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 JAVA):

Solution:

import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 * @author pttrung
 */
public class B_Round_429_Div1 {

    public static long MOD = 1000000007;

    public static void main(String[] args) throws FileNotFoundException {
        // PrintWriter out = new PrintWriter(new FileOutputStream(new File(
        // "output.txt")));
        PrintWriter out = new PrintWriter(System.out);
        Scanner in = new Scanner();
        int n = in.nextInt();
        int m = in.nextInt();
        int[] data = new int[n];
        ArrayList<Integer>[] map = new ArrayList[n];

        for (int i = 0; i < n; i++) {
            map[i] = new ArrayList();
            data[i] = in.nextInt();

        }
        int[][] edge = new int[m][2];
        int[] count = new int[n];

        for (int i = 0; i < m; i++) {
            for (int j = 0; j < 2; j++) {
                edge[i][j] = in.nextInt() - 1;
                count[edge[i][j]]++;
            }
            map[edge[i][0]].add(i);
            map[edge[i][1]].add(i);

        }
        boolean[] check = new boolean[m];
        boolean[] special = new boolean[n];
        int[] pa = new int[n];
        Arrays.fill(pa, -1);
        int root = -1;
        for (int i = 0; i < n; i++) {
            if (data[i] != -1 && count[i] % 2 != data[i]) {
                root = i;
                LinkedList<Integer> q = new LinkedList();
                q.add(i);
                pa[i] = i;
                while (!q.isEmpty()) {
                    int node = q.poll();
                    for (int j : map[node]) {
                        int nxt = nxt(edge[j], node);
                        if (pa[nxt] == -1) {
                            pa[nxt] = j;
                            q.add(nxt);
                        }
                    }
                }
                break;
            }
        }
        boolean ok = false;
        int total = 0;
        int re = m;
        int other = -1;
        for (int i = 0; i < n; i++) {
            if (data[i] != -1 && count[i] % 2 != data[i]) {
                special[i] = true;
                total++;
                int st = i;
                while (st != root && !check[pa[st]]) {
                    check[pa[st]] = true;
                    st = nxt(edge[pa[st]], st);
                    if(data[st] == -1){
                        other = st;
                    }
                    re--;
                }
            } else if (data[i] == -1) {
                other = i;
            }
        }
        if (total % 2 == 0) {
            ok = true;
        } else if (other != -1) {
            total++;
            special[other] = true;
            ok = true;
            int st = other;
            while (st != root && !check[pa[st]]) {
                check[pa[st]] = true;
                st = nxt(edge[pa[st]], st);
                re--;
            }
        }
        if (!ok) {
            out.println(-1);
        } else {
            int[] level = new int[n];
            int[] num = new int[n];
            if (root != -1) {
                for (int i = 0; i < n; i++) {
                    map[i] = new ArrayList();
                }
                for (int i = 0; i < m; i++) {
                    if (check[i]) {
                        int u = edge[i][0];
                        int v = edge[i][1];
                        map[u].add(i);
                        map[v].add(i);
                    }
                }

                update(root, root, edge, special, level, num, map);
                for (int i = 0; i < m; i++) {
                    if (check[i]) {
                        int u = edge[i][0];
                        int v = edge[i][1];
                        if (level[u] < level[v]) {
                            if (num[v] % 2 == 0) {
                                check[i] = false;
                                re++;
                            }
                        } else {
                            if (num[u] % 2 == 0) {
                                check[i] = false;
                                re++;
                            }
                        }
                    }
                }
            }

            int[] post = new int[n];
            for (int i = 0; i < m; i++) {
                if (!check[i]) {
                    post[edge[i][0]]++;
                    post[edge[i][1]]++;
                    //System.out.println(Arrays.toString(edge[i]));

                }
            }
            for (int i = 0; i < n; i++) {
                if (data[i] != -1 && data[i] != (post[i] % 2)) {
                    System.out.println("VCL " + " " + other + " " + total + " " + (i + 1) + " " + (root + 1) + " " + post[i] + " " + count[i] + " " + level[i] + " " + map[i]);
                    for (int j : map[i]) {
                        int u = edge[j][0];
                        int v = edge[j][1];
                        System.out.println(u + " " + v + " " + level[u] + " " + level[v] + " " + num[u] + " " + num[v]);
                    }

                }
            }

            out.println(re);
            for (int i = 0; i < m; i++) {
                if (!check[i]) {
                    out.println((i + 1));
                    //System.out.println(Arrays.toString(edge[i]));            
                }
            }
            //System.out.println(Arrays.toString(post));

        }
        out.close();
    }

    static int update(int index, int pa, int[][] edge, boolean[] special, int[] level, int[] num, ArrayList<Integer>[] map) {
        int result = special[index] ? 1 : 0;
        for (int i : map[index]) {
            int nxt = nxt(edge[i], index);
            if (nxt != pa) {
                level[nxt] = 1 + level[index];
                result += update(nxt, index, edge, special, level, num, map);
            }
        }
        return num[index] = result;
    }

    static int nxt(int[] edge, int node) {
        return edge[0] == node ? edge[1] : edge[0];
    }

    public static int[] KMP(String val) {
        int i = 0;
        int j = -1;
        int[] result = new int[val.length() + 1];
        result[0] = -1;
        while (i < val.length()) {
            while (j >= 0 && val.charAt(j) != val.charAt(i)) {
                j = result[j];
            }
            j++;
            i++;
            result[i] = j;
        }
        return result;

    }

    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;
    }

    public static int digit(long n) {
        int result = 0;
        while (n > 0) {
            n /= 10;
            result++;
        }
        return result;
    }

    public static double dist(long a, long b, long x, long y) {
        double val = (b - a) * (b - a) + (x - y) * (x - y);
        val = Math.sqrt(val);
        double other = x * x + a * a;
        other = Math.sqrt(other);
        return val + other;

    }

    public static class Point implements Comparable<Point> {

        int x, y;

        public Point(int start, int end) {
            this.x = start;
            this.y = end;
        }

        @Override
        public int hashCode() {
            int hash = 5;
            hash = 47 * hash + this.x;
            hash = 47 * hash + this.y;
            return hash;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (getClass() != obj.getClass()) {
                return false;
            }
            final Point other = (Point) obj;
            if (this.x != other.x) {
                return false;
            }
            if (this.y != other.y) {
                return false;
            }
            return true;
        }

        @Override
        public int compareTo(Point o) {
            return Integer.compare(x, o.x);
        }
    }

    public static class FT {

        long[] data;

        FT(int n) {
            data = new long[n];
        }

        public void update(int index, long value) {
            while (index < data.length) {
                data[index] += value;
                index += (index & (-index));
            }
        }

        public long get(int index) {
            long result = 0;
            while (index > 0) {
                result += data[index];
                index -= (index & (-index));
            }
            return result;

        }
    }

    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static long pow(long a, long b, long MOD) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2, MOD);
        if (b % 2 == 0) {
            return val * val % MOD;
        } else {
            return val * (val * a % MOD) % MOD;

        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //  br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}