Problem: Robot Bender decided to make Fray a birthday present. He drove n nails and numbered them from 1 to n in some order. Bender decided to make a picture using metal rods. The picture is a closed polyline, which vertices should be nails (in the given order). The segments of the polyline should be parallel to the coordinate axes. Polyline is allowed to have self-intersections. Bender can take a rod and fold it exactly once in any place to form an angle of 90 degrees. Then he can attach the place of the fold to some unoccupied nail and attach two ends of this rod to adjacent nails. A nail is considered unoccupied if there is no rod attached to it (neither by it's end nor the by the fold place). No rod could be used twice. It is not required to use all the rods.

Help Bender to solve this difficult task.

Input

The first line contains two positive integers n and m (4 ≤ n ≤ 500, 2 ≤ m ≤ 500, n is even) — the amount of nails and the amount of rods. i-th of the following n lines contains a pair of integers, denoting the coordinates of the i-th nail. Nails should be connected in the same order as they are given in the input. The last line contains m integers — the lenghts of the rods. All coordinates do not exceed 104 by absolute value. Lengths of the rods are between 1 and 200 000. No rod can be used twice. It is guaranteed that all segments of the given polyline are parallel to coordinate axes. No three consecutive nails lie on the same line.

Output

If it is impossible to solve Bender's problem, output NO. Otherwise, output YES in the first line, and in the second line output n numbers — i-th of them should be the number of rod, which fold place is attached to the i-th nail, or -1, if there is no such rod.

If there are multiple solutions, print any of them.

Examples

Input

4 2
0 0
0 2
2 2
2 0
4 4


Output

YES
1 -1 2 -1 


Input

6 3
0 0
1 0
1 1
2 1
2 2
0 2
3 2 3


Output

YES
1 -1 2 -1 3 -1 


Input

6 3
0 0
1 0
1 1
2 1
2 2
0 2
2 2 3


Output

NO

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.InputMismatchException;

/**
 * @author Egor Kulikov (egor@egork.net)
 *         Created on 14.03.2010
 */
public class TaskA implements Runnable {
	private InputReader in;
	private PrintWriter out;

	public static void main(String[] args) throws InterruptedException {
		TaskA solver = new TaskA();
		Thread t = new Thread(solver);
		t.start();
		t.join();
//		solver.run();
		solver.out.close();
	}

	public TaskA() {
//		String id = getClass().getName().toLowerCase();
//		try {
//			System.setIn(new FileInputStream(id + ".in"));
//			System.setOut(new PrintStream(new FileOutputStream(id + ".out")));
//			System.setIn(new FileInputStream("input.txt"));
//			System.setOut(new PrintStream(new FileOutputStream("output.txt")));
//		} catch (FileNotFoundException e) {
//			throw new RuntimeException();
//		}
		in = new InputReader(System.in);
		out = new PrintWriter(System.out);
	}

	public void run() {
		int n = in.readInt();
		int m = in.readInt();
		int[] x = new int[n];
		int[] y = new int[n];
		for (int i = 0; i < n; i++) {
			x[i] = in.readInt();
			y[i] = in.readInt();
		}
		int[] a = new int[m];
		for (int i = 0; i < m; i++)
			a[i] = in.readInt();
		for (int i = 0; i < 2; i++) {
			boolean good = true;
			boolean[] w = new boolean[m];
			int[] ans = new int[n];
			Arrays.fill(ans, -1);
			for (int j = i; j < n; j += 2) {
				int t = j;
				int u = (j + 1) % n;
				int v = (j + 2) % n;
				int len = Math.abs(x[t] - x[u]) + Math.abs(x[v] - x[u]) + Math.abs(y[t] - y[u]) + Math.abs(y[v] - y[u]);
				boolean found = false;
				for (int k = 0; k < m; k++) {
					if (a[k] == len && !w[k]) {
						w[k] = true;
						found = true;
						ans[u] = k + 1;
						break;
					}
				}
				if (!found) {
					good = false;
					break;
				}
			}
			if (good) {
				out.println("YES");
				out.print(ans[0]);
				for (int j = 1; j < n; j++)
					out.print(" " + ans[j]);
				out.println();
				return;
			}
		}
		out.println("NO");
	}

	private static class InputReader {
		private InputStream stream;
		private byte[] buf = new byte[1000];
		private int curChar, numChars;

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

		private 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 long readLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long 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 String readString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuffer res = new StringBuffer();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

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

		private String readLine0() {
			StringBuffer buf = new StringBuffer();
			int c = read();
			while (c != '\n' && c != -1) {
				buf.appendCodePoint(c);
				c = read();
			}
			return buf.toString();
		}

		public String readLine() {
			String s = readLine0();
			while (s.trim().length() == 0)
				s = readLine0();
			return s;
		}

		public String readLine(boolean ignoreEmptyLines) {
			if (ignoreEmptyLines)
				return readLine();
			else
				return readLine0();
		}

		public BigInteger readBigInteger() {
			try {
				return new BigInteger(readString());
			} catch (NumberFormatException e) {
				throw new InputMismatchException();
			}
		}

		public char readCharacter() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			return (char) c;
		}

		public double readDouble() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') {
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) {
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}
	}
}