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 PYTHON3):

Solution:
import sys
input=sys.stdin.readline

class UnionFind:
    def __init__(self,n):
        self.par=[i for i in range(n)]
        self.rank=[0]*n
    def find(self,x):
        if self.par[x]==x:
            return x
        else:
            self.par[x]=self.find(self.par[x])
            return self.par[x]
    def union(self,x,y):
        x=self.find(x)
        y=self.find(y)
        if x==y:
            return
        if self.rank[x]<self.rank[y]:
            self.par[x]=y
        else:
            self.par[y]=x
            if self.rank[x]==self.rank[y]:
                self.rank[x]+=1
    def same_check(self,x,y):
        return self.find(x)==self.find(y)

def main():
    n,m,q=map(int,input().split())
    E=[]
    uf=UnionFind(n)
    for _ in range(q):
        a,b,c=map(int,input().split())
        if c:
            E.append((a,b)) 
        else:
            uf.union(a,b)
    s=set()
    for i in range(n):
        s.add(uf.find(i))
    k=len(s)
    if E and (k<=2 or m==n-1):
        print('No')
        return
    for a,b in E:
        if uf.same_check(a,b):
            print('No')
            return
    print('Yes' if m<=n+k*(k-3)//2 else 'No')

if __name__=='__main__':
    main()