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<bits/stdc++.h>
int n,k,a,b,c,ds,fa[200010],L[200010],R[200010],d;
int ask(int x){return x==fa[x]?x:fa[x]=ask(fa[x]);}
long long m;
int main(){
    scanf("%d%lld%d",&n,&m,&k);ds=n;
    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)L[++d]=a,R[d]=b;
    }
    for(int i=1;i<=d;i++)if(ask(L[i])==ask(R[i]))return puts("No"),0;
    puts((m+ds-n>1ll*ds*(ds-1)/2)||(d&&(ds==2||m<n))?"No":"Yes");
    return 0;
}