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.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;

public class E {
	FastScanner in = new FastScanner(System.in);
	PrintWriter out = new PrintWriter(System.out);

	int INF = 10000000;

	/*------------Dinic(Max Flow)------------*/
	class Dinic {
		class Edge {
			int to, cap;
			int flow = 0;
			Edge rev;
			
			Edge(int to, int cap) {
				this.to = to;
				this.cap = cap;
			}
			
			void setRevEdge(Edge rev) {
				this.rev = rev;
			}
		}
		
		int N;
		int tank;
		int[] ptr, Q, dist;
		
		ArrayList<Edge>[] g;

		public Dinic(int N) {
			this.N = N;
			g = new ArrayList[N + 2];
			for (int i = 0; i < N + 2; i++)
				g[i] = new ArrayList<Edge>();
			
			ptr = new int[N + 2];
			Q = new int[N + 2];
			dist = new int[N + 2];
		}
		
		void displayAnswer() {
			int n = N / 2;
			int[][] res = new int[n][n];
			for (int i = 0; i < n; i++) {
				for (Edge e : g[i+1]) {
					if (e.to == 0) continue;
					res[i][e.to - n - 1] = e.flow; 
				}
				for (int j = 0; j < n; j++) {
					System.out.print(res[i][j] + " ");
				}
				System.out.println();
			}
		}
		
		public void addEdge(int from, int to, int cap) {
			Edge e1 = new Edge(to, cap);
			Edge e2 = new Edge(from, 0);
			e1.setRevEdge(e2);
			e2.setRevEdge(e1);
			g[from].add(e1);
			g[to].add(e2);
		}
		
		boolean dinic_bfs(int src)	{
			Arrays.fill(dist, -1);
			dist[src] = 0;
			int sizeQ = 0;
			Q[sizeQ++] = src;
			for (int i = 0; i < sizeQ; i++) {
				int u = Q[i];
				for (Edge e : g[u]) {
					if (dist[e.to] < 0 && e.flow < e.cap) {
						dist[e.to] = dist[u] + 1;
						Q[sizeQ++] = e.to;
					}
				}
			}
			return dist[tank] >= 0;
		}
		
		int dinic_dfs(int u, int f) {
			if (u == tank) return f;
			for ( ; ptr[u] < g[u].size(); ptr[u]++) {
				Edge e = g[u].get(ptr[u]);
				if (dist[e.to] == dist[u] + 1 && e.flow < e.cap) {
					int df = dinic_dfs(e.to, Math.min(f, e.cap - e.flow));
					if (df > 0) {
						e.flow += df;
						e.rev.flow -= df;
						return df;
					}
				}
			}
			
			return 0;
		}
		
		public int getMaxFlow(int src, int tank) {
			this.tank = tank;
			
			int res = 0;
			while (dinic_bfs(src)) {
				Arrays.fill(ptr, 0);
				while (true) {
					int df = dinic_dfs(src, Integer.MAX_VALUE);
					if (df == 0) break;
					res += df;
				}
			}
			
			return res;
		}
	}
	/*-----------------end---------------------*/
	
	public void run() {
		int n = in.nextInt();
		int m = in.nextInt();
		int[] a = in.nextIntArray(n);
		int[] b = in.nextIntArray(n);
		
		boolean[][] g = new boolean[n][n];
		for (int i = 0; i < m; i++) {
			int from = in.nextInt() - 1, to = in.nextInt() - 1;
			g[from][to] = g[to][from] = true;
		}
		
		Dinic din = new Dinic(2 * n);
		
		int src = 0, tank = 2 * n + 1;
		for (int i = 0; i < n; i++) {
			din.addEdge(src, i + 1, a[i]);
			din.addEdge(n + i + 1, tank, b[i]);
		}
		
		for (int i = 0; i < n; i++) {
			int from = i + 1;
			for (int j = 0; j < n; j++) {
				int to = n + j + 1;
				if (g[i][j] || i == j) {
					din.addEdge(from, to, INF);
				}
			}
		}
		
		int totalA = 0, totalB = 0;
		for (int i = 0; i < n; i++) {
			totalA += a[i];
			totalB += b[i];
		}
		
		int flow = din.getMaxFlow(src, tank);
		if (flow == totalA && flow == totalB) {
			System.out.println("YES");
			din.displayAnswer();
		} else {
			System.out.println("NO");
		}
		
		/*
		int totalA = 0, totalB = 0;
		boolean can = true;
		int[] reqMin = new int[n];
		for (int i = 0; i < n; i++) {
			int sum = 0;
			totalA += a[i];
			totalB += b[i];
			for (int j = 0; j < n; j++) {
				if (g[i][j]) {
					sum += a[j];
				}
			}
			if (sum + a[i] < b[i]) can = false;
			reqMin[i] = Math.max(0, b[i] - sum);
		}
		
		if (!can || totalA != totalB) {
			System.out.println("NO");
			return;
		}
		
		System.out.println("YES");
		int[][] res = new int[n][n];
		for (int i = 0; i < n; i++) {
			res[i][i] = reqMin[i];
		}
		
		int[] now = Arrays.copyOf(a, n);
		boolean[] vis = new boolean[n];
		for (int i = 0; i < n; i++) {
			int next = -1, max = Integer.MIN_VALUE;
			for (int j = 0; j < n; j++) {
				if (vis[j]) continue;
				
				int x = 0;
				for (int k = 0; k < n; k++) {
					if (g[j][k]) x += b[k] - now[k];
				}
				if (max < x) {
					max = x;
					next = j;
				}
			}
			vis[next] = true;
			for (int k = 0; k < n; k++) if (g[next][k]) {
				int val = Math.max(0, b[k] - now[k]);
				val = Math.min(val, a[next] - reqMin[next]);
				val = Math.min(val, now[next]);
				now[next] -= val;
				now[k] += val;
				res[next][k] += val;
			}
		}
		for (int i = 0; i < n; i++) {
			int sum = 0;
			for (int j = 0; j < n; j++) if (i != j) 
				sum += res[i][j];
			res[i][i] = a[i] - sum;
			for (int j = 0; j < n; j++) {
				System.out.print(res[i][j] + " ");
			}
			System.out.println();
		}
//		System.out.println(Arrays.toString(now));
	*/
		out.close();
	}

	public static void main(String[] args) {
		new E().run();
	}

	public void mapDebug(int[][] a) {
		System.out.println("--------map display---------");

		for (int i = 0; i < a.length; i++) {
			for (int j = 0; j < a[i].length; j++) {
				System.out.printf("%3d ", a[i][j]);
			}
			System.out.println();
		}

		System.out.println("----------------------------");
		System.out.println();
	}

	public void debug(Object... obj) {
		System.out.println(Arrays.deepToString(obj));
	}

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

		public FastScanner(InputStream stream) {
			this.stream = stream;
			//stream = new FileInputStream(new File("dec.in"));

		}

		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++];
		}

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

		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

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

		int[] nextIntArray(int n) {
			int[] array = new int[n];
			for (int i = 0; i < n; i++)
				array[i] = nextInt();

			return array;
		}

		int[][] nextIntMap(int n, int m) {
			int[][] map = new int[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextIntArray(m);
			}
			return map;
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		long[] nextLongArray(int n) {
			long[] array = new long[n];
			for (int i = 0; i < n; i++)
				array[i] = nextLong();

			return array;
		}

		long[][] nextLongMap(int n, int m) {
			long[][] map = new long[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextLongArray(m);
			}
			return map;
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		double[] nextDoubleArray(int n) {
			double[] array = new double[n];
			for (int i = 0; i < n; i++)
				array[i] = nextDouble();

			return array;
		}

		double[][] nextDoubleMap(int n, int m) {
			double[][] map = new double[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextDoubleArray(m);
			}
			return map;
		}

		String next() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		String[] nextStringArray(int n) {
			String[] array = new String[n];
			for (int i = 0; i < n; i++)
				array[i] = next();

			return array;
		}

		String nextLine() {
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}
	}
}