You are given a tree consisting of n nodes numbered from 1 to n. The weights of edges of the tree can be any binary integer satisfying following Q conditions.

- 
		Each condition is of form u, v, x where u, v are nodes of the tree and x is a binary number. 

		For satisfying this condition,  sum of the weight of all the edges present in the path from node u to v of the tree, should have even if x = 0, odd otherwise. 
	

Now, you have to find out number of ways of assigning 0/1 (binary) weights to the edges of the tree satisfying the above conditions.
As the answer could be quite large, print your answer modulo 109 + 7.

-----Input-----
- The first line of input contains a single integer T denoting number of test cases.
- For each test case:
	
- First line contains two space separated integers n, Q.
- Each of the next n - 1 lines will contain two space separated integer  u, v denoting that there is an edge between vertex u and v in the tree.
- Each of the next Q lines will contain three space separated integer  u, v, x denoting a condition as stated in the probelm.

-----Output-----
- For each test case, output a single integer corresponding to the answer of the problem.

-----Constraints-----
- 1 ≤ u, v ≤ n
- 0 ≤ x ≤ 1

-----Subtasks-----
Subtask #1 : (10 points)
- Sum of each of variables n and Q over all the test cases ≤ 20

Subtask #2 : (20 points)
- Sum of each of variables n and Q over all the test cases ≤ 100

Subtask #3 : (30 points)
- Sum of each of variables n and Q over all the test cases ≤ 5000

Subtask #4 : (40 points)
- Sum of each of variables n and Q over all the test cases ≤ 100000

-----Example-----
Input:
3
3 2
1 2
1 3
1 2 0
1 3 0
3 0
1 2
2 3
3 1
1 2
2 3
1 2 1

Output:
1
4
2

-----Explanation-----
In the first example, 
You can only set the weight of each edge equal to 0 for satisfying the given condition. So, there is exactly one way of doing this. Hence answer is 1.

In the second example, 
There are two edges and there is no condition on the edges. So, you can assign them in 4 ways. 

In the third example, 
You have to assign the weight of edge between node 1 and 2 to 1. You can assign the remaining edge from 2 to 3 either 0 or 1. So, the answer is 2.

Difficulty: interview

Starter code:

Solutions:
import sys

def powc(x,n,m):
  res = 1
  xx=x
  while n:
    if n&1:
      res = (res*xx)%m
    xx=xx*xx%m
    n >>= 1
  return res

def circles(u):
  r = 0
  S = [(u,-1,0)]
  Visited[u] = 0
  for s in S:
    for e in V[s[0]]:
      if e[0] != s[1]:
        if Visited[e[0]]==-1: 
          Visited[e[0]] = s[2]^e[1]
          S.append((e[0], s[0], s[2]^e[1])) 
        elif Visited[e[0]] != s[2]^e[1]:
          return -1
        else:
          r += s[0]<e[0]
  return r

T = int(sys.stdin.readline())
for _ in range(T):
  is_bad = False
  empty = 0
  n,Q = list(map(int, sys.stdin.readline().split()))
  for _ in range(n-1):
    sys.stdin.readline() 
  paths = []
  V=list(map(list,[[]]*n))
  for q in range(Q):
    u,v,x = list(map(int, sys.stdin.readline().split()))
    u-=1
    v-=1
    if (v,x^1) in V[u]:
      is_bad = True
    elif (v,x) in V[u]:
      empty += 1
    elif u!=v:
      V[u].append((v,x))
      V[v].append((u,x))
    elif x==1:
      is_bad = True
    else:
      empty += 1
    paths.append((u,v,x))
  if is_bad:
    print(0)
  elif n<=1:
    print(1)
  else:
    Visited = [-1]*n
    components = 0
    for i in range(n):
      if Visited[i]==-1:
        components += 1
        c = circles(i)
        if c==-1:
          is_bad = True
          break
        empty += c
    if is_bad:
      print(0)
    else:
      print(powc(2,n-1-(Q-empty),10**9+7)) 


import sys

def powc(x,n,m):
  res = 1
  xx=x
  while n:
    if n&1:
      res = (res*xx)%m
    xx=xx*xx%m
    n >>= 1
  return res

def circles(u):
  r = 0
  S = [(u,-1,0)]
  Been = [-1]*n
  Been[u] = 0
  for s in S:
    Visited[s[0]] = 1
    for e in V[s[0]]:
      if e[0] != s[1]:
        if Been[e[0]]==-1: 
          Been[e[0]] = s[2]^e[1]
          S.append((e[0], s[0], s[2]^e[1])) 
        elif Been[e[0]] != s[2]^e[1]:
          return -1
        else:
          r += s[0]<e[0]
  return r

T = int(sys.stdin.readline())
for _ in range(T):
  is_bad = False
  empty = 0
  n,Q = list(map(int, sys.stdin.readline().split()))
  for _ in range(n-1):
    sys.stdin.readline() 
  paths = []
  V=list(map(list,[[]]*n))
  E = []
  for q in range(Q):
    u,v,x = list(map(int, sys.stdin.readline().split()))
    u-=1
    v-=1
    if (v,x^1) in V[u]:
      is_bad = True
    elif (v,x) in V[u]:
      empty += 1
    elif u!=v:
      E.append((u,v,x))
      V[u].append((v,x))
      V[v].append((u,x))
    elif x==1:
      is_bad = True
    else:
      empty += 1
    paths.append((u,v,x))
  if is_bad:
    print(0)
  elif n<=1:
    print(1)
  else:
    Visited = [0]*n
    components = 0
    for i in range(n):
      if Visited[i]==0:
        components += 1
        c = circles(i)
        if c==-1:
          is_bad = True
          break
        empty += c
    if is_bad:
      print(0)
    else:
      print(powc(2,n-1-(Q-empty),10**9+7)) 


import sys

def powc(x,n,m):
  res = 1
  xx=x
  while n:
    if n&1:
      res = (res*xx)%m
    xx=xx*xx%m
    n >>= 1
  return res

def circles(u):
  r = 0
  S = [(u,-1,0)]
  Been = [-1]*n
  for s in S:
    if Been[s[0]]!=-1:
      if Been[s[0]][1] != s[2]:
        return -1
      r += 1
      continue
    Been[s[0]] = (0,s[2])
    Visited[s[0]] = 1
    for e in V[s[0]]:
      if e[0] != s[1]:
        if Been[e[0]]==-1: 
          S.append((e[0], s[0], s[2]^e[1])) 
  return r

T = int(sys.stdin.readline())
for _ in range(T):
  is_bad = False
  empty = 0
  n,Q = list(map(int, sys.stdin.readline().split()))
  for _ in range(n-1):
    sys.stdin.readline() 
  paths = []
  V=list(map(list,[[]]*n))
  E = []
  for q in range(Q):
    u,v,x = list(map(int, sys.stdin.readline().split()))
    u-=1
    v-=1
    if (v,x^1) in V[u]:
      is_bad = True
    elif (v,x) in V[u]:
      empty += 1
    elif u!=v:
      E.append((u,v,x))
      V[u].append((v,x))
      V[v].append((u,x))
    elif x==1:
      is_bad = True
    else:
      empty += 1
    paths.append((u,v,x))
  if is_bad:
    print(0)
  elif n<=1:
    print(1)
  else:
    Visited = [0]*n
    components = 0
    for i in range(n):
      if Visited[i]==0:
        components += 1
        c = circles(i)
        if c==-1:
          is_bad = True
          break
        empty += c
    if is_bad:
      print(0)
    else:
      print(powc(2,n-1-(Q-empty),10**9+7)) 


import sys

def powc(x,n,m):
  res = 1
  xx=x
  while n:
    if n&1:
      res = (res*xx)%m
    xx=xx*xx%m
    n >>= 1
  return res

def findRoot():
  S = [(0,-1)]
  for u in S:
    for w in V[u[0]]:
      if w[0]!=u[1]:
        S.append((w[0],u[0]))
  S = [(S[-1][0],-1,0)]
  D = [0]*n
  for u in S:
    for w in V[u[0]]:
      if w[0]!=u[1]:
        D[w[0]]=u[2]+1
        S.append((w[0],u[0],u[2]+1))
  d = S[-1][2]
  size = d
  u = S[-1][0]
  while size/2<d:
    for w in V[u]:
      if D[w[0]]+1==D[u]:
        u = w[0]
        d -= 1
        break 
  return u
  
class Node:
  def __init__(self, value, edge, parent = None):
    self.value = value
    self.edge = edge
    if parent:
      parent.addChild(self)
    else:
      self.parent = None
    self.children = []
  def addChild(self, node):
    node.parent = self
    self.children.append(node)
  def __repr__(self):
    r = repr(self.value)
    for v in self.children:
      r += ' ' + repr(v)
    return r


def hangTree(root):
  global NodesArray
  NodesArray = [None]*n
  S=[(root, Node(root,-1),-1)]
  NodesArray[root] = S[0][1]
  for u in S:
    for v in V[u[0]]:
      if v[0] != u[2]:
        node = Node(v[0],v[1],u[1])
        NodesArray[v[0]] = node
        S.append((v[0],node,u[0]))

def findPath2(u,v):
  n0 = NodesArray[u]
  n1 = NodesArray[v]
  q = [0]*n
  while n0.parent:
    q[n0.edge] ^= 1
    n0 = n0.parent
  while n1.parent:
    q[n1.edge] ^= 1
    n1 = n1.parent
  return q
         
T = int(sys.stdin.readline())
for _ in range(T):
  n,Q = list(map(int,sys.stdin.readline().split()))
  V = list(map(list,[[]]*n))
  W = [0]*n
  for i in range(n-1):
    u,v = list(map(int,sys.stdin.readline().split()))
    u-=1
    v-=1
    V[u].append((v,i))
    V[v].append((u,i))
    W[u] += 1
    W[v] += 1
  easy = n==1
  root = findRoot()
  hangTree(root)
  M = []
  for _ in range(Q):
    u,v,x = list(map(int,sys.stdin.readline().split()))
    if not easy:
      q = findPath2(u-1,v-1)
      q[-1] = x
      M.append(q)
  if easy:
    print(1)
    continue
  empty = [0]*n
  bad = [0]*n
  bad[-1] = 1
  is_there_bad = False
  empty_cnt = 0
  i = 0
  for q in M:
    i += 1
    if q == empty:
      empty_cnt += 1
      continue
    if q == bad:
      is_there_bad = True
      break
    o = q.index(1)
    for next in range(i,Q):
      if M[next][o]==1:
        for k in range(n):
          M[next][k] ^= q[k]
  if is_there_bad:
    print(0)
  else:
    print(powc(2,n-1-Q+empty_cnt,10**9+7))


import sys

def powc(x,n,m):
  res = 1
  xx=x
  while n:
    if n&1:
      res = (res*xx)%m
    xx=xx*xx%m
    n >>= 1
  return res


def findPath(u,v,x):
  S = [(u,v,x)]
  for s in S:
    if s[0]==v:
      return s[2]
    for e in V[s[0]]: 
      if e[0] != s[1]:
        S.append((e[0],s[0],s[2]^e[1]))
  return None

T = int(sys.stdin.readline())
for _ in range(T):
  is_bad = False
  empty = 0
  n,Q = list(map(int, sys.stdin.readline().split(' ')))
  for _ in range(n-1):
    sys.stdin.readline() 
  paths = []
  V=list(map(list,[[]]*n))
  E = []
  for q in range(Q):
    u,v,x = list(map(int, sys.stdin.readline().split(' ')))
    u-=1
    v-=1
    if (v,x^1) in V[u]:
      is_bad = True
    elif (v,x) in V[u]:
      empty += 1
    else:
      E.append((u,v,x))
      V[u].append((v,x))
      V[v].append((u,x))
    paths.append((u,v,x))
  if is_bad:
    print(0)
  else:
    while E:
      e = E.pop()
      x = findPath(e[0],e[1],e[2]) 
      V[e[0]].remove((e[1],e[2]))
      V[e[1]].remove((e[0],e[2]))
      if x==1:
        is_bad = True
        break
      if x==0:
        empty += 1
    if is_bad:
      print(0)
    else:
      print(powc(2,n-1-(Q-empty),10**9+7))


def modpow(a,x):
	if(x==0):
		return 1;
	elif(x%2==0):
		t=modpow(a,x/2);
		return (t*t)%(1000000007);
	else:
		t=modpow(a,x/2);
		return (t*t*a)%(1000000007);
		
					
T=eval(input());
ans=[0]*T;
for j in range(T):
	[N,Q]=[int(x) for x in (input()).split()];
	for i in range(N-1):
		input();
	comp=list(range(N+1));
	revcomp=[];
	for i in range(N+1):
		revcomp.append([i]);	
	sumcomp=[0]*(N+1);
	flag=True;
	rank=0;
	for i in range(Q):
		if(not(flag)):
			input();
		else:	
			[u,v,x]=[int(x) for x in (input()).split()];
			if(comp[u]==comp[v]):
				if(not((sumcomp[u]+sumcomp[v])%2==(x%2))):
					flag=False;
			else:
				rank=rank+1;
				n1=len(revcomp[comp[u]]);
				n2=len(revcomp[comp[v]]);
				if(n1<n2):
					oldsu=sumcomp[u];
					l=revcomp[comp[v]];
					for w in revcomp[comp[u]]:
						l.append(w);
						comp[w]=comp[v];
						sumcomp[w]=(sumcomp[w]+sumcomp[v]+x+oldsu)%2;
					#revcomp[comp[u]]=[];	
				else:
					oldsv=sumcomp[v];
					l=revcomp[comp[u]];
					for w in revcomp[comp[v]]:
						l.append(w);
						comp[w]=comp[u];
						sumcomp[w]=(sumcomp[w]+sumcomp[u]+x+oldsv)%2;
					#revcomp[comp[v]]=[];	
	if(not(flag)):
		ans[j]=0;
	else:
		ans[j]=modpow(2,(N-rank-1));

for j in range(T):
	print((ans[j]));			


def modpow(a,x):
	if(x==0):
		return 1;
	elif(x%2==0):
		t=modpow(a,x/2);
		return (t*t)%(1000000007);
	else:
		t=modpow(a,x/2);
		return (t*t*a)%(1000000007);
		
			
		
			
T=eval(input());
ans=[0]*T;
for j in range(T):
	[N,Q]=[int(x) for x in (input()).split()];
	for i in range(N-1):
		input();
	comp=list(range(N+1));
	revcomp=[];
	for i in range(N+1):
		revcomp.append([i]);	
	sumcomp=[0]*(N+1);
	flag=True;
	rank=0;
	for i in range(Q):
		if(not(flag)):
			input();
		else:	
			[u,v,x]=[int(x) for x in (input()).split()];
			if(comp[u]==comp[v]):
				if(not((sumcomp[u]+sumcomp[v])%2==(x%2))):
					flag=False;
			else:
				rank=rank+1;
				n1=len(revcomp[comp[u]]);
				n2=len(revcomp[comp[v]]);
				if(n1<n2):
					oldsu=sumcomp[u];
					l=revcomp[comp[v]];
					for w in revcomp[u]:
						l.append(w);
						comp[w]=comp[v];
						sumcomp[w]=(sumcomp[w]+sumcomp[v]+x+oldsu)%2;
				else:
					oldsv=sumcomp[v];
					l=revcomp[comp[u]];
					for w in revcomp[v]:
						l.append(w);
						comp[w]=comp[u];
						sumcomp[w]=(sumcomp[w]+sumcomp[u]+x+oldsv)%2;
	if(not(flag)):
		ans[j]=0;
	else:
		ans[j]=modpow(2,(N-rank-1));

for j in range(T):
	print((ans[j]));			
							
								
			
		



T=eval(input());
ans=[0]*T;
for j in range(T):
	[N,Q]=[int(x) for x in (input()).split()];
	for i in range(N-1):
		input();
	comp=list(range(N+1));
	revcomp=[];
	for i in range(N+1):
		revcomp.append([i]);	
	sumcomp=[0]*(N+1);
	flag=True;
	rank=0;
	for i in range(Q):
		if(not(flag)):
			input();
		else:	
			[u,v,x]=[int(x) for x in (input()).split()];
			if(comp[u]==comp[v]):
				if(not((sumcomp[u]+sumcomp[v])%2==(x%2))):
					flag=False;
			else:
				rank=rank+1;
				n1=len(revcomp[comp[u]]);
				n2=len(revcomp[comp[v]]);
				if(n1<n2):
					oldsu=sumcomp[u];
					l=revcomp[comp[v]];
					for w in revcomp[u]:
						l.append(w);
						comp[w]=comp[v];
						sumcomp[w]=(sumcomp[w]+sumcomp[v]+x+oldsu)%2;
				else:
					oldsv=sumcomp[v];
					l=revcomp[comp[u]];
					for w in revcomp[v]:
						l.append(w);
						comp[w]=comp[u];
						sumcomp[w]=(sumcomp[w]+sumcomp[u]+x+oldsv)%2;
	if(not(flag)):
		ans[j]=0;
	else:
		ans[j]=2**(N-rank-1);

for j in range(T):
	print((ans[j]));