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.math.BigInteger;
import java.util.*;

/**
 * Created by Leonti on 2016-04-10.
 */
public class CF {
    public static void main(String[] args) {
        InputReader inputReader = new InputReader(System.in);
        PrintWriter printWriter = new PrintWriter(System.out, true);

        int n = inputReader.nextInt();
        int m = inputReader.nextInt();
        ArrayList<IslandPair> islandPairs = new ArrayList<>(n - 1);
        ArrayList<Bridge> bridges = new ArrayList<>(m);
        long lPrev = inputReader.nextLong();
        long rPrev = inputReader.nextLong();
        long l, r;
        for (int i = 0; i < n - 1; i++) {
            l = inputReader.nextLong();
            r = inputReader.nextLong();
            islandPairs.add(new IslandPair(l - rPrev, r - lPrev, i));
            lPrev = l;
            rPrev = r;
        }

        for (int i = 0; i < m; i++) {
            bridges.add(new Bridge(inputReader.nextLong(), i + 1));
        }

        Collections.sort(islandPairs);
        Collections.sort(bridges);

        boolean isPossible = true;
        int[] res = new int[n - 1];
        int lastPairIndex = 0;
        Bridge nextBridge;
        IslandPair nextPair;
        PriorityQueue<IslandPair> currentIslands =
                new PriorityQueue<>((IslandPair i1, IslandPair i2) -> {
                    int cmp = 0;
                    if (i1.finish - i2.finish > 0) {
                        cmp = 1;
                    } else if (i1.finish - i2.finish < 0) {
                        cmp = -1;
                    }
                    if (cmp == 0) {
                        if (i1.start - i2.start < 0) {
                            cmp = -1;
                        } else if (i1.start - i2.start > 0) {
                            cmp = 1;
                        }
                        if (cmp == 0) {
                            if (i1.index - i2.index < 0) {
                                cmp = -1;
                            } else {
                                cmp = 1;
                            }
                        }
                    }
                    return cmp;
                });

        for (int i = 0; i < m; i++) {
            nextBridge = bridges.get(i);
            for (int j = lastPairIndex; j < n - 1; j++) {
                nextPair = islandPairs.get(j);
                if (nextBridge.length >= nextPair.start && nextBridge.length <= nextPair.finish) {
                    currentIslands.add(nextPair);
                    lastPairIndex++;
                } else {
                    break;
                }
            }

            nextPair = currentIslands.poll();

            if (nextPair == null) {
                continue;
            } else if (nextPair.finish < nextBridge.length) {
                isPossible = false;
                break;
            }

            res[nextPair.index] = nextBridge.index;
        }

        if (isPossible) {
            for (int i : res) {
                if (i == 0) {
                    isPossible = false;
                    break;
                }
            }
        }

        if (!isPossible) {
            printWriter.print("No");
        } else {
            printWriter.println("Yes");
            for (int i : res) {
                printWriter.print(i + " ");
            }
        }

        printWriter.close();
    }

    private static class Bridge implements Comparable<Bridge> {
        private long length;
        private int index;

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

        @Override
        public int compareTo(Bridge o) {
            int res = 0;
            if (this.length - o.length < 0 ) {
                res = -1;
            } else if (this.length - o.length > 0) {
                res = 1;
            }
            return res;
        }
    }

    private static class IslandPair implements Comparable<IslandPair> {
        private long start;
        private long finish;
        private int index;

        public IslandPair(long start, long finish, int index) {
            this.start = start;
            this.finish = finish;
            this.index = index;
        }

        @Override
        public int compareTo(IslandPair o) {
            int res = 0;
            if (this.start - o.start < 0) {
                res = -1;
            } else if (this.start - o.start > 0) {
                res = 1;
            }
            if (res == 0) {
                if (this.finish - o.finish < 0) {
                    res = -1;
                } else if (this.finish - o.finish > 0) {
                    res = 1;
                }
            }
            return res;
        }

        @Override
        public boolean equals(Object obj) {
            return ((IslandPair) obj).index == this.index;
        }

        @Override
        public int hashCode() {
            return this.index;
        }
    }

    private static class InputReader {
        private final BufferedReader reader;
        private StringTokenizer tokenizer;

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

        public int[] nextIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; ++i) {
                array[i] = nextInt();
            }
            return array;
        }

        public long[] nextLongArray(int size) {
            long[] array = new long[size];
            for (int i = 0; i < size; ++i) {
                array[i] = nextLong();
            }
            return array;
        }

        public double[] nextDoubleArray(int size) {
            double[] array = new double[size];
            for (int i = 0; i < size; ++i) {
                array[i] = nextDouble();
            }
            return array;
        }

        public String[] nextStringArray(int size) {
            String[] array = new String[size];
            for (int i = 0; i < size; ++i) {
                array[i] = next();
            }
            return array;
        }

        public boolean[][] nextBooleanTable(int rows, int columns, char trueCharacter) {
            boolean[][] table = new boolean[rows][columns];
            for (int i = 0; i < rows; ++i) {
                String row = next();
                assert row.length() == columns;
                for (int j = 0; j < columns; ++j) {
                    table[i][j] = (row.charAt(j) == trueCharacter);
                }
            }
            return table;
        }

        public char[][] nextCharTable(int rows, int columns) {
            char[][] table = new char[rows][];
            for (int i = 0; i < rows; ++i) {
                table[i] = next().toCharArray();
                assert table[i].length == columns;
            }
            return table;
        }

        public int[][] nextIntTable(int rows, int columns) {
            int[][] table = new int[rows][columns];
            for (int i = 0; i < rows; i++) {
                for (int j = 0; j < columns; j++) {
                    table[i][j] = nextInt();
                }
            }
            return table;
        }

        public long[][] nextLongTable(int rows, int columns) {
            long[][] table = new long[rows][columns];
            for (int i = 0; i < rows; i++) {
                for (int j = 0; j < columns; j++) {
                    table[i][j] = nextLong();
                }
            }
            return table;
        }

        public double[][] nextDoubleTable(int rows, int columns) {
            double[][] table = new double[rows][columns];
            for (int i = 0; i < rows; i++) {
                for (int j = 0; j < columns; j++) {
                    table[i][j] = nextDouble();
                }
            }
            return table;
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public BigInteger nextBigInteger() {
            return new BigInteger(next());
        }

        public boolean hasNext() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                String line = readLine();
                if (line == null) {
                    return false;
                }
                tokenizer = new StringTokenizer(line);
            }
            return true;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(readLine());
            }
            return tokenizer.nextToken();
        }

        public String readLine() {
            String line;
            try {
                line = reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }
    }
}