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 B {

    final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    class Bridge implements Comparable<Bridge> {
        long l;
        int index;

        public Bridge(long l, int index) {
            this.l = l;
            this.index = index;
        }

        @Override
        public int compareTo(Bridge o) {
            return Long.compare(this.l, o.l);
        }
    }

    class Strait implements Comparable<Strait> {
        long min;
        long max;
        int index;

        public Strait(long min, long max, int index) {
            this.min = min;
            this.max = max;
            this.index = index;
        }

        @Override
        public int compareTo(Strait o) {
            return Long.compare(this.min, o.min);
        }
    }

	void solve() throws IOException {
        int n = readInt();
        int m = readInt();
        long prevS = readLong();
        long prevF = readLong();
        Strait[] straits = new Strait[n-1];
        for(int i = 0; i < n-1; i++) {
            long curS = readLong();
            long curF = readLong();
            long min = curS - prevF;
            long max = curF - prevS;
            straits[i] = new Strait(min, max, i);
            prevS = curS;
            prevF = curF;
        }

        Bridge[] bridges = new Bridge[m];
        for(int i = 0; i < m; i++) {
            bridges[i] = new Bridge(readLong(), i+1);
        }
        Arrays.sort(straits);
        Arrays.sort(bridges);

        int[] matching = new int[n-1];
        Arrays.fill(matching, -1);

        TreeSet<Strait> available = new TreeSet<Strait>(new Comparator<Strait>() {
            @Override
            public int compare(Strait o1, Strait o2) {
                if(o1.max == o2.max) {
                    return Integer.compare(o1.index, o2.index);
                }
                return Long.compare(o1.max, o2.max);
            }
        });

        int pointer = 0;

        for(int i = 0; i < m; i++) {
            Bridge curBridge = bridges[i];
            while (pointer < n-1) {
                Strait curStrait = straits[pointer];
                if(curBridge.l >= curStrait.min) {
                    available.add(curStrait);
                    pointer++;
                } else {
                    break;
                }
            }

            while (!available.isEmpty()) {
                Strait curStrait = available.pollFirst();
                if(curBridge.l <= curStrait.max) {
                    matching[curStrait.index] = curBridge.index;
                    break;
                }
            }
        }

        boolean check = true;
        for(int i = 0; i < n-1; i++) {
            if(matching[i] == -1) {
                check = false;
            }
        }

        if(!check) {
            out.println("No");
        } else {
            out.println("Yes");
            for(int i: matching) {
                out.print(i + " ");
            }
        }
    }

    void init() throws FileNotFoundException {
        if (ONLINE_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    int[] readArr(int n) throws IOException {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = readInt();
        }
        return res;
    }

    long[] readArrL(int n) throws IOException {
        long[] res = new long[n];
        for (int i = 0; i < n; i++) {
            res[i] = readLong();
        }
        return res;
    }

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

    public void run() {
        try {
            long t1 = System.currentTimeMillis();
            init();
            solve();
            out.close();
            long t2 = System.currentTimeMillis();
            System.err.println("Time = " + (t2 - t1));
        } catch (Exception e) {
            e.printStackTrace(System.err);
            System.exit(-1);
        }
    }
}