#include<bits/stdc++.h>
#define ll long long
#define ull unsigned ll
#define uint unsigned
#define pii pair<int,int>
#define pll pair<ll,ll>
#define PB push_back
#define fi first
#define se second
#define For(i,j,k) for (int i=(int)(j);i<=(int)(k);i++)
#define Rep(i,j,k) for (int i=(int)(j);i>=(int)(k);i--)
#define CLR(a,v) memset(a,v,sizeof(a));
#define CPY(a,b) memcpy(a,b,sizeof(a));
using namespace std;
const int N=100005;
int n,Q,con,fa[N];
vector<pii> E;
ll m;
int get(int x){
	return x==fa[x]?x:fa[x]=get(fa[x]);
}
int main(){
	scanf("%d%lld%d",&n,&m,&Q); con=n;
	For(i,1,n) fa[i]=i;
	For(i,1,Q){
		int x,y,v;
		scanf("%d%d%d",&x,&y,&v);
		++x; ++y;
		if (v==0){
			x=get(x); y=get(y);
			if (x!=y) fa[x]=y,--con;
		}
		else
			E.PB(pii(x,y));
	}
	if (m==n-1){
		puts(E.size()?"No":"Yes");
		return 0;
	}
	For(i,0,E.size()-1){
		int x=get(E[i].fi);
		int y=get(E[i].se);
		if (x==y) return puts("No"),0;
	}
	ll up=1ll*con*(con-1)/2+n-con;
	puts(up>=m?"Yes":"No");
} 
### Prompt

Your task is to create 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>
#define ll long long
#define ull unsigned ll
#define uint unsigned
#define pii pair<int,int>
#define pll pair<ll,ll>
#define PB push_back
#define fi first
#define se second
#define For(i,j,k) for (int i=(int)(j);i<=(int)(k);i++)
#define Rep(i,j,k) for (int i=(int)(j);i>=(int)(k);i--)
#define CLR(a,v) memset(a,v,sizeof(a));
#define CPY(a,b) memcpy(a,b,sizeof(a));
using namespace std;
const int N=100005;
int n,Q,con,fa[N];
vector<pii> E;
ll m;
int get(int x){
	return x==fa[x]?x:fa[x]=get(fa[x]);
}
int main(){
	scanf("%d%lld%d",&n,&m,&Q); con=n;
	For(i,1,n) fa[i]=i;
	For(i,1,Q){
		int x,y,v;
		scanf("%d%d%d",&x,&y,&v);
		++x; ++y;
		if (v==0){
			x=get(x); y=get(y);
			if (x!=y) fa[x]=y,--con;
		}
		else
			E.PB(pii(x,y));
	}
	if (m==n-1){
		puts(E.size()?"No":"Yes");
		return 0;
	}
	For(i,0,E.size()-1){
		int x=get(E[i].fi);
		int y=get(E[i].se);
		if (x==y) return puts("No"),0;
	}
	ll up=1ll*con*(con-1)/2+n-con;
	puts(up>=m?"Yes":"No");
} 
```