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.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.TreeSet;

public class Problem310D {
	public static void main(String[] args) throws IOException {
		InputReader reader = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = reader.readInt();
		int m = reader.readInt();
		long[] l = new long[n];
		long[] r = new long[n];
		for (int i = 0; i < n; i++) {
			l[i] = reader.readLong();
			r[i] = reader.readLong();
		}
		Bridge[] a = new Bridge[m];
		for (int i = 0; i < m; i++) {
			long len = reader.readLong();
			a[i] = new Bridge(i, len);
		}
		Arrays.sort(a);
		Query[] q = new Query[n - 1];
		for (int i = 0; i < n - 1; i++) {
			q[i] = new Query(l[i + 1] - r[i], r[i + 1] - l[i], i);
		}
		Arrays.sort(q);
		int[] ans = new int[n - 1];
		boolean flag = false;
		TreeSet<Bridge> set = new TreeSet<>();
		Bridge seeker = new Bridge(-1, 0);
		for (int i = 0, j = 0; i < n - 1; i++) {
			while (j < m && a[j].len <= q[i].high) {
				set.add(a[j]);
				j++;
			}
			seeker.len = q[i].low;
			Bridge tmp = set.higher(seeker);
			if (tmp == null) {
				out.println("No");
				flag = true;
				break;
			}
			ans[q[i].id] = tmp.id;
			set.remove(tmp);
		}
		if (!flag) {
			out.println("Yes");
			for (int x : ans) {
				out.print((x + 1) + " ");
			}
		}
		out.close();
	}

	static class Bridge implements Comparable<Bridge> {
		int id;
		long len;

		public int compareTo(Bridge o) {
			// System.out.println(len+" "+o.len);
			if (len != o.len)
				return len < o.len ? -1 : 1;
			return Integer.compare(id, o.id);
		}

		public Bridge(int id, long len) {
			this.id = id;
			this.len = len;
		}
	}

	static class Query implements Comparable<Query> {
		long low, high;
		int id;

		public int compareTo(Query o) {
			return Long.compare(high, o.high);
		}

		public Query(long low, long high, int id) {
			this.low = low;
			this.high = high;
			this.id = id;
		}
	}

	static final class InputReader {
		private final InputStream stream;
		private final byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		private int read() throws IOException {
			if (curChar >= numChars) {
				curChar = 0;
				numChars = stream.read(buf);
				if (numChars <= 0) {
					return -1;
				}
			}
			return buf[curChar++];
		}

		public final int readInt() throws IOException {
			return (int) readLong();
		}

		public final long readLong() throws IOException {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
				if (c == -1)
					throw new IOException();
			}
			boolean negative = false;
			if (c == '-') {
				negative = true;
				c = read();
			}
			long res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return negative ? -res : res;
		}

		public final int[] readIntArray(int size) throws IOException {
			int[] array = new int[size];
			for (int i = 0; i < size; i++) {
				array[i] = readInt();
			}
			return array;
		}

		public final long[] readLongArray(int size) throws IOException {
			long[] array = new long[size];
			for (int i = 0; i < size; i++) {
				array[i] = readLong();
			}
			return array;
		}

		public final String readString() throws IOException {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.append((char) c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	}
}
