#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
#include <bits/stdc++.h>
using namespace std;
template<class t> inline t read(t &x){
	char c=getchar();bool f=0;x=0;
	while(!isdigit(c)) f|=c=='-',c=getchar();
	while(isdigit(c)) x=(x<<1)+(x<<3)+(c^48),c=getchar();
	if(f) x=-x;return x;
}
template<class t,class ...A> inline void read(t &x,A &...a){
	read(x);read(a...);
}
template<class t> inline void write(t x){
	if(x<0) putchar('-'),write(-x);
	else{if(x>9) write(x/10);putchar('0'+x%10);}
}

#define int long long

const int N=1e5+5;
int a[N],b[N],c[N],n,m,q,sz,f[N],c0;

void OK(){
	puts("Yes");
	exit(0);
}

void GG(){
	puts("No");
	exit(0);
}

int getf(int x){
	if(f[x]==x) return x;
	return f[x]=getf(f[x]);
}

bool merge(int x,int y){
	x=getf(x);y=getf(y);
	if(x==y) return 0;
	f[x]=y;sz--;
	return 1;
}

signed main(){
	read(n,m,q);sz=n;
	for(int i=1;i<=n;i++) f[i]=i;
	for(int i=1;i<=q;i++){
		read(a[i],b[i],c[i]);
		if(!c[i]) c0++,merge(a[i],b[i]);
	}
	if(m<=n-1){
		if(m<n-1) GG();
		if(q==c0) OK();
		GG();
	}
	int l=n,r=n-sz+sz*(sz-1)/2;
	for(int i=1;i<=q;i++) if(c[i]&&getf(a[i])==getf(b[i])) GG();
	if(m>=l&&m<=r) OK();
	else GG();
}
### 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
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
#include <bits/stdc++.h>
using namespace std;
template<class t> inline t read(t &x){
	char c=getchar();bool f=0;x=0;
	while(!isdigit(c)) f|=c=='-',c=getchar();
	while(isdigit(c)) x=(x<<1)+(x<<3)+(c^48),c=getchar();
	if(f) x=-x;return x;
}
template<class t,class ...A> inline void read(t &x,A &...a){
	read(x);read(a...);
}
template<class t> inline void write(t x){
	if(x<0) putchar('-'),write(-x);
	else{if(x>9) write(x/10);putchar('0'+x%10);}
}

#define int long long

const int N=1e5+5;
int a[N],b[N],c[N],n,m,q,sz,f[N],c0;

void OK(){
	puts("Yes");
	exit(0);
}

void GG(){
	puts("No");
	exit(0);
}

int getf(int x){
	if(f[x]==x) return x;
	return f[x]=getf(f[x]);
}

bool merge(int x,int y){
	x=getf(x);y=getf(y);
	if(x==y) return 0;
	f[x]=y;sz--;
	return 1;
}

signed main(){
	read(n,m,q);sz=n;
	for(int i=1;i<=n;i++) f[i]=i;
	for(int i=1;i<=q;i++){
		read(a[i],b[i],c[i]);
		if(!c[i]) c0++,merge(a[i],b[i]);
	}
	if(m<=n-1){
		if(m<n-1) GG();
		if(q==c0) OK();
		GG();
	}
	int l=n,r=n-sz+sz*(sz-1)/2;
	for(int i=1;i<=q;i++) if(c[i]&&getf(a[i])==getf(b[i])) GG();
	if(m>=l&&m<=r) OK();
	else GG();
}
```