Problem: 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 di, 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, di = - 1 or it's degree modulo 2 is equal to di. 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 ≤ 3·105, n - 1 ≤ m ≤ 3·105) — number of vertices and edges.

The second line contains n integers d1, d2, ..., dn ( - 1 ≤ di ≤ 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.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
mt19937_64 rng((unsigned long long)new char);
const double eps = 1e-5;
const int maxn = 3e5 + 10;
const long long INF = 1e18;
const int mod = 998244353;
int n, m;
int d[maxn];
struct no {
  int u, v, id;
};
vector<no> edge, se;
vector<int> ans;
int pa[maxn];
vector<pair<int, int>> g[maxn];
int find(int x) { return x == pa[x] ? x : pa[x] = find(pa[x]); }
int fa[maxn];
int dep[maxn];
stack<int> ss;
int id[maxn];
void dfs(int u, int f, int d) {
  dep[u] = d;
  ss.push(u);
  for (auto r : g[u]) {
    if (r.first == f) continue;
    id[r.first] = r.second;
    fa[r.first] = u;
    dfs(r.first, u, d + 1);
  }
}
int cur[maxn];
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  cin >> n >> m;
  bool hn = 0;
  bool cs = 0;
  for (int t = (0); t < (n); ++t) {
    cin >> d[t];
    if (d[t] == -1)
      hn = 1;
    else
      cs ^= d[t];
  }
  if (!hn && cs) {
    cout << -1;
    return 0;
  }
  if (cs) {
    bool fi = 0;
    for (int t = (0); t < (n); ++t) {
      if (d[t] == -1 && !fi) {
        fi = 1;
        d[t] = 1;
      } else if (d[t] == -1)
        d[t] = 0;
    }
  } else if (hn) {
    for (int t = (0); t < (n); ++t)
      if (d[t] == -1) d[t] = 0;
  }
  for (int t = (0); t < (m); ++t) {
    int u, v;
    cin >> u >> v;
    --u, --v;
    edge.push_back({u, v, t});
  }
  for (int t = (0); t < (n); ++t) pa[t] = t;
  int cnt = 0;
  for (int t = (0); t < (m); ++t) {
    int &u = edge[t].u, &v = edge[t].v;
    int fu = find(u), fv = find(v);
    if (fu != fv) {
      pa[fu] = fv;
      se.push_back(edge[t]);
      g[u].push_back({v, t}), g[v].push_back({u, t});
      if (++cnt == n - 1) break;
    }
  }
  dfs(0, -1, 0);
  while (!ss.empty()) {
    int c = ss.top();
    ss.pop();
    if (cur[c] != d[c]) ans.push_back(id[c] + 1), cur[fa[c]] ^= 1;
  }
  cout << ans.size() << "\n";
  for (auto r : ans) cout << r << "\n";
}