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.BufferedWriter;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashSet;
import java.util.List;
import java.util.TreeSet;

public class Main {
	static HashSet<String> set = new HashSet<String>();
	public static void main(String[] args) throws NumberFormatException,
	IOException {
		Solve solve = new Solve();
		solve.solve();
	}
}
class Solve{
	ContestScanner in;
	Solve() throws FileNotFoundException{
		in = new ContestScanner();
	}
	void solve() throws IOException{
		int n = in.nextInt();
		int m = in.nextInt();
		Is[] is = new Is[n];
		for(int i=0; i<n; i++){
			is[i] = new Is(in.nextLong(), in.nextLong());
		}
		Prob[] p = new Prob[n-1];
		for(int i=0; i<n-1; i++){
			p[i] = new Prob(i, is[i+1].l-is[i].r, is[i+1].r-is[i].l);
		}
		Arrays.sort(p);
		Bridge[] a = new Bridge[m];
		for(int i=0; i<m; i++){
			a[i] = new Bridge(i, in.nextLong());
		}
		int idx = 0;
		Arrays.sort(a);
		List<Ans> ans = new ArrayList<Ans>();
		TreeSet<Bridge> set = new TreeSet<Bridge>();
		Bridge seeker = new Bridge(0, -1);
		for(int i=0; i<n-1; i++){
			while(idx < m && a[idx].len <= p[i].max) set.add(a[idx++]);
			seeker.len = p[i].min;
			Bridge b = set.ceiling(seeker);
			if(b == null){
				System.out.println("No");
				return;
			}
			set.remove(b);
			ans.add(new Ans(p[i].id, b.id+1));
		}
		
//		for(int i=0; i<m; i++){
//			if(!p[idx].use(a[i].len)) continue;
//			ans.add(new Ans(p[idx++].id, a[i].id+1));
//			if(idx == n-1) break;
//		}
//		if(ans.size() < n-1){
//			System.out.println("No");
//			return;
//		}
		Collections.sort(ans);
		System.out.println("Yes");
		StringBuilder sb = new StringBuilder();
		for(Ans r: ans){
			sb.append(r+" ");
		}
		System.out.println(sb.toString().trim());
	}
}

class Ans implements Comparable<Ans>{
	int id;
	int bid;
	Ans(int id, int bid){
		this.id = id;
		this.bid = bid;
	}
	
	@Override
	public int compareTo(Ans o) {
		return id-o.id;
	}
	
	public String toString(){
		return bid+"";
	}
}

class Bridge implements Comparable<Bridge>{
	long len;
	int id;
	Bridge(int id, long len){
		this.len = len;
		this.id = id;
	}
	@Override
	public int compareTo(Bridge o) {
		if(len != o.len) return Long.compare(len, o.len);
		return id-o.id;
	}
}

class Prob implements Comparable<Prob>{
	long min, max;
	int id;
	Prob(int id, long min, long max){
		this.min = min;
		this.max = max;
		this.id = id;
	}
	
	boolean use(long len){
		return min<=len && len<=max;
	}
	@Override
	public int compareTo(Prob o) {
		if(max != o.max) return Long.compare(max, o.max);
		return Long.compare(min, o.min);
	}
}

class Is{
	long l, r;
	Is(long l, long r){
		this.l = l;
		this.r = r;
	}
}

class Timer{
	long time;
	public void set(){
		time = System.currentTimeMillis();
	}
	
	public long stop(){
		return System.currentTimeMillis()-time;
	}
}

class Node{
	int id;
	ArrayList<Node> edge = new ArrayList<Node>();
	public Node(int id) {
		this.id = id;
	}
	public void createEdge(Node node) {
		edge.add(node);
	}
}

class MyComp implements Comparator<int[]> {
	final int idx;
	public MyComp(int idx){
		this.idx = idx;
	}
	public int compare(int[] a, int[] b) {
		return a[idx] - b[idx];
	}
}

class Reverse implements Comparator<Integer> {
	public int compare(Integer arg0, Integer arg1) {
		return arg1 - arg0;
	}
}


class ContestWriter {
	private PrintWriter out;

	public ContestWriter(String filename) throws IOException {
		out = new PrintWriter(new BufferedWriter(new FileWriter(filename)));
	}

	public ContestWriter() throws IOException {
		out = new PrintWriter(System.out);
	}

	public void println(String str) {
		out.println(str);
	}
	
	public void println(Object obj) {
		out.println(obj);
	}

	public void print(String str) {
		out.print(str);
	}
	
	public void print(Object obj) {
		out.print(obj);
	}

	public void close() {
		out.close();
	}
}

class ContestScanner {
	private BufferedReader reader;
	private String[] line;
	private int idx;

	public ContestScanner() throws FileNotFoundException {
		reader = new BufferedReader(new InputStreamReader(System.in));
	}

	public ContestScanner(String filename) throws FileNotFoundException {
		reader = new BufferedReader(new InputStreamReader(new FileInputStream(
				filename)));
	}

	public String nextToken() throws IOException {
		if (line == null || line.length <= idx) {
			line = reader.readLine().trim().split(" ");
			idx = 0;
		}
		return line[idx++];
	}
	
	public String readLine() throws IOException{
		return reader.readLine();
	}

	public long nextLong() throws IOException, NumberFormatException {
		return Long.parseLong(nextToken());
	}

	public int nextInt() throws NumberFormatException, IOException {
		return (int) nextLong();
	}

	public double nextDouble() throws NumberFormatException, IOException {
		return Double.parseDouble(nextToken());
	}
}