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>
#pragma comment(linker, "/STACK:256000000")
using namespace std;
const int INF = 1000001000;
const long long INFLL = INF * 1LL * INF;
const int mod = 1000 * 1000 * 1000 + 7;
const int mod9 = 1000 * 1000 * 1000 + 9;
const int modr = 99990001;
const long double PI = 3.1415926535897932385;
template <class T>
void zero(T val, T& first) {
  first = val;
}
template <class T, class... Targs>
void zero(T val, T& first, Targs&... Fargs) {
  first = val;
  zero(val, Fargs...);
}
template <class T, class T2>
std::istream& operator>>(std::istream& is, pair<T, T2>& p) {
  return is >> p.first >> p.second;
}
template <class T>
std::istream& readN(T& first, int n, int st = 0) {
  for (int i = st, iend = (st + n - 1); i <= iend; i++) cin >> first[i];
  return cin;
}
template <class T>
std::istream& readS(set<T>& first, int n) {
  T second = *first.rbegin();
  for (int i = 0, iend = (n - 1); i <= iend; i++) {
    cin >> second;
    first.insert(second);
  }
  return cin;
}
template <class T>
std::istream& read(T& first) {
  return cin >> first;
}
template <class T, class... Targs>
std::istream& read(T& first, Targs&... Fargs) {
  return read(first), read(Fargs...);
}
template <class T, class T2>
std::ostream& operator<<(std::ostream& os, pair<T, T2> p) {
  return os << p.first << " " << p.second;
}
template <class T>
std::ostream& operator<<(std::ostream& os, vector<T> v) {
  bool f = true;
  for (auto second : v) {
    if (!f) os << ' ';
    os << second;
    f = false;
  }
  return os;
}
template <class T>
std::ostream& operator<<(std::ostream& os, set<T> v) {
  bool f = true;
  for (auto second : v) {
    if (!f) os << ' ';
    os << second;
    f = false;
  }
  return os;
}
template <class T>
std::ostream& operator<<(std::ostream& os, multiset<T> v) {
  bool f = true;
  for (auto second : v) {
    if (!f) os << ' ';
    os << second;
    f = false;
  }
  return os;
}
template <class T, class T2>
std::ostream& operator<<(std::ostream& os, map<T, T2> v) {
  bool f = true;
  for (pair<T, T2> second : v) {
    if (!f) os << ' ';
    os << second.first << "=>" << second.second;
    f = false;
  }
  return os;
}
template <class T>
std::ostream& outV(T first, char del = ' ') {
  bool f = true;
  for (auto second : first) {
    if (!f) cout << del;
    cout << second;
    f = false;
  }
  return cout;
}
template <class T>
std::ostream& outN(T first, int n = -1, int st = 0) {
  for (int i = st, iend = (n == -1 ? (int)first.size() - 1 : st + n - 1);
       i <= iend; i++) {
    cout << first[i];
    if (i < iend) cout << ' ';
  }
  return cout;
}
template <class T>
std::ostream& outAN(T first, int n = -1, int st = 0) {
  for (int i = st, iend = (n - 1); i <= iend; i++) {
    cout << first[i];
    if (i < iend) cout << ' ';
  }
  return cout;
}
template <class T>
std::ostream& outA2(T first, int n, int m) {
  for (int i = 0, iend = (n - 1); i <= iend; i++) {
    for (int j = 0, jend = (m - 1); j <= jend; j++)
      cout << first[i][j] << (j == m - 1 ? '\n' : ' ');
  }
  return cout;
}
template <class T>
std::ostream& out(T first) {
  return cout << first;
}
template <class T, class... Targs>
std::ostream& out(T first, Targs... Fargs) {
  return out(first) << " ", out(Fargs...);
}
template <typename T>
void srt(T& a, int st, int fn, bool isArr) {
  sort(a + st, a + fn + 1);
}
template <class T>
void srt(T& a, int st = 0, int fn = 0) {
  sort(a.begin() + st, fn ? a.begin() + fn + 1 : a.end());
}
template <typename T>
T rev_num(T a) {
  T r = 0;
  for (; a; a /= 10) r = r * 10 + a % 10;
  return r;
}
template <typename T>
void rev(T& a, int st, int fn, bool isArr) {
  reverse(a + st, a + fn + 1);
}
template <class T>
void rev(T& a, int st = 0, int fn = 0) {
  reverse(a.begin() + st, fn ? a.begin() + fn + 1 : a.end());
}
long long sqr(long long a) { return a * a; };
long long sqr(int a) { return a * 1LL * a; };
long double sqr(long double a) { return a * a; };
long long sqDist(pair<long long, long long> first,
                 pair<long long, long long> second) {
  return sqr(first.first - second.first) + sqr(first.second - second.second);
}
long double dist(pair<long long, long long> first,
                 pair<long long, long long> second) {
  return sqrt(sqDist(first, second));
}
long long phi(int n) {
  int res = n;
  for (long long i = 2; i * i <= n; i++)
    if (n % i == 0) {
      while (n % i == 0) n /= i;
      res -= res / i;
    }
  if (n > 1) res -= res / n;
  return res;
}
long long bpm(long long a, long long n = -2, long long m = mod) {
  n = n < 0 ? n + m : n;
  long long r = 1;
  while (n) {
    if (n & 1) r = (r * a) % m;
    a = (a * a) % m;
    n >>= 1;
  }
  return r;
}
unsigned long long gcd(unsigned long long a, unsigned long long b) {
  while (b) {
    a %= b;
    swap(a, b);
  }
  return a;
}
long long gcd_cb(long long a, long long b, long long& first,
                 long long& second) {
  if (!b) {
    first = 1;
    second = 0;
    return a;
  }
  long long x1, y1, g;
  g = gcd_cb(b, a % b, x1, y1);
  first = y1;
  second = x1 - a / b * y1;
  return g;
}
vector<long long> fact;
void fact_prec(int n = 20) {
  fact.resize(n + 1);
  fact[0] = 1;
  for (int i = 1, iend = (n); i <= iend; i++) {
    fact[i] = fact[i - 1] * i;
  }
}
vector<long double> factd;
void fact_precd(int n = 146) {
  factd.resize(n + 1);
  factd[0] = 1;
  for (int i = 1, iend = (n); i <= iend; i++) {
    factd[i] = factd[i - 1] * i;
  }
}
string str(long long a) {
  string r = "";
  for (; a; a /= 10) r += a % 10 + '0';
  rev(r);
  return r;
}
template <class T>
int bitc(T first) {
  int r = 0;
  for (T d = first; d > 0; d >>= 1) {
    r += d & 1;
  }
  return r;
}
const int N = 1000006;
int d[N], lvl[N], p[N], dc[N], vs[N];
bool used[N], uv[N];
pair<int, int> r[N];
vector<pair<int, int> > g[N];
void dfs(int v, int pr = 0, int lv = 0) {
  if (uv[v]) return;
  uv[v] = true;
  lvl[v] = lv;
  p[v] = pr;
  for (pair<int, int> first : g[v]) {
    dfs(first.first, first.second, lv + 1);
  }
}
int main() {
  int n, m;
  read(n, m);
  int stv = 1;
  for (int i = 1, iend = (n); i <= iend; i++) {
    read(d[i]);
    if (d[i] == -1) stv = i;
    if (d[i] == 1 && d[stv] == 0) stv = i;
    vs[i] = i;
  }
  for (int i = 0, iend = (m - 1); i <= iend; i++) {
    int first, second;
    read(first, second);
    g[first].push_back({second, i + 1});
    g[second].push_back({first, i + 1});
    r[i + 1] = {first, second};
  }
  dfs(stv);
  vector<int> ans;
  sort(vs + 1, vs + 1 + n, [](int v1, int v2) { return lvl[v1] > lvl[v2]; });
  for (int i = 1, iend = (n); i <= iend; i++) {
    int id = vs[i];
    if (d[id] >= 0 && d[id] % 2 != dc[id] % 2) {
      pair<int, int> cd = r[p[id]];
      dc[cd.first]++;
      dc[cd.second]++;
      ans.push_back(p[id]);
    }
  }
  if (d[stv] >= 0 && d[stv] != dc[stv] % 2) {
    puts("-1");
  } else {
    out(ans.size()) << "\n";
    out(ans) << "\n";
  }
  return 0;
}