Andrewid the Android is a galaxy-famous detective. He is now chasing a criminal hiding on the planet Oxa-5, the planet almost fully covered with water.

The only dry land there is an archipelago of n narrow islands located in a row. For more comfort let's represent them as non-intersecting segments on a straight line: island i has coordinates [li, ri], besides, ri < li + 1 for 1 ≤ i ≤ n - 1.

To reach the goal, Andrewid needs to place a bridge between each pair of adjacent islands. A bridge of length a can be placed between the i-th and the (i + 1)-th islads, if there are such coordinates of x and y, that li ≤ x ≤ ri, li + 1 ≤ y ≤ ri + 1 and y - x = a. 

The detective was supplied with m bridges, each bridge can be used at most once. Help him determine whether the bridges he got are enough to connect each pair of adjacent islands.

Input

The first line contains integers n (2 ≤ n ≤ 2·105) and m (1 ≤ m ≤ 2·105) — the number of islands and bridges.

Next n lines each contain two integers li and ri (1 ≤ li ≤ ri ≤ 1018) — the coordinates of the island endpoints.

The last line contains m integer numbers a1, a2, ..., am (1 ≤ ai ≤ 1018) — the lengths of the bridges that Andrewid got.

Output

If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes), otherwise print in the first line "Yes" (without the quotes), and in the second line print n - 1 numbers b1, b2, ..., bn - 1, which mean that between islands i and i + 1 there must be used a bridge number bi. 

If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case.

Examples

Input

4 4
1 4
7 8
9 10
12 14
4 5 3 8


Output

Yes
2 3 1 


Input

2 2
11 14
17 18
2 9


Output

No


Input

2 1
1 1
1000000000000000000 1000000000000000000
999999999999999999


Output

Yes
1 

Note

In the first sample test you can, for example, place the second bridge between points 3 and 8, place the third bridge between points 7 and 10 and place the first bridge between points 10 and 14.

In the second sample test the first bridge is too short and the second bridge is too long, so the solution doesn't exist.
import java.io.*;
import java.util.*;

public class CCCC {
	InputStream is;

	int __t__ = 1;
	int __f__ = 0;
	int __FILE_DEBUG_FLAG__ = __f__;
	String __DEBUG_FILE_NAME__ = "src/T";

	FastScanner in;
	PrintWriter out;

	class Bridge implements Comparable<Bridge> {
		int id;
		long len;

		Bridge(int id, long len) {
			this.id = id;
			this.len = len;
		}

		public int compareTo(Bridge s) {
			return Long.compare(len, s.len);
		}

		public String toString() {
			return getClass().getName() + " : " + id + " " + len;
		}
	}
	
	class State implements Comparable<State> {
		int id;
		long min;
		long max;

		State(int id, long min, long max) {
			this.id = id;
			this.min = min;
			this.max = max;
		}

		public int compareTo(State s) {
			if (min != s.min) return Long.compare(min, s.min);
			return Long.compare(max, s.max);
		}

		public String toString() {
			return getClass().getName() + " : " + id + " " + min + " " + max;
		}
	}
	
	class XX implements Comparable<XX> {
		int id;
		long val;

		XX(int id, long val) {
			this.id = id;
			this.val = val;
		}

		public int compareTo(XX s) {
			return Long.compare(val, s.val);
		}

		public String toString() {
			return getClass().getName() + " : " + id + " " + val;
		}
	}
	
	class YY implements Comparable<YY> {
		int id;
		long len;

		YY(int id, long len) {
			this.id = id;
			this.len = len;
		}

		public int compareTo(YY s) {
			if (len != s.len) return Long.compare(len, s.len);
			return id - s.id;
		}

		public String toString() {
			return getClass().getName() + " : " + id + " " + len;
		}
	}
	
	public void solve() {
		int n = in.nextInt(), m = in.nextInt();
		long[] l = new long[n];
		long[] r = new long[n];
		for (int i = 0; i < n; i++) {
			l[i] = in.nextLong();
			r[i] = in.nextLong();
		}
		long[] a = in.nextLongArray(m);
		
		State[] state = new State[n-1];
		for (int i = 0; i < n - 1; i++) {
			state[i] = new State(i, l[i+1] - r[i], r[i+1] - l[i]);
		}
		Arrays.sort(state);
		
		TreeSet<YY> br = new TreeSet<YY>();
		for (int i = 0; i < m; i++) {
			br.add(new YY(i, a[i]));
		}
		
		PriorityQueue<XX> pq = new PriorityQueue<XX>();
		for (int i = 0; i < n - 1; i++) {
			pq.add(new XX(i, state[i].min));
			pq.add(new XX(i, state[i].max));
		}
		
		boolean[] used = new boolean[n-1];
		
		int[] res = new int[n-1];
		while (!pq.isEmpty()) {
			XX next = pq.poll();
			if (!used[next.id]) {
				used[next.id] = true;
			} else {
				YY y = br.ceiling(new YY(-1, state[next.id].min));
				if (y != null && y.len <= state[next.id].max) {
					res[state[next.id].id] = y.id + 1;
					br.remove(y);
				} else {
					System.out.println("No");
					return;
				}
			}
		}

		out.println("Yes");
		for (int i = 0; i < n - 1; i++) {
			out.print(res[i] + " ");
		}
		out.println();
		out.close();
		
		/*
		Bridge[] br = new Bridge[m];
		for (int i = 0; i < m; i++) {
			br[i] = new Bridge(i, a[i]);
		}
		Arrays.sort(br);
		
		int[] res = new int[n-1];
		int ptr = 0;
		for (int i = 0; i < n - 1; i++) {
			while (ptr < m && state[i].min > br[ptr].len) {
				ptr++;
			}
			if (ptr == m || state[i].max < br[ptr].len) {
				System.out.println("No");
				return;
			}
			System.out.println(state[i].toString() + " " + br[ptr].toString());

			res[state[i].id] = br[ptr].id + 1;
			ptr++;
		}
		
		out.println("Yes");
		for (int i = 0; i < n - 1; i++) {
			out.print(res[i] + " ");
		}
		out.println();
		out.close();
		*/
	}

	public void run() {
		if (__FILE_DEBUG_FLAG__ == __t__) {
			try {
				is = new FileInputStream(__DEBUG_FILE_NAME__);
			} catch (FileNotFoundException e) {
				// TODO 自動生成された catch ブロック
				e.printStackTrace();
			}
			System.out.println("FILE_INPUT!");
		} else {
			is = System.in;
		}
		in = new FastScanner(is);
		out = new PrintWriter(System.out);

		solve();
	}

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

