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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.Arrays;
import java.util.Iterator;
import java.util.PriorityQueue;
import java.util.AbstractQueue;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.util.AbstractCollection;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.Comparator;
import java.io.InputStream;
import java.util.function.IntFunction;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 29);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            BCaseOfFugitive solver = new BCaseOfFugitive();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class BCaseOfFugitive {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.ri();
            int m = in.ri();
            long[][] islands = new long[n][2];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < 2; j++) {
                    islands[i][j] = in.rl();
                }
            }
            Require[] reqs = new Require[n - 1];
            for (int i = 0; i < n - 1; i++) {
                reqs[i] = new Require(i, islands[i + 1][0] - islands[i][1], islands[i + 1][1] - islands[i][0]);
            }
            Bridge[] bridges = new Bridge[m];
            for (int i = 0; i < m; i++) {
                bridges[i] = new Bridge();
                bridges[i].id = i;
                bridges[i].len = in.rl();
            }
            Require[] sortedByL = reqs.clone();
            Arrays.sort(sortedByL, Comparator.comparingLong(x -> x.l));
            PriorityQueue<Require> pqByR = new PriorityQueue<>(n, Comparator.comparingLong(x -> x.r));
            Arrays.sort(bridges, Comparator.comparingLong(x -> x.len));
            SimplifiedDeque<Require> dq = new Range2DequeAdapter<>(i -> sortedByL[i], 0, sortedByL.length - 1);
            for (Bridge b : bridges) {
                while (!dq.isEmpty() && dq.peekFirst().l <= b.len) {
                    pqByR.add(dq.removeFirst());
                }
                if (pqByR.isEmpty()) {
                    continue;
                }
                if (pqByR.peek().r < b.len) {
                    out.println("No");
                    return;
                }
                pqByR.remove().match = b.id;
            }
            if (!pqByR.isEmpty() || !dq.isEmpty()) {
                out.println("No");
                return;
            }
            out.println("Yes");
            for (Require r : reqs) {
                out.append(r.match + 1).append(' ');
            }
        }

    }

    static class Bridge {
        long len;
        int id;

    }

    static interface SimplifiedDeque<T> extends SimplifiedStack<T> {
        T peekFirst();

        T removeFirst();

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int ri() {
            return readInt();
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

        public long rl() {
            return readLong();
        }

        public long readLong() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            long val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class Range2DequeAdapter<T> implements SimplifiedDeque<T> {
        IntFunction<T> data;
        int l;
        int r;

        public Range2DequeAdapter(IntFunction<T> data, int l, int r) {
            this.data = data;
            this.l = l;
            this.r = r;
        }

        public boolean isEmpty() {
            return l > r;
        }

        public T peekFirst() {
            return data.apply(l);
        }

        public T removeFirst() {
            return data.apply(l++);
        }

        public Iterator<T> iterator() {
            return new Iterator<T>() {
                int iter = l;


                public boolean hasNext() {
                    return iter <= r;
                }


                public T next() {
                    return data.apply(iter++);
                }
            };
        }

    }

    static class Require {
        int match;
        int leftId;
        long l;
        long r;

        public Require(int leftId, long l, long r) {
            this.leftId = leftId;
            this.l = l;
            this.r = r;
        }

    }

    static interface SimplifiedStack<T> extends Iterable<T> {
        boolean isEmpty();

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private static final int THRESHOLD = 1 << 13;
        private final Writer os;
        private StringBuilder cache = new StringBuilder(THRESHOLD * 2);

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        private void afterWrite() {
            if (cache.length() < THRESHOLD) {
                return;
            }
            flush();
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput append(int c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput append(String c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput println(String c) {
            return append(c).println();
        }

        public FastOutput println() {
            return append(System.lineSeparator());
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }
}

