#include<bits/stdc++.h>
using namespace std;
#define maxn 100000
#define LL long long
int fa[maxn+5],a[maxn+5],b[maxn+5],c[maxn+5];
int Find(int x){
	return fa[x]==x?x:fa[x]=Find(fa[x]);
}
int main(){
	int n,q,u,v,cnt;LL m;scanf("%d%lld%d",&n,&m,&q),cnt=n;
	for(int i=0;i<n;i++)fa[i]=i;
	bool fl=0;
	for(int i=0;i<q;i++)scanf("%d%d%d",a+i,b+i,c+i),fl|=c[i];
	if(fl&&m==n-1){puts("No");return 0;}
	for(int i=0;i<q;i++){
		if(c[i])continue;
		int x=Find(a[i]),y=Find(b[i]);
		if(x!=y)fa[x]=y,cnt--;
	}
	for(int i=0;i<q;i++){
		if(!c[i])continue;
		int x=Find(a[i]),y=Find(b[i]);
		if(x==y){puts("No");return 0;}
	}
	if(fl&&cnt==2||m>(n-cnt)+1ll*cnt*(cnt-1)/2){puts("No");return 0;}
	puts("Yes");
	return 0;
} 
### Prompt

Please provide a cpp coded solution to the problem described below:

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;
#define maxn 100000
#define LL long long
int fa[maxn+5],a[maxn+5],b[maxn+5],c[maxn+5];
int Find(int x){
	return fa[x]==x?x:fa[x]=Find(fa[x]);
}
int main(){
	int n,q,u,v,cnt;LL m;scanf("%d%lld%d",&n,&m,&q),cnt=n;
	for(int i=0;i<n;i++)fa[i]=i;
	bool fl=0;
	for(int i=0;i<q;i++)scanf("%d%d%d",a+i,b+i,c+i),fl|=c[i];
	if(fl&&m==n-1){puts("No");return 0;}
	for(int i=0;i<q;i++){
		if(c[i])continue;
		int x=Find(a[i]),y=Find(b[i]);
		if(x!=y)fa[x]=y,cnt--;
	}
	for(int i=0;i<q;i++){
		if(!c[i])continue;
		int x=Find(a[i]),y=Find(b[i]);
		if(x==y){puts("No");return 0;}
	}
	if(fl&&cnt==2||m>(n-cnt)+1ll*cnt*(cnt-1)/2){puts("No");return 0;}
	puts("Yes");
	return 0;
} 
```