#include<bits/stdc++.h>
using namespace std;
#define ll long long
const int N=114514;
int fa[N],u[N],v[N],t[N];
int n,q;
ll num,cnt,m;
int find(int x){
	return fa[x]==x?x:fa[x]=find(fa[x]);
}
void merge(int x,int y){
	if(x!=y) num--,fa[x]=y,cnt++;
} 
int main(){
	scanf("%d%d%d",&n,&m,&q);num=n;
	for(int i=1;i<=n;i++)fa[i]=i;
	for(int i=1;i<=q;i++){
		scanf("%d%d%d",&u[i],&v[i],&t[i]);u[i]++,v[i]++;
		if(!t[i]) merge(find(u[i]),find(v[i])),q--,i--;
	}
	if(m<=n-1){
		if(m<n-1)puts("No");
		else if(!q) puts("Yes");
		else puts("No");
		return 0;
	}for(int i=1;i<=q;i++){
		if(find(u[i])==find(v[i])){
			puts("No");return 0;
		}
	}ll r=1ll*cnt+((num*(num-1))/2);
	if(m>=n&&m<=r)puts("Yes");
	else puts("No");
	return 0;
}
### Prompt

In cpp, your task is to solve 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;
#define ll long long
const int N=114514;
int fa[N],u[N],v[N],t[N];
int n,q;
ll num,cnt,m;
int find(int x){
	return fa[x]==x?x:fa[x]=find(fa[x]);
}
void merge(int x,int y){
	if(x!=y) num--,fa[x]=y,cnt++;
} 
int main(){
	scanf("%d%d%d",&n,&m,&q);num=n;
	for(int i=1;i<=n;i++)fa[i]=i;
	for(int i=1;i<=q;i++){
		scanf("%d%d%d",&u[i],&v[i],&t[i]);u[i]++,v[i]++;
		if(!t[i]) merge(find(u[i]),find(v[i])),q--,i--;
	}
	if(m<=n-1){
		if(m<n-1)puts("No");
		else if(!q) puts("Yes");
		else puts("No");
		return 0;
	}for(int i=1;i<=q;i++){
		if(find(u[i])==find(v[i])){
			puts("No");return 0;
		}
	}ll r=1ll*cnt+((num*(num-1))/2);
	if(m>=n&&m<=r)puts("Yes");
	else puts("No");
	return 0;
}
```