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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.util.concurrent.ArrayBlockingQueue;

/**
 * Created by dhamada on 15/05/30.
 */
public class E {

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        int m = in.nextInt();
        int[] a = new int[n];
        int[] b = new int[n];
        int sumA = 0;
        int sumB = 0;
        for (int i = 0; i < n ; i++) {
            a[i] = in.nextInt();
            sumA += a[i];
        }
        for (int i = 0; i < n ; i++) {
            b[i] = in.nextInt();
            sumB += b[i];
        }

        int[][] graph = buildGraph(in, n, m);

        MaxFlowDinic flow = new MaxFlowDinic();
        flow.init(n*2+2);

        int source = n*2;
        int sink = source+1;
        for (int i = 0; i < n ; i++) {
            flow.edge(source, i, a[i]);
            flow.edge(n+i, sink, b[i]);
        }
        for (int i = 0 ; i < n ; i++) {
            for (int to : graph[i]) {
                flow.edge(i, n+to, sumA);
            }
            flow.edge(i, n+i, sumA);
        }
        int max = flow.max_flow(source, sink);
        if (max != sumA || sumA != sumB) {
            out.println("NO");
        } else {
            out.println("YES");

            int[][] table = new int[n][n];
            for (int i = 0 ; i < n ; i++) {
                for (MaxFlowDinic.Edge e : flow.graph.get(i)) {
                    if (e.to >= n && e.to < source) {
                        table[i][e.to-n] = sumA - e.cap;
                    }
                }
            }
            for (int i = 0 ; i < n ; i++) {
                StringBuilder line = new StringBuilder();
                for (int j = 0; j < n; j++) {
                    line.append(' ').append(table[i][j]);
                }
                out.println(line.substring(1));
            }
        }


        out.flush();
    }


    static class MaxFlowDinic {
        public class Edge {
            int to;
            int cap;
            int rev;
            public Edge(int _to, int _cap, int _rev) {
                to = _to;
                cap = _cap;
                rev = _rev;
            }
        }
        public Map<Integer, List<Edge>> graph = new HashMap<>();
        public int[] level;
        public int[] itr;
        public void init(int size) {
            for (int i = 0 ; i < size ; i++) {
                graph.put(i, new ArrayList<>());
            }
            level = new int[size];
            itr = new int[size];
        }
        public void edge(int from, int to, int cap) {
            graph.get(from).add(new Edge(to, cap, graph.get(to).size()));
            graph.get(to).add(new Edge(from, 0, graph.get(from).size() - 1));
        }
        public int dfs(int v, int t, int f) {
            if (v == t) return f;
            for (int i = itr[v] ; i < graph.get(v).size() ; i++) {
                itr[v] = i;
                Edge e = graph.get(v).get(i);
                if (e.cap > 0 && level[v] < level[e.to]) {
                    int d = dfs(e.to, t, Math.min(f, e.cap));
                    if (d > 0) {
                        e.cap -= d;
                        graph.get(e.to).get(e.rev).cap += d;
                        return d;
                    }
                }
            }
            return 0;
        }

        public void bfs(int s) {
            Arrays.fill(level, -1);
            Queue<Integer> q = new ArrayBlockingQueue<>(graph.size()+10);
            level[s] = 0;
            q.add(s);
            while (q.size() >= 1) {
                int v = q.poll();
                for (int i = 0; i < graph.get(v).size() ; i++) {
                    Edge e = graph.get(v).get(i);
                    if (e.cap > 0 && level[e.to] < 0) {
                        level[e.to] = level[v] + 1;
                        q.add(e.to);
                    }
                }
            }
        }

        public int max_flow(int s, int t) {
            int flow = 0;
            while (true) {
                bfs(s);
                if (level[t] < 0) {
                    return flow;
                }
                Arrays.fill(itr, 0);
                while (true) {
                    int f = dfs(s, t, Integer.MAX_VALUE);
                    if (f <= 0) {
                        break;
                    }
                    flow += f;
                }
            }
        }
    }



    static int[][] buildGraph(InputReader in, int n, int m) {
        int[][] edges = new int[m][];
        int[][] graph = new int[n][];
        int[] deg = new int[n];
        for (int i = 0 ; i < m ; i++) {
            int a = in.nextInt()-1;
            int b = in.nextInt()-1;
            deg[a]++;
            deg[b]++;
            edges[i] = new int[]{a, b};
        }
        for (int i = 0 ; i < n ; i++) {
            graph[i] = new int[deg[i]];
        }
        for (int i = 0 ; i < m ; i++) {
            int a = edges[i][0];
            int b = edges[i][1];
            graph[a][--deg[a]] = b;
            graph[b][--deg[b]] = a;
        }
        return graph;
    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

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

        private int next() {
            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 char nextChar() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            if ('a' <= c && c <= 'z') {
                return (char)c;
            }
            if ('A' <= c && c <= 'Z') {
                return (char)c;
            }
            throw new InputMismatchException();
        }

        public String nextToken() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char)c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

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

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

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

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

    static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }
}