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.util.*;
import java.io.*;
import java.math.*;
import java.lang.*;

public class Main {
    private static FastReader sc = new FastReader(System.in);
    private static OutputWriter out = new OutputWriter(System.out);
    private static HashMap<Integer, ArrayList<Integer>> graph;
    private static int n;
    private static int[] d;
    private static Edge[] edges;
    private static HashMap<Integer, ArrayList<Edge>> mst;
    private static ArrayList<Edge> mstEdges;
    private static ArrayList<Edge> ans;

    public static void main(String[] args) throws Exception {
        n = sc.nextInt();
        int m = sc.nextInt();
        d = new int[n];
        graph = new HashMap<>();
        for (int i = 0; i < n; i++) graph.put(i, new ArrayList<>());
        for (int i = 0; i < n; i++) d[i] = sc.nextInt();
        edges = new Edge[m];
        for (int i = 0; i < m; i++) {
            int u = sc.nextInt() - 1;
            int v = sc.nextInt() - 1;
            graph.get(u).add(v);
            graph.get(v).add(u);
            edges[i] = new Edge(i, u, v);
        }
        if (!changeDegree()) {
            System.out.println(-1);
            System.exit(0);
        }
//        System.out.println(Arrays.toString(d));

        MST();
        ans = new ArrayList<>();
        for (Edge e : mst.get(0)) {
            dfs(other(e, 0), e);
        }

        out.printLine(ans.size());
        for (Edge e : ans) {
            out.printLine(e.id + 1);
        }
        out.close();
    }

    private static void dfs(int u, Edge e) {
        if (mst.get(u).size() == 1) {
            if (d[u] == 1) {
                ans.add(e);
                d[u] = 0;
                d[other(e, u)] = 1 - d[other(e, u)];
            }
            return;
        }

        for (Edge ez : mst.get(u)) {
            if (ez.id != e.id) dfs(other(ez, u), ez);
        }

        if (d[u] == 1) {
            ans.add(e);
            d[u] = 0;
            d[other(e, u)] = 1 - d[other(e, u)];
        }
    }

    private static int other(Edge e, int u) {
        if (e.u == u) return e.v;
        return e.u;
    }

    private static void MST() {
        mst = new HashMap<>();
        mstEdges = new ArrayList<>();
        for (int i = 0; i < n; i++) mst.put(i, new ArrayList<>());
        UnionFind uf = new UnionFind(n);
        for (int i = 0; i < edges.length; i++) {
            int u = edges[i].u, v = edges[i].v;
            if (!uf.connected(u, v)) {
                uf.union(u, v);
                mst.get(u).add(edges[i]);
                mst.get(v).add(edges[i]);
                mstEdges.add(edges[i]);
            }
        }
    }

    private static boolean changeDegree() {
        int sum = 0;
        for (int i = 0; i < n; i++) {
            if (d[i] != -1) sum += d[i];
        }
        for (int i = 0; i < n; i++) {
            if (d[i] == -1 && sum % 2 == 0) {
                d[i] = 0;
            } else if (d[i] == -1 && sum % 2 == 1) {
                d[i] = 1;
                sum++;
            }
        }
        return sum % 2 == 0;
    }
}

class Edge {
    int id, u, v;
    public Edge(int i, int p, int q) {
        id = i;
        u = p;
        v = q;
    }
    public String toString() {
        return "id = " + id + " " + u + " " + v;
    }
}

class UnionFind {
    int[] id, sz;
    int n;

    public UnionFind(int n) {
        this.n = n;
        id = new int[n];
        sz = new int[n];
        for (int i = 0; i < n; i++) {
            id[i] = i;
            sz[i] = 1;
        }
    }

    private int root(int i) {
        while (i != id[i]) {
            id[i] = id[id[i]];
            i = id[i];
        }
        return i;
    }

    public boolean connected(int u, int v) {
        return root(u) == root(v);
    }

    public void union(int u, int v) {
        int p = root(u);
        int q = root(v);
        if (sz[p] <= sz[q]) {
            id[p] = id[q];
            sz[q] += sz[p];
        } else {
            id[q] = id[p];
            sz[p] += sz[q];
        }
    }
}

class FastReader {
    private boolean finished = false;

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

    public FastReader(InputStream stream) {
        this.stream = stream;
    }

    public int read() {
        if (numChars == -1) {
            throw new InputMismatchException();
        }
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0) {
                return -1;
            }
        }

        return buf[curChar++];
    }

    public int peek() {
        if (numChars == -1) {
            return -1;
        }
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                return -1;
            }
            if (numChars <= 0) {
                return -1;
            }
        }
        return buf[curChar];
    }

    public int nextInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c == ',') {
                c = read();
            }
            if (c < '0' || c > '9') {
                throw new InputMismatchException();
            }
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public long nextLong() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9') {
                throw new InputMismatchException();
            }
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public String nextString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    public boolean isSpaceChar(int c) {
        if (filter != null) {
            return filter.isSpaceChar(c);
        }
        return isWhitespace(c);
    }

    public static boolean isWhitespace(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    private String readLine0() {
        StringBuilder buf = new StringBuilder();
        int c = read();
        while (c != '\n' && c != -1) {
            if (c != '\r') {
                buf.appendCodePoint(c);
            }
            c = read();
        }
        return buf.toString();
    }

    public String nextLine() {
        String s = readLine0();
        while (s.trim().length() == 0)
            s = readLine0();
        return s;
    }

    public String nextLine(boolean ignoreEmptyLines) {
        if (ignoreEmptyLines) {
            return nextLine();
        } else {
            return readLine0();
        }
    }

    public BigInteger nextBigInteger() {
        try {
            return new BigInteger(nextString());
        } catch (NumberFormatException e) {
            throw new InputMismatchException();
        }
    }

    public char nextCharacter() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        return (char) c;
    }

    public double nextDouble() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        double res = 0;
        while (!isSpaceChar(c) && c != '.') {
            if (c == 'e' || c == 'E') {
                return res * Math.pow(10, nextInt());
            }
            if (c < '0' || c > '9') {
                throw new InputMismatchException();
            }
            res *= 10;
            res += c - '0';
            c = read();
        }
        if (c == '.') {
            c = read();
            double m = 1;
            while (!isSpaceChar(c)) {
                if (c == 'e' || c == 'E') {
                    return res * Math.pow(10, nextInt());
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                m /= 10;
                res += (c - '0') * m;
                c = read();
            }
        }
        return res * sgn;
    }

    public boolean isExhausted() {
        int value;
        while (isSpaceChar(value = peek()) && value != -1)
            read();
        return value == -1;
    }

    public String next() {
        return nextString();
    }

    public SpaceCharFilter getFilter() {
        return filter;
    }

    public void setFilter(SpaceCharFilter filter) {
        this.filter = filter;
    }

    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}

class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(objects[i]);
        }
    }

    public void printLine(Object... objects) {
        print(objects);
        writer.println();
    }

    public void close() {
        writer.close();
    }

    public void flush() {
        writer.flush();
    }

}