Leha plays a computer game, where is on each level is given a connected graph with n vertices and m edges. Graph can contain multiple edges, but can not contain self loops. Each vertex has an integer d_{i}, which can be equal to 0, 1 or  - 1. To pass the level, he needs to find a «good» subset of edges of the graph or say, that it doesn't exist. Subset is called «good», if by by leaving only edges from this subset in the original graph, we obtain the following: for every vertex i, d_{i} =  - 1 or it's degree modulo 2 is equal to d_{i}. Leha wants to pass the game as soon as possible and ask you to help him. In case of multiple correct answers, print any of them.


-----Input-----

The first line contains two integers n, m (1 ≤ n ≤ 3·10^5, n - 1 ≤ m ≤ 3·10^5) — number of vertices and edges.

The second line contains n integers d_1, d_2, ..., d_{n} ( - 1 ≤ d_{i} ≤ 1) — numbers on the vertices.

Each of the next m lines contains two integers u and v (1 ≤ u, v ≤ n) — edges. It's guaranteed, that graph in the input is connected.


-----Output-----

Print  - 1 in a single line, if solution doesn't exist. Otherwise in the first line k — number of edges in a subset. In the next k lines indexes of edges. Edges are numerated in order as they are given in the input, starting from 1.


-----Examples-----
Input
1 0
1

Output
-1

Input
4 5
0 0 0 -1
1 2
2 3
3 4
1 4
2 4

Output
0

Input
2 1
1 1
1 2

Output
1
1

Input
3 3
0 -1 1
1 2
2 3
1 3

Output
1
2



-----Note-----

In the first sample we have single vertex without edges. It's degree is 0 and we can not get 1.

Difficulty: HARD
Tags: Graph algorithms

Graph traversal

Constructive algorithms

Dynamic programming

Data structures
Skill types: Dynamic programming

Data structures

Starter code:

Solutions:
import sys
(n, m) = list(map(int, sys.stdin.readline().split()))
d = list(map(int, sys.stdin.readline().split()))
gph = [[] for _ in range(n)]
for _ in range(m):
	(u, v) = list(map(int, sys.stdin.readline().split()))
	u -= 1
	v -= 1
	gph[u].append((v, _))
	gph[v].append((u, _))
t = -1
if d.count(1) % 2 == 1:
	if -1 not in d:
		print(-1)
		return
	t = d.index(-1)
ans = [False] * m
vis = [False] * n
ed = [(-1, -1)] * n
rets = [d[u] == 1 or u == t for u in range(n)]
stk = [[0, iter(gph[0])]]
while len(stk) > 0:
	u = stk[-1][0]
	vis[u] = True
	try:
		while True:
			(v, i) = next(stk[-1][1])
			if not vis[v]:
				ed[v] = (u, i)
				stk.append([v, iter(gph[v])])
				break
	except StopIteration:
		(p, e) = ed[u]
		if p >= 0 and rets[u]:
			rets[p] = not rets[p]
			ans[e] = True
		stk.pop()
		pass
print(ans.count(True))
print('\n'.join([str(i + 1) for i in range(m) if ans[i]]))


import sys
input = sys.stdin.readline
(n, m) = map(int, input().split())
d = list(map(int, input().split()))
g = {}

def push(g, u, v, i):
	if u not in g:
		g[u] = []
	if v not in g:
		g[v] = []
	g[u].append([v, i + 1])
	g[v].append([u, i + 1])
for i in range(m):
	(u, v) = map(int, input().split())
	push(g, u - 1, v - 1, i)

def solve(d, g):
	pos = []
	S = 0
	for (i, x) in enumerate(d):
		if x == -1:
			pos.append(i)
		else:
			S += x
	if S % 2 == 1:
		if len(pos) == 0:
			return (False, None)
		d[pos[0]] = 1
		for x in pos[1:]:
			d[x] = 0
	else:
		for x in pos:
			d[x] = 0
	root = 0
	S = [root]
	edge = [-1]
	used = [0] * n
	used[root] = 1
	p = [None] * n
	i = 0
	while i < len(S):
		u = S[i]
		if u in g:
			for (v, edge_) in g[u]:
				if v == p[u] or used[v] == 1:
					continue
				p[v] = u
				used[v] = 1
				S.append(v)
				edge.append(edge_)
		i += 1
	ans = []
	r = [0] * n
	for (v, edge_) in zip(S[1:][::-1], edge[1:][::-1]):
		if r[v] ^ d[v] == 1:
			u = p[v]
			r[u] = 1 - r[u]
			ans.append(str(edge_))
	return (True, ans)
(flg, ans) = solve(d, g)
if flg == False:
	print(-1)
else:
	print(len(ans))
	print('\n'.join(ans))


import os, io
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
import sys
import heapq
INF = 10 ** 9

def Dijkstra(graph, start, m):
	dist = [INF] * len(graph)
	parent = [INF] * len(graph)
	queue = [(0, start)]
	while queue:
		(path_len, v) = heapq.heappop(queue)
		if dist[v] == INF:
			dist[v] = path_len
			for w in graph[v]:
				if dist[w[0]] == INF:
					parent[w[0]] = [v, w[1]]
					heapq.heappush(queue, (dist[v] + 1, w[0]))
	return (dist, parent)
(n, m) = map(int, input().split())
d = list(map(int, input().split()))
graph = []
for i in range(n):
	graph.append([])
for i in range(m):
	(u, v) = map(int, input().split())
	graph[u - 1].append([v - 1, i])
	graph[v - 1].append([u - 1, i])
count = 0
flag = 0
for i in range(n):
	if d[i] == 1:
		count += 1
	elif d[i] == -1:
		flag = 1
if count % 2 == 1 and flag == 0:
	print(-1)
	sys.exit()
if count % 2 == 1:
	for i in range(n):
		if d[i] == -1 and flag == 1:
			d[i] = 1
			flag = 0
		elif d[i] == -1:
			d[i] = 0
else:
	for i in range(n):
		if d[i] == -1:
			d[i] = 0
(dist, parent) = Dijkstra(graph, 0, m)
actualused = [0] * m
children = [0] * n
actualchildren = [0] * n
for i in range(1, n):
	children[parent[i][0]] += 1
stack = []
for i in range(n):
	if children[i] == actualchildren[i]:
		stack.append(i)
while stack:
	curr = stack.pop()
	if curr == 0:
		break
	p = parent[curr]
	k = p[0]
	if d[curr] == 1:
		actualused[p[1]] = 1
		d[k] = 1 - d[k]
	actualchildren[k] += 1
	if actualchildren[k] == children[k]:
		stack.append(k)
ans = []
for i in range(m):
	if actualused[i]:
		ans.append(str(i + 1))
print(len(ans))
print(' '.join(ans))