Valera has n counters numbered from 1 to n. Some of them are connected by wires, and each of the counters has a special button.

Initially, all the counters contain number 0. When you press a button on a certain counter, the value it has increases by one. Also, the values recorded in all the counters, directly connected to it by a wire, increase by one.

Valera and Ignat started having a dispute, the dispute is as follows. Ignat thought of a sequence of n integers a1, a2, ..., an. Valera should choose some set of distinct counters and press buttons on each of them exactly once (on other counters the buttons won't be pressed). If after that there is a counter with the number i, which has value ai, then Valera loses the dispute, otherwise he wins the dispute.

Help Valera to determine on which counters he needs to press a button to win the dispute.

Input

The first line contains two space-separated integers n and m (1 ≤ n, m ≤ 105), that denote the number of counters Valera has and the number of pairs of counters connected by wires.

Each of the following m lines contains two space-separated integers ui and vi (1 ≤ ui, vi ≤ n, ui ≠ vi), that mean that counters with numbers ui and vi are connected by a wire. It is guaranteed that each pair of connected counters occurs exactly once in the input.

The last line contains n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 105), where ai is the value that Ignat choose for the i-th counter.

Output

If Valera can't win the dispute print in the first line -1.

Otherwise, print in the first line integer k (0 ≤ k ≤ n). In the second line print k distinct space-separated integers — the numbers of the counters, where Valera should push buttons to win the dispute, in arbitrary order.

If there exists multiple answers, you are allowed to print any of them.

Examples

Input

5 5
2 3
4 1
1 5
5 3
2 1
1 1 2 0 2


Output

2
1 2


Input

4 2
1 2
3 4
0 0 0 0


Output

3
1 3 4
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Queue;
import java.util.Set;
import java.util.StringTokenizer;

public class Solver {

    StringTokenizer st;
    BufferedReader in;
    PrintWriter out;

    public static void main(String[] args) throws NumberFormatException,
            IOException {
        Solver solver = new Solver();
        solver.open();
        long time = System.currentTimeMillis();
        solver.solve();
        if (!"true".equals(System.getProperty("ONLINE_JUDGE"))) {
            System.out.println("Spent time: "
                    + (System.currentTimeMillis() - time));
            System.out.println("Memory: "
                    + (Runtime.getRuntime().totalMemory() - Runtime
                            .getRuntime().freeMemory()));
        }
        solver.close();
    }

    public void open() throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
    }

    public String nextToken() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            String line = in.readLine();
            if (line == null)
                return null;
            st = new StringTokenizer(line);
        }
        return st.nextToken();
    }

    public int nextInt() throws NumberFormatException, IOException {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws NumberFormatException, IOException {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws NumberFormatException, IOException {
        return Double.parseDouble(nextToken());
    }

    public void solve() throws NumberFormatException, IOException {
        int n = nextInt();
        int m = nextInt();
        List<Integer>[] graph = new List[n];
        for (int i = 0; i < n; i++)
            graph[i] = new ArrayList<Integer>();

        for (int i = 0; i < m; i++) {
            int from = nextInt() - 1;
            int to = nextInt() - 1;
            graph[from].add(to);
            graph[to].add(from);
        }

        int[] a = new int[n];
        Queue<Integer> queue = new LinkedList<Integer>();
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
            if (a[i] == 0)
                queue.add(i);
        }
        List<Integer> result = new ArrayList<Integer>();
        int[] b = new int[n];

        while (!queue.isEmpty()) {
            int next = queue.remove();

            if (a[next] != b[next])
                continue;
            
            result.add(next);
            b[next]++;
            
            for(int to:graph[next]){
                b[to]++;
                if (b[to]==a[to]) queue.add(to);
            }
        }
        
        out.println(result.size());
        for(int ans:result){
            out.print(ans+1);
            out.print(' ');
        }
    }

    public void close() {
        out.flush();
        out.close();
    }
}