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.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.PrintStream;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

/*
public class _556D {

}

 */

public class _556D {

	class node
	{
		public long si;
		public long p;

		public node(long si, long p) 
		{
			super();
			this.si = si;
			this.p = p;
		}
	}

	public void solve() throws FileNotFoundException {
		InputStream inputStream = System.in;

		InputHelper inputHelper = new InputHelper(inputStream);

		PrintStream out = System.out;

		//actual solution
		int n = inputHelper.readInteger();
		int m = inputHelper.readInteger();

		HashMap<Integer, Integer> h = new HashMap<Integer, Integer>();

		List[] sl = new List[m + 2];
		List[] el = new List[m + 2];

		List<node> nl = new ArrayList<_556D.node>();

		for(int i = 0; i < m + 2; i++)
		{
			sl[i] = new ArrayList<Integer>();
			el[i] = new ArrayList<Integer>();
		}

		for(int i = 0; i < n; i++)
		{
			long l = inputHelper.readLong();
			long r = inputHelper.readLong();

			//h.put(l, r);

			nl.add(new node(l, r));
		}

		List<node> al = new ArrayList<node>();

		for(int i = 0; i < m; i++)
		{
			long a = inputHelper.readLong();

			al.add(new node(a, i));
		}

		Collections.sort(al, new Comparator<node>() {

			public int compare(node o1, node o2) {
				return (int) Math.signum(o1.si - o2.si);
			}
		});
		
		HashMap<Integer, Integer> h2 = new HashMap<Integer, Integer>();
		
		for(int i = 0; i < al.size(); i++)
		{
			h2.put(i, (int)al.get(i).p);
		}
		
		for(int i = 1; i < n; i++)
		{
			long maxd = nl.get(i).p - nl.get(i - 1).si;
			long mind = nl.get(i).si - nl.get(i - 1).p;

			int si = ceil(al, mind);
			int ei = floor(al, maxd);

			if(si == -1 || ei == -1 || si > ei)
			{
				System.out.println("No");
				return;
			}
				
			sl[si].add(i);
			el[ei + 1].add(i);

			h.put(i, ei + 1);
		}

		PriorityQueue<node> pq = new PriorityQueue<node>(n, new Comparator<node>() {

			public int compare(node o1, node o2) {
				return (int) Math.signum(o1.p - o2.p);
			}
		});
		
		HashSet<Integer> es = new HashSet<Integer>();

		int fg = 0;
		int[] ans = new int[n + 1];
		for(int i = 0; i < m; i++)
		{
			for(int j = 0; j < sl[i].size(); j++)
			{
				pq.add(new node((Integer)sl[i].get(j), h.get((Integer)sl[i].get(j))));
			}

			for(int j = 0; j < el[i].size(); j++)
			{
				es.add((Integer)el[i].get(j));
			}

			node pn = null;
			while(pq.size() > 0)
			{
				pn = pq.poll();

				if(es.contains((int)pn.si))
				{
					pn = null;
					continue;
				}
				else
				{
					break;
				}
			}
			
			if(pn != null)
			{
				ans[(int)pn.si] = h2.get(i);
				fg++;
				es.add((int)pn.si);
			}
		}

		if(fg == n - 1)
		{
			System.out.println("Yes");
			for(int i = 1; i < n; i++)
			{
				System.out.print(ans[i] + 1);
				System.out.print(" ");
			}
		}
		else
		{
			System.out.println("No");
		}
		//end here
	}

	private int ceil(List<node> nl, long num) 
	{
		int mid;
		int min = 0;
		int max = nl.size() - 1;
		
		while(min <= max)
		{
			mid = min + (max - min) / 2;
			
			if((nl.get(mid).si >= num) && (mid == 0 || nl.get(mid - 1).si < num))
			{
				return mid;
			}
			
			if((nl.get(mid).si >= num) && (nl.get(mid - 1).si >= num))
			{
				max = mid - 1;
			}
			
			if(nl.get(mid).si < num)
			{
				min = mid + 1;
			}
		}
		
		return -1;
	}
	
	private int floor(List<node> nl, long num) 
	{
		int mid;
		int min = 0;
		int max = nl.size() - 1;
		
		while(min <= max)
		{
			mid = min + (max - min) / 2;
			
			if((nl.get(mid).si <= num) && (mid == nl.size() - 1 || nl.get(mid + 1).si > num))
			{
				return mid;
			}
			
			if((nl.get(mid).si <= num) && (nl.get(mid + 1).si <= num))
			{
				min = mid + 1;
			}
			
			if(nl.get(mid).si > num)
			{
				max = mid - 1;
			}
		}
		
		return -1;
	}

	public static void main(String[] args) throws FileNotFoundException {
		(new _556D()).solve();
	}

	class InputHelper {
		StringTokenizer tokenizer = null;
		private BufferedReader bufferedReader;

		public InputHelper(InputStream inputStream) {
			InputStreamReader inputStreamReader = new InputStreamReader(
					inputStream);
			bufferedReader = new BufferedReader(inputStreamReader, 16384);
		}

		public String read() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					String line = bufferedReader.readLine();
					if (line == null) {
						return null;
					}
					tokenizer = new StringTokenizer(line);
				} catch (IOException e) {
					e.printStackTrace();
				}
			}

			return tokenizer.nextToken();
		}

		public Integer readInteger() {
			return Integer.parseInt(read());
		}

		public Long readLong() {
			return Long.parseLong(read());
		}
	}
}