Problem: In the country there are n cities and m bidirectional roads between them. Each city has an army. Army of the i-th city consists of ai soldiers. Now soldiers roam. After roaming each soldier has to either stay in his city or to go to the one of neighboring cities by at moving along at most one road.

Check if is it possible that after roaming there will be exactly bi soldiers in the i-th city.

Input

First line of input consists of two integers n and m (1 ≤ n ≤ 100, 0 ≤ m ≤ 200).

Next line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 100).

Next line contains n integers b1, b2, ..., bn (0 ≤ bi ≤ 100).

Then m lines follow, each of them consists of two integers p and q (1 ≤ p, q ≤ n, p ≠ q) denoting that there is an undirected road between cities p and q. 

It is guaranteed that there is at most one road between each pair of cities.

Output

If the conditions can not be met output single word "NO".

Otherwise output word "YES" and then n lines, each of them consisting of n integers. Number in the i-th line in the j-th column should denote how many soldiers should road from city i to city j (if i ≠ j) or how many soldiers should stay in city i (if i = j).

If there are several possible answers you may output any of them.

Examples

Input

4 4
1 2 6 3
3 5 3 1
1 2
2 3
3 4
4 2


Output

YES
1 0 0 0 
2 0 0 0 
0 5 1 0 
0 0 2 1 


Input

2 0
1 2
2 1


Output

NO

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.stream.Stream;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author jtnydv25
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader2 in = new InputReader2(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE {
        public static void addEdge(List<TaskE.Edge>[] graph, int s, int t, int cap) {
            graph[s].add(new TaskE.Edge(s, t, graph[t].size(), cap));
            graph[t].add(new TaskE.Edge(t, s, graph[s].size() - 1, 0));
        }

        public static int maxFlow(List<TaskE.Edge>[] graph, int s, int t) {
            int flow = 0;
            int[] q = new int[graph.length];
            while (true) {
                int qt = 0;
                q[qt++] = s;
                TaskE.Edge[] pred = new TaskE.Edge[graph.length];
                for (int qh = 0; qh < qt && pred[t] == null; qh++) {
                    int cur = q[qh];
                    for (TaskE.Edge e : graph[cur]) {
                        if (pred[e.t] == null && e.cap > e.f) {
                            pred[e.t] = e;
                            q[qt++] = e.t;
                        }
                    }
                }
                if (pred[t] == null)
                    break;
                int df = Integer.MAX_VALUE;
                for (int u = t; u != s; u = pred[u].s)
                    df = Math.min(df, pred[u].cap - pred[u].f);
                for (int u = t; u != s; u = pred[u].s) {
                    pred[u].f += df;
                    graph[pred[u].t].get(pred[u].rev).f -= df;
                }
                flow += df;
            }
            return flow;
        }

        public void solve(int testNumber, InputReader2 in, OutputWriter out) {
            int n = in.nextInt(), m = in.nextInt();
            int[] a = new int[n + 1];
            int[] b = new int[n + 1];
            for (int i = 1; i <= n; i++) {
                a[i] = in.nextInt();
            }
            for (int i = 1; i <= n; i++) {
                b[i] = in.nextInt();
                b[i] -= a[i];
            }
            List<Integer>[] graph = Stream.generate(ArrayList::new).limit(n + 1).toArray(List[]::new);
            for (int i = 1; i <= m; i++) {
                int p = in.nextInt(), q = in.nextInt();
                graph[p].add(q);
                graph[q].add(p);
            }
            List<TaskE.Edge>[] graph2 = Stream.generate(ArrayList::new).limit(2 * n + 3).toArray(List[]::new);
            int totalsupply = 0, totaldemand = 0;
            for (int i = 1; i <= n; i++) {
                if (b[i] < 0) {
                    //supply node
                    addEdge(graph2, 0, i, -b[i]);
                    totalsupply -= b[i];
                } else {
                    // demand node
                    addEdge(graph2, i, 2 * n + 1, b[i]);
                    totaldemand += b[i];
                }
            }
            for (int i = 1; i <= n; i++) {
                addEdge(graph2, i, i + n, a[i]);
                for (int j : graph[i]) {
                    addEdge(graph2, i + n, j, a[i]);
                }
            }
            int flow = maxFlow(graph2, 0, 2 * n + 1);
            if (flow != totaldemand || totalsupply != totaldemand) {
                out.print("NO");
            } else {
                out.println("YES");
                for (int i = 1; i <= n; i++) {
                    int total = 0;
                    int[] ans = new int[n + 1];
                    for (TaskE.Edge e : graph2[i + n]) {
                        ans[e.t] = e.f;
                        if (e.t != i) total += e.f;
                    }
                    ans[i] = a[i] - total;
                    for (int j = 1; j <= n; j++) out.print(ans[j] + " ");
                    out.println("");
                }
            }

        }

        static class Edge {
            int s;
            int t;
            int rev;
            int cap;
            int f;

            public Edge(int s, int t, int rev, int cap) {
                this.s = s;
                this.t = t;
                this.rev = rev;
                this.cap = cap;
            }

        }

    }

    static class InputReader2 {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader2(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }

    static 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 close() {
            writer.close();
        }

        public void println(String s) {
            writer.println(s);
        }

        public void print(String i) {
            writer.print(i);
        }

    }
}