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.util.Arrays;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.io.IOException;
import java.util.AbstractCollection;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Tifuera
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskB solver = new TaskB();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskB {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int n = in.nextInt();
        int m = in.nextInt();

        Island[] islands = new Island[n];
        PairOfIslands[] pairs = new PairOfIslands[n - 1];
        for (int i = 0; i < n; i++) {
            long l = in.nextLong();
            long r = in.nextLong();
            islands[i] = new Island(l, r, i);
        }

        for (int i = 0; i < n - 1; i++) {
            pairs[i] = new PairOfIslands(islands[i], islands[i + 1]);
        }

        Bridge[] bridges = new Bridge[m];
        for (int i = 0; i < m; i++) {
            long len = in.nextLong();
            bridges[i] = new Bridge(len, i + 1);
        }

        Arrays.sort(bridges);
        //sort by min length
        Arrays.sort(pairs, new Comparator<PairOfIslands>() {
            public int compare(PairOfIslands o1, PairOfIslands o2) {
                if (o1.min != o2.min) {
                    return Long.compare(o1.min, o2.min);
                } else {
                    return o1.first.id - o2.first.id;
                }
            }
        });

        int[] result = new int[n - 1];
        PriorityQueue<PairOfIslands> pq = new PriorityQueue<>(new Comparator<PairOfIslands>() {
            public int compare(PairOfIslands o1, PairOfIslands o2) {
                if (o1.max != o2.max) {
                    return Long.compare(o1.max, o2.max);
                } else {
                    return o1.first.id - o2.first.id;
                }
            }
        });

        int pairPtr = 0;
        Arrays.fill(result, -1);
        for (int bId = 0; bId < m; bId++) {
            Bridge current = bridges[bId];
            while (pairPtr < pairs.length && pairs[pairPtr].min <= current.length) {
                pq.add(pairs[pairPtr]);
                pairPtr++;
            }

            while (!pq.isEmpty()) {
                PairOfIslands candidate = pq.poll();
                if (candidate.max >= current.length /*&& candidate.min <= current.length*/) {
                    result[candidate.first.id] = current.id;
                    break;
                }
            }
        }

        boolean isOk = true;
        for (int r : result) {
            if (r == -1) {
                isOk = false;
                break;
            }
        }
        if (isOk) {
            out.println("Yes");
            for (int r : result) {
                out.print(r + " ");
            }
        } else {
            out.println("No");
        }
    }

    public static class PairOfIslands {
        Island first;
        Island second;
        long min;
        long max;

        public PairOfIslands(Island first, Island second) {
            this.first = first;
            this.second = second;
            min = second.left - first.right;
            max = second.right - first.left;
        }
    }

    public static class Island {
        long left;
        long right;
        int id;

        public Island(long left, long right, int id) {
            this.left = left;
            this.right = right;
            this.id = id;
        }
    }

    public static class Bridge implements Comparable<Bridge> {
        long length;
        int id;

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

        public int compareTo(Bridge o) {
            if (length != o.length) {
                return Long.compare(length, o.length);
            }
            return id - o.id;
        }
    }
}

class InputReader {
    private BufferedReader reader;
    private String[] currentArray;
    private int curPointer;

    public InputReader(InputStream inputStream) {
        reader = new BufferedReader(new InputStreamReader(inputStream));
    }


    public int nextInt() {
        if ((currentArray == null) || (curPointer >= currentArray.length)) {
            try {
                currentArray = reader.readLine().split(" ");
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            curPointer = 0;
        }
        return Integer.parseInt(currentArray[curPointer++]);
    }

    public long nextLong() {
        if ((currentArray == null) || (curPointer >= currentArray.length)) {
            try {
                currentArray = reader.readLine().split(" ");
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            curPointer = 0;
        }
        return Long.parseLong(currentArray[curPointer++]);
    }

}

