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.BufferedWriter;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;
import java.math.BigInteger;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.Iterator;
import java.io.IOException;
import java.util.Arrays;
import java.io.InputStream;
import java.io.OutputStreamWriter;
import java.util.Comparator;

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

class TaskE {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        int n=in.readInt(), m=in.readInt(), n1=0, n2=0;
        int[] A=IOUtils.readIntArray(in, n), B= IOUtils.readIntArray(in, n);
        Graph graph=new Graph(2*n+2);
        for (int i=0; i<n; i++) {
            graph.addFlowEdge(0, i+1, A[i]);
            graph.addFlowEdge(n+i+1, 2*n+1, B[i]);
            graph.addFlowEdge(i+1, n+i+1, Long.MAX_VALUE);
        }
        while (m-->0) {
            int a=in.readInt(), b=in.readInt();
            graph.addFlowEdge(a, n+b, Long.MAX_VALUE);
            graph.addFlowEdge(b, n+a, Long.MAX_VALUE);
        }
        long s1=ArrayUtils.sumArray(A), s2=ArrayUtils.sumArray(B);
        if (s1!=s2 || s1!=MaxFlow.dinic(graph, 0, 2*n+1)) {
            out.printLine("NO");
            return;
        }
        out.printLine("YES");
        long[][] table=new long[n][n];
        for (int i=0; i<graph.edgeCount(); i++) {
            int a=graph.source(i), b=graph.destination(i);
            if (a>=1 && a<=n && b>=n+1 && b<=2*n) table[a-1][b-n-1]=graph.flow(i);
        }
        for (long[] i: table) out.printLine(i);
    }
}

class InputReader {

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

    public InputReader(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 readInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int 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 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;
    }

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

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

    public void printLine(long[] array) {
        print(array);
        writer.println();
    }

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

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

}

class IOUtils {

    public static int[] readIntArray(InputReader in, int size) {
        int[] array = new int[size];
        for (int i = 0; i < size; i++)
            array[i] = in.readInt();
        return array;
    }

}

class Graph {
    public static final int REMOVED_BIT = 0;

    protected int vertexCount;
    protected int edgeCount;

    private int[] firstOutbound;
    private int[] firstInbound;

    private Edge[] edges;
    private int[] nextInbound;
    private int[] nextOutbound;
    private int[] from;
    private int[] to;
    private long[] weight;
    public long[] capacity;
    private int[] reverseEdge;
    private int[] flags;

    public Graph(int vertexCount) {
        this(vertexCount, vertexCount);
    }

    public Graph(int vertexCount, int edgeCapacity) {
        this.vertexCount = vertexCount;
        firstOutbound = new int[vertexCount];
        Arrays.fill(firstOutbound, -1);

        from = new int[edgeCapacity];
        to = new int[edgeCapacity];
        nextOutbound = new int[edgeCapacity];
        flags = new int[edgeCapacity];
    }

    public int addEdge(int fromID, int toID, long weight, long capacity, int reverseEdge) {
        ensureEdgeCapacity(edgeCount + 1);
        if (firstOutbound[fromID] != -1)
            nextOutbound[edgeCount] = firstOutbound[fromID];
        else
            nextOutbound[edgeCount] = -1;
        firstOutbound[fromID] = edgeCount;
        if (firstInbound != null) {
            if (firstInbound[toID] != -1)
                nextInbound[edgeCount] = firstInbound[toID];
            else
                nextInbound[edgeCount] = -1;
            firstInbound[toID] = edgeCount;
        }
        this.from[edgeCount] = fromID;
        this.to[edgeCount] = toID;
        if (capacity != 0) {
            if (this.capacity == null)
                this.capacity = new long[from.length];
            this.capacity[edgeCount] = capacity;
        }
        if (weight != 0) {
            if (this.weight == null)
                this.weight = new long[from.length];
            this.weight[edgeCount] = weight;
        }
        if (reverseEdge != -1) {
            if (this.reverseEdge == null) {
                this.reverseEdge = new int[from.length];
                Arrays.fill(this.reverseEdge, 0, edgeCount, -1);
            }
            this.reverseEdge[edgeCount] = reverseEdge;
        }
        if (edges != null)
            edges[edgeCount] = createEdge(edgeCount);
        return edgeCount++;
    }

    protected final GraphEdge createEdge(int id) {
        return new GraphEdge(id);
    }

    public final int addFlowWeightedEdge(int from, int to, long weight, long capacity) {
        if (capacity == 0) {
            return addEdge(from, to, weight, 0, -1);
        } else {
            int lastEdgeCount = edgeCount;
            addEdge(to, from, -weight, 0, lastEdgeCount + entriesPerEdge());
            return addEdge(from, to, weight, capacity, lastEdgeCount);
        }
    }

    protected int entriesPerEdge() {
        return 1;
    }

    public final int addFlowEdge(int from, int to, long capacity) {
        return addFlowWeightedEdge(from, to, 0, capacity);
    }

    public final int vertexCount() {
        return vertexCount;
    }

    public final int edgeCount() {
        return edgeCount;
    }

    public final int firstOutbound(int vertex) {
        int id = firstOutbound[vertex];
        while (id != -1 && isRemoved(id))
            id = nextOutbound[id];
        return id;
    }

    public final int nextOutbound(int id) {
        id = nextOutbound[id];
        while (id != -1 && isRemoved(id))
            id = nextOutbound[id];
        return id;
    }

    public final int source(int id) {
        return from[id];
    }

    public final int destination(int id) {
        return to[id];
    }

    public final long capacity(int id) {
        if (capacity == null)
            return 0;
        return capacity[id];
    }

    public final long flow(int id) {
        if (reverseEdge == null)
            return 0;
        return capacity[reverseEdge[id]];
    }

    public final void pushFlow(int id, long flow) {
        if (flow == 0)
            return;
        if (flow > 0) {
            if (capacity(id) < flow)
                throw new IllegalArgumentException("Not enough capacity");
        } else {
            if (flow(id) < -flow)
                throw new IllegalArgumentException("Not enough capacity");
        }
        capacity[id] -= flow;
        capacity[reverseEdge[id]] += flow;
    }

    public final boolean flag(int id, int bit) {
        return (flags[id] >> bit & 1) != 0;
    }

    public final boolean isRemoved(int id) {
        return flag(id, REMOVED_BIT);
    }

    protected void ensureEdgeCapacity(int size) {
        if (from.length < size) {
            int newSize = Math.max(size, 2 * from.length);
            if (edges != null)
                edges = resize(edges, newSize);
            from = resize(from, newSize);
            to = resize(to, newSize);
            nextOutbound = resize(nextOutbound, newSize);
            if (nextInbound != null)
                nextInbound = resize(nextInbound, newSize);
            if (weight != null)
                weight = resize(weight, newSize);
            if (capacity != null)
                capacity = resize(capacity, newSize);
            if (reverseEdge != null)
                reverseEdge = resize(reverseEdge, newSize);
            flags = resize(flags, newSize);
        }
    }

    protected final int[] resize(int[] array, int size) {
        int[] newArray = new int[size];
        System.arraycopy(array, 0, newArray, 0, array.length);
        return newArray;
    }

    private long[] resize(long[] array, int size) {
        long[] newArray = new long[size];
        System.arraycopy(array, 0, newArray, 0, array.length);
        return newArray;
    }

    private Edge[] resize(Edge[] array, int size) {
        Edge[] newArray = new Edge[size];
        System.arraycopy(array, 0, newArray, 0, array.length);
        return newArray;
    }

    protected class GraphEdge implements Edge {
        protected int id;

        protected GraphEdge(int id) {
            this.id = id;
        }

    }

}

class ArrayUtils {

    public static long sumArray(int[] array) {
        long result = 0;
        for (int element : array)
            result += element;
        return result;
    }

}

class MaxFlow {
    private final Graph graph;
    private int source;
    private int destination;
    private int[] queue;
    private int[] distance;
    private int[] nextEdge;

    private MaxFlow(Graph graph, int source, int destination) {
        this.graph = graph;
        this.source = source;
        this.destination = destination;
        int vertexCount = graph.vertexCount();
        queue = new int[vertexCount];
        distance = new int[vertexCount];
        nextEdge = new int[vertexCount];
    }

    public static long dinic(Graph graph, int source, int destination) {
        return new MaxFlow(graph, source, destination).dinic();
    }

    private long dinic() {
        long totalFlow = 0;
        while (true) {
            edgeDistances();
            if (distance[destination] == -1)
                break;
            Arrays.fill(nextEdge, -2);
            totalFlow += dinicImpl(source, Long.MAX_VALUE);
        }
        return totalFlow;
    }

    private void edgeDistances() {
        Arrays.fill(distance, -1);
        distance[source] = 0;
        int size = 1;
        queue[0] = source;
        for (int i = 0; i < size; i++) {
            int current = queue[i];
            int id = graph.firstOutbound(current);
            while (id != -1) {
                if (graph.capacity(id) != 0) {
                    int next = graph.destination(id);
                    if (distance[next] == -1) {
                        distance[next] = distance[current] + 1;
                        queue[size++] = next;
                    }
                }
                id = graph.nextOutbound(id);
            }
        }
    }

    private long dinicImpl(int source, long flow) {
        if (source == destination)
            return flow;
        if (flow == 0 || distance[source] == distance[destination])
            return 0;
        int id = nextEdge[source];
        if (id == -2)
            nextEdge[source] = id = graph.firstOutbound(source);
        long totalPushed = 0;
        while (id != -1) {
            int nextDestinationID = graph.destination(id);
            if (graph.capacity(id) != 0 && distance[nextDestinationID] == distance[source] + 1) {
                long pushed = dinicImpl(nextDestinationID, Math.min(flow, graph.capacity(id)));
                if (pushed != 0) {
                    graph.pushFlow(id, pushed);
                    flow -= pushed;
                    totalPushed += pushed;
                    if (flow == 0)
                        return totalPushed;
                }
            }
            nextEdge[source] = id = graph.nextOutbound(id);
        }
        return totalPushed;
    }
}

interface Edge {
}