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.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 * 
 * @author pttrung
 */
public class E_Round_304_Div2 {

	public static long MOD = 1000000007;
	static long min;

	public static void main(String[] args) throws FileNotFoundException {
		// PrintWriter out = new PrintWriter(new FileOutputStream(new File(
		// "output.txt")));
		PrintWriter out = new PrintWriter(System.out);
		Scanner in = new Scanner();
		int n = in.nextInt();
		int 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();
		}
		int need = 0;
		int dif = 0;
		for (int i = 1; i <= n; i++) {
			b[i] = in.nextInt();
			need +=  a[i];
			if (b[i] > a[i]) {
				
				dif += (b[i] - a[i]);
			} else {
				dif -= (a[i] - b[i]);
			}
		}

		Point[] data = new Point[m];
		for (int i = 0; i < m; i++) {
			data[i] = new Point(in.nextInt(), in.nextInt());
		}
		if (dif == 0) {
			int index = n + 1;
			int[] point = new int[n + 1];
			for (int i = 1; i <= n; i++) {
				point[i] = index++;
			}
			int[][] map = new int[2 + 2 * n][2 + 2 * n];
			int end = 2 * n + 1;
			for (int i = 1; i <= n; i++) {
				map[0][i] = a[i];
				map[i][point[i]] = 1000;
				
				map[point[i]][end] = b[i];
				
			}
			
			for (Point p : data) {
				map[p.x][point[p.y]] = 1000;
				
				map[p.y][point[p.x]] = 1000;
				
			}
			int max = 0;
			while (true) {
				int[] pa = new int[2 * n + 2];
				Arrays.fill(pa, -1);
				pa[0] = 0;
				LinkedList<Integer> q = new LinkedList();
				q.add(0);

				while (!q.isEmpty()) {
					int node = q.pollFirst();
					for (int i = 0; i < 2 * n + 2; i++) {
						if (map[node][i] > 0 && pa[i] == -1) {

							pa[i] = node;
							q.add(i);
						}
					}
				}
				if (pa[end] == -1) {
					break;
				}
				min = Integer.MAX_VALUE;
				augment(end, map, pa);
				if (min == 0) {
					break;
				}
				max += min;
			}
			//System.out.println(max);
			if (need == max) {
				out.println("YES");
				int[][] result = new int[n + 1][n + 1];
				int[] o = new int[n + 1];
				for (Point p : data) {
					if (map[p.x][point[p.y]] < 1000) {
						result[p.x][p.y] = 1000 - map[p.x][point[p.y]] ;
						o[p.x] += result[p.x][p.y];
					} 
					if (map[p.y][point[p.x]] < 1000) {
						result[p.y][p.x] = 1000 - map[p.y][point[p.x]] ;
						o[p.y] += result[p.y][p.x];
					}
				}
				for (int i = 1; i <= n; i++) {

					for (int j = 1; j <= n; j++) {
						if (i == j) {
							// System.out.println(o[i] + " " + a[i]);
							out.print((a[i] - o[i]) + " ");
						} else {
							out.print(result[i][j] + " ");
						}
					}
					out.println();
				}
			} else {
				out.println("NO");
			}
		} else {
			out.println("NO");
		}
		out.close();
	}

	public static void augment(int index, int[][] map, int[] pa) {
		if (pa[index] != index) {
			min = Math.min(min, map[pa[index]][index]);

			augment(pa[index], map, pa);
			map[pa[index]][index] -= min;
			map[index][pa[index]] += min;
		}
	}

	public static int[] KMP(String val) {
		int i = 0;
		int j = -1;
		int[] result = new int[val.length() + 1];
		result[0] = -1;
		while (i < val.length()) {
			while (j >= 0 && val.charAt(j) != val.charAt(i)) {
				j = result[j];
			}
			j++;
			i++;
			result[i] = j;
		}
		return result;

	}

	public static boolean nextPer(int[] data) {
		int i = data.length - 1;
		while (i > 0 && data[i] < data[i - 1]) {
			i--;
		}
		if (i == 0) {
			return false;
		}
		int j = data.length - 1;
		while (data[j] < data[i - 1]) {
			j--;
		}
		int temp = data[i - 1];
		data[i - 1] = data[j];
		data[j] = temp;
		Arrays.sort(data, i, data.length);
		return true;
	}

	public static int digit(long n) {
		int result = 0;
		while (n > 0) {
			n /= 10;
			result++;
		}
		return result;
	}

	public static double dist(long a, long b, long x, long y) {
		double val = (b - a) * (b - a) + (x - y) * (x - y);
		val = Math.sqrt(val);
		double other = x * x + a * a;
		other = Math.sqrt(other);
		return val + other;

	}

	public static class Point implements Comparable<Point> {

		int x, y;

		public Point(int start, int end) {
			this.x = start;
			this.y = end;
		}

		@Override
		public int hashCode() {
			int hash = 5;
			hash = 47 * hash + this.x;
			hash = 47 * hash + this.y;
			return hash;
		}

		@Override
		public boolean equals(Object obj) {
			if (obj == null) {
				return false;
			}
			if (getClass() != obj.getClass()) {
				return false;
			}
			final Point other = (Point) obj;
			if (this.x != other.x) {
				return false;
			}
			if (this.y != other.y) {
				return false;
			}
			return true;
		}

		@Override
		public int compareTo(Point o) {
			return x - o.x;
		}
	}

	public static class FT {

		long[] data;

		FT(int n) {
			data = new long[n];
		}

		public void update(int index, long value) {
			while (index < data.length) {
				data[index] += value;
				index += (index & (-index));
			}
		}

		public long get(int index) {
			long result = 0;
			while (index > 0) {
				result += data[index];
				index -= (index & (-index));
			}
			return result;

		}
	}

	public static long gcd(long a, long b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	public static long pow(long a, long b) {
		if (b == 0) {
			return 1;
		}
		if (b == 1) {
			return a;
		}
		long val = pow(a, b / 2);
		if (b % 2 == 0) {
			return val * val % MOD;
		} else {
			return val * (val * a % MOD) % MOD;

		}
	}

	static class Scanner {

		BufferedReader br;
		StringTokenizer st;

		public Scanner() throws FileNotFoundException {
			// System.setOut(new PrintStream(new
			// BufferedOutputStream(System.out), true));
			br = new BufferedReader(new InputStreamReader(System.in));
			// br = new BufferedReader(new InputStreamReader(new
			// FileInputStream(new File("input.txt"))));
		}

		public String next() {

			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception e) {
					throw new RuntimeException();
				}
			}
			return st.nextToken();
		}

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

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

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

		public String nextLine() {
			st = null;
			try {
				return br.readLine();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}

		public boolean endLine() {
			try {
				String next = br.readLine();
				while (next != null && next.trim().isEmpty()) {
					next = br.readLine();
				}
				if (next == null) {
					return true;
				}
				st = new StringTokenizer(next);
				return st.hasMoreTokens();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}
	}
}