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.*;
import java.util.*;

public class Solution{
	InputStream is;
	static PrintWriter out;
	String INPUT = "";
	static long mod = (long)1e9+7L;
	
	ArrayList<Integer> adj[];
	boolean vis[];
	int[] d;
	int n, m;
	public void solve(){
		n = ni(); m = ni();
		adj = new ArrayList[n];
		for(int i = 0; i < n; i++){
			adj[i] = new ArrayList<Integer>();
		}
		d = na(n);
		if(!okd(d)){
			out.println("-1");
			return;
		}

		vis = new boolean[n];

		Pair[] a = new Pair[m];
		for(int i = 0; i < m; i++){
			int x = ni()-1, y = ni()-1;
			adj[x].add(y);
			adj[y].add(x);
			if(x <= y){
				a[i] = new Pair(x, y);
			}
			else{
				a[i] = new Pair(y, x);
			}
		}

		vis = new boolean[n];
		//dfs(0);
//out.println(Arrays.toString(al));
		//Arrays.fill(vis, false);
		//for(int i = 0; i < n; i++){
		//	adj[i].clear();
		//}
		ans = new TreeSet<Pair>();
		dfs1(0, -1);
		//for(int i = 0; i < n; i++){
			//al[i].clear();
		//}
		out.println(ans.size());
		TreeSet<Pair> set = new TreeSet<Pair>();
		for(int i = 0; i < m; i++){
			if(!set.contains(a[i])){
				if(ans.contains(a[i]) || ans.contains(new Pair(a[i].sc, a[i].fs))){
					out.println(i+1);
					set.add(a[i]);
				}
			}
		}
	}
	/*void dfs(int u){
		vis[u] = true;
		for(Integer v : adj[u]){
			if(!vis[v]){
				al[v].add(u);
				al[u].add(v);
				dfs(v);
			}
		}
		adj[u].clear();
	}*/
	TreeSet<Pair> ans;
	void dfs1(int u, int p){
		//out.println(u+" "+p);
		vis[u] = true;
		int ct = 0;
		for(Integer v : adj[u]){
			if(!vis[v]){
				dfs1(v, u);
			}
		}

		if(p == -1)
			return;

		if(d[u] == 1){
			ans.add(new Pair(u, p));
			d[p] = (d[p]+1)%2;
		}
		adj[u].clear();
	}
	boolean okd(int[] d){
		int neg = 0, sum = 0;
		for(int i = 0; i < d.length; i++){
			if(d[i] == -1){
				neg += 1;
			}
			else{
				sum = (sum+d[i])%2;
			}
		}

		if(sum == 0){
			for(int i = 0; i < d.length; i++){
				if(d[i] == -1){
					d[i] = 0;
				}
			}
			return true;
		}
		else if(sum == 1 && neg == 0){
			return false;
		}
		else{
			boolean done = false;
			for(int i = 0; i < d.length; i++){
				if(d[i] == -1 && !done){
					d[i] = 1;
					done = true;
				}
				else if(d[i] == -1){
					d[i] = 0;
				}
			}
			return true;
		}
	}
	

	void run(){
		is = new DataInputStream(System.in);
		out = new PrintWriter(System.out);
		int t=1;while(t-->0)solve();
		out.flush();
	}
	public static void main(String[] args)throws Exception{new Solution().run();}
	long mod(long v, long m){if(v<0){long q=(Math.abs(v)+m-1L)/m;v=v+q*m;}return v%m;}
    long mod(long v){if(v<0){long q=(Math.abs(v)+mod-1L)/mod;v=v+q*mod;}return v%mod;}
	//Fast I/O code is copied from uwi code.
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	private int readByte(){
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	private String ns(){
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	private char[] ns(int n){
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	private char[][] nm(int n, int m){
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	private int[] na(int n){
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	private int ni(){
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	private long nl(){
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	static  int i(long x){return (int)Math.round(x);}
	static class Pair implements Comparable<Pair>{
		long fs,sc;
		Pair(long a,long b){
			fs=a;sc=b;
		}
		public int compareTo(Pair p){
			if(this.fs>p.fs)return 1;
			else if(this.fs<p.fs)return -1;
			else{
				return i(this.sc-p.sc);
			}
			//return i(this.sc-p.sc);
		}
		public String toString(){
			return "("+fs+","+sc+")";
		}	
	}
	
}