000
#define ll long long
int n,k;
ll m;
int fa[Maxn+5],left[Maxn+5],right[Maxn+5];
int ask(int x){
	return x==fa[x]?x:fa[x]=ask(fa[x]);
}
int main(){
	scanf("%d%lld%d",&n,&m,&k);
	int ds=n;
	int a,b,c;
	int len=0;
	for(int i=0;i<n;i++){
		fa[i]=i;
	}
	while(k--){
		scanf("%d%d%d",&a,&b,&c);
		int p=ask(a),q=ask(b);
		if(c==0&&p!=q){
			ds--;
			fa[q]=p;
		}
		if(c==1){
			left[++len]=a;
			right[len]=b;
		}
	}
	for(int i=1;i<=len;i++){
		if(ask(left[i])==ask(right[i])){
			puts("No");
			return 0;
		}
	}
	if((m+ds-n>1ll*ds*(ds-1)/2)||(len&&(ds==2||m<n))){
		puts("No");
	}
	else{
		puts("Yes");
	}
	return 0;
}