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.IOException;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.TreeSet;

public class CF1_310B {
  
  static Reader sc = new Reader();
  static PrintWriter out = new PrintWriter(System.out);
  
  public static void main(String[] args) throws IOException {
    int n = sc.nextInt();
    int m = sc.nextInt();
    
    if (m < n - 1) {
      out.println("No");
      out.close();
      return;
    }
    
    ArrayList<Triple<Long, Long, Integer>> segs = new ArrayList<Triple<Long, Long, Integer>>();
    
    Triple<Long, Long, Integer> prevIsland = new Triple<Long, Long, Integer>(sc.nextLong(), sc.nextLong(), 1);
    
    for (int i = 0; i < n - 1; i++) {
      Triple<Long, Long, Integer> curIsland = new Triple<Long, Long, Integer>(sc.nextLong(), sc.nextLong(), i + 2);
      long longest = curIsland.second - prevIsland.first;
      long shortest = curIsland.first - prevIsland.second;
      Triple<Long, Long, Integer> curSeg = new Triple<Long, Long, Integer>(longest, shortest, i + 1);
      segs.add(curSeg);
      prevIsland = curIsland;
    }
    
    TreeSet<Pair<Long,Integer>> tree = new TreeSet<Pair<Long,Integer>>();
    
    for (int i = 0; i < m; i++) {
      tree.add(new Pair<Long, Integer>(sc.nextLong(), i + 1));
    }
    
    int[] whichBridge = new int[n - 1];
    
    Collections.sort(segs);
    
    boolean bad = false;
    
    for (int i = 0; i < n - 1; i++) {
      Pair<Long, Integer> found = tree.ceiling(new Pair<Long, Integer>(segs.get(i).second, -1));
      if (found != null && found.first <= segs.get(i).first) {
        whichBridge[segs.get(i).third - 1] = found.second;
        tree.remove(found);
      } else {
        bad = true;
        break;
      }
    }
    
    if (bad) {
      out.println("No");
    } else {
      out.println("Yes");
      print(whichBridge);
    }
    
    out.close();
    return;
  }

  public static class Pair<U extends Comparable<U>, V extends Comparable<V>> implements
          Comparable<Pair<U, V>> {
    public final U first;
    public final V second;

    public Pair(U first, V second) {
      this.first = first;
      this.second = second;
    }

    public int compareTo(Pair<U, V> that) {
      int value = this.first.compareTo(that.first);
      if (value != 0)
        return value;
      return this.second.compareTo(that.second);
    }

    @Override
    public boolean equals(Object other) {
      if (!(other instanceof Pair)) {
        return false;
      }
      Pair that = (Pair<U, V>) other;
      return this.first.equals(that.first) && this.second.equals(that.second);
    }

    @Override
    public int hashCode() {
      return 31 * (527 + first.hashCode()) + second.hashCode();
    }

    @Override
    public String toString() {
      return "(" + first + ", " + second + ")";
    }
  }

  public static class Triple<U extends Comparable<U>, V extends Comparable<V>, W extends Comparable<W>>
          implements Comparable<Triple<U, V, W>> {
    public final U first;
    public final V second;
    public final W third;

    public Triple(U first, V second, W third) {
      this.first = first;
      this.second = second;
      this.third = third;
    }

    public int compareTo(Triple<U, V, W> that) {
      int value = this.first.compareTo(that.first);
      if (value != 0)
        return value;
      value = this.second.compareTo(that.second);
      if (value != 0)
        return value;
      return this.third.compareTo(that.third);
    }

    @Override
    public boolean equals(Object other) {
      if (!(other instanceof Triple)) {
        return false;
      }
      Triple that = (Triple<U, V, W>) other;
      return this.first.equals(that.first) && this.second.equals(that.second)
              && this.third.equals(that.third);
    }

    @Override
    public int hashCode() {
      return 31 * (31 * (527 + first.hashCode()) + second.hashCode()) + third.hashCode();
    }

    @Override
    public String toString() {
      return "(" + first + ", " + second + ", " + third + ")";
    }
  }

  static void print(int[] A) {for (int i = 0; i < A.length; i++) {if (i != 0) {out.print(' ');}out.print(A[i]);}out.println();}
  
  static class Reader {
    boolean consume = false; final private int BUFFER_SIZE = 1 << 12;private byte[] buffer;private int bufferPointer, bytesRead;private boolean reachedEnd = false;public Reader() {buffer = new byte[BUFFER_SIZE];bufferPointer = 0;bytesRead = 0;}
    public boolean hasNext() {return !reachedEnd;} private void fillBuffer() throws IOException {bytesRead = System.in.read(buffer, bufferPointer = 0, BUFFER_SIZE);if (bytesRead == -1) {buffer[0] = -1;reachedEnd = true;}}
    private void consumeSpaces() throws IOException {while (read() <= ' ' && reachedEnd == false);bufferPointer--;} private byte read() throws IOException {if (bufferPointer == bytesRead) {fillBuffer();}return buffer[bufferPointer++];}
    public String next() throws IOException {StringBuilder sb = new StringBuilder();consumeSpaces();byte c = read();do {sb.append((char) c);} while ((c = read()) > ' ');if (consume) {consumeSpaces();};if (sb.length() == 0) {return null;}return sb.toString();}
    public String nextLine() throws IOException {StringBuilder sb = new StringBuilder();byte c;boolean read = false;while ((c = read()) != -1) {if (c == '\n') {read = true;break;}if (c >= ' ')sb.append((char) c);}if (!read) {return null;}return sb.toString();}
    public int nextInt() throws IOException {consumeSpaces();int ret = 0;      byte c = read();boolean neg = (c == '-');if (neg) {c = read();}do {ret = ret * 10 + c - '0';} while ((c = read()) >= '0' && c <= '9');if (consume) {consumeSpaces();}if (neg) {return -ret;}return ret;}
    public long nextLong() throws IOException {consumeSpaces();long ret = 0;byte c = read();boolean neg = (c == '-');if (neg) {c = read();}do {ret = ret * 10L + c - '0';} while ((c = read()) >= '0' && c <= '9');if (consume) {consumeSpaces();}if (neg) {return -ret;}return ret;}
    public double nextDouble() throws IOException {consumeSpaces();double ret = 0;double div = 1;byte c = read();boolean neg = (c == '-');if (neg) {c = read();}do {ret = ret * 10 + c - '0';} while ((c = read()) >= '0' && c <= '9');if (c == '.') {while ((c = read()) >= '0' && c <= '9') {ret += (c - '0') / (div *= 10);}}if (consume) {consumeSpaces();}if (neg) {return -ret;}return ret;}    public int[] nextIntArray(int n) throws IOException {int[] a = new int[n];for (int i = 0; i < n; i++) {a[i] = nextInt();}return a;}
    public int[][] nextIntMatrix(int n, int m) throws IOException {int[][] grid = new int[n][m];for (int i = 0; i < n; i++) {grid[i] = nextIntArray(m);}return grid;}
    public char[][] nextCharacterMatrix(int n) throws IOException {char[][] a = new char[n][];for (int i = 0; i < n; i++) {a[i] = next().toCharArray();}return a;}
    public void close() throws IOException {if (System.in == null) {return;} else {System.in.close();}}
  }
  
  /*
  long s = System.currentTimeMillis();
  debug(System.currentTimeMillis() - s + "ms");
   */
}
