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.Arrays;
import java.util.Comparator;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class Main {
    public static void main(String[] args) throws Exception {

        IOUtils ut = new IOUtils(System.in, System.out);
        new Solution(ut);
        ut.close();
    }
}

class Solution {
    IOUtils io;

    int n, m;
    Gap[] gaps;
    int[] answer;

    public Solution(IOUtils io) throws Exception {
        this.io = io;

        n = io.readInt();
        m = io.readInt();

        gaps = new Gap[n - 1];
        answer = new int[n - 1];

        long pl = 0, pr = 0;
        for (int i = 0; i < n; i++) {
            long l = io.readLong();
            long r = io.readLong();

            if (i > 0) {
                gaps[i - 1] = new Gap(l - pr, r - pl, i - 1);
            }
            pr = r;
            pl = l;
        }

        Arrays.sort(gaps, new GapComparator());

        TreeSet<Bridge> set = new TreeSet<Bridge>(new BridgeComparator());

        for (int i = 0; i < m; i++) {
            long l = io.readLong();
            set.add(new Bridge(l, i));
        }

        for (int i = 0; i < n - 1; i++) {
            Gap g = gaps[i];
            Bridge b = set.higher(new Bridge(g.a, -1));
            if (b == null) {
                io.writeln("No");
                return;
            }
            if (b.length > g.b) {
                io.writeln("No");
                return;
            }
            answer[g.index] = b.index;
            set.remove(b);
        }

        io.writeln("Yes");
        for (int i = 0; i < n - 1; i++) {
            io.write(String.format("%d ", answer[i] + 1));
        }
        io.writeln();
    }

    class Bridge {
        public long length;
        public int index;

        public Bridge(long l, int i) {
            length = l;
            index = i;
        }
    }

    class BridgeComparator implements Comparator<Bridge> {
        public int compare(Bridge b1, Bridge b2) {
            if (b1.length > b2.length || (b1.length == b2.length && b1.index > b2.index)) return 1;
            if (b2.length > b1.length || (b2.length == b1.length && b2.index > b1.index)) return -1;
            return 0;
        }
    }

    class Gap {
        public long a, b;
        public int index;

        public Gap(long aa, long bb, int i) {
            a = aa;
            b = bb;
            index = i;
        }
    }

    class GapComparator implements Comparator<Gap> {
        public int compare(Gap b1, Gap b2) {
            if (b1.b > b2.b || (b1.b == b2.b && b1.a > b2.a) || (b1.b == b2.b && b1.a == b2.a && b1.index > b2.index)) return 1;
            if (b2.b > b1.b || (b2.b == b1.b && b2.a > b1.a) || (b2.b == b1.b && b2.a == b1.a && b2.index > b1.index)) return -1;
            return 0;
        }
    }
}

class IOUtils {
    public BufferedReader in;
    public PrintWriter out;
    StringTokenizer st = null;

    public IOUtils(InputStream inStream, OutputStream outStream) {
        in = new BufferedReader(new InputStreamReader(inStream));
        out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outStream)));
    }

    private void read_input() throws Exception {
        while (st == null || !(st.hasMoreTokens())) {
            st = new StringTokenizer(in.readLine());
        }
    }

    public void close() throws Exception {
        out.flush();
        in.close();
        out.close();
    }

    public String read() throws Exception {
        read_input();
        return st.nextToken();
    }

    public int readInt() throws Exception {
        read_input();
        return Integer.parseInt(st.nextToken());
    }

    public long readLong() throws Exception {
        read_input();
        return Long.parseLong(st.nextToken());
    }

    public double readDouble() throws Exception {
        read_input();
        return Double.parseDouble(st.nextToken());
    }

    public void writeln(String i) throws Exception {
        out.println(i);
    }

    public void write(String i) throws Exception {
        out.print(i);
    }

    public void writeln() throws Exception {
        out.print("\n");
    }

    public void write(int i) throws Exception {
        out.print(i);
    }

    public void writeln(int i) throws Exception {
        out.println(i);
    }

    public void write(long i) throws Exception {
        out.print(i);
    }

    public void writeln(long i) throws Exception {
        out.println(i);
    }
}
