555_B. Case of Fugitive
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.
```python
#!/usr/bin/env python
# 556D_fug.py - Codeforces.com 556D Fug quiz
#
# Copyright (C) 2015 Sergey
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#       http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

"""
Input

The first line contains integers n and m - the number of islands and bridges.

Next n lines each contain two integers li and ri - the coordinates of the
island endpoints.

The last line contains m integer numbers a1..am - 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, 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
"""

# Standard libraries
import unittest
import sys
import re

# Additional libraries
import heapq


###############################################################################
# Fug Class
###############################################################################


class Fug:
    """ Fug representation """

    def __init__(self, args):
        """ Default constructor """
        self.list = args[0]
        self.alist = args[1]
        self.gn = len(self.list) - 1

        # Sorted list of bridges
        self.asrt = sorted((n, i) for i, n in enumerate(self.alist))

        # List of gaps between islands
        self.gaps = []
        prevli = self.list[0]
        for i in range(self.gn):
            li = self.list[i+1]
            min = li[0] - prevli[1]
            max = li[1] - prevli[0]
            self.gaps.append((min, max, i))
            prevli = li

        # Sorted list of gaps between islands
        self.gsrt = sorted(self.gaps)

        self.gmin = [n[0] for n in self.gsrt]
        self.result = [None]*self.gn
        self.heap = []

    def iterate(self):

        j = 0
        for (b, i) in self.asrt:

            # Traverse gmin array
            while j < self.gn and self.gmin[j] <= b:
                it = self.gsrt[j]
                heapq.heappush(self.heap, (it[1], it[0], it[2]))
                j += 1

            # Update result and remove the element from lists
            if self.heap:
                (mmax, mmin, mi) = self.heap[0]
                if mmin <= b and mmax >= b:
                    self.result[mi] = i + 1
                    heapq.heappop(self.heap)

            yield

    def calculate(self):
        """ Main calcualtion function of the class """

        for it in self.iterate():
            pass

        answer = ""
        for (i, n) in enumerate(self.result):
            if n is None:
                return "No"
            answer += (" " if i > 0 else "") + str(n)

        return "Yes\n" + answer


###############################################################################
# Executable code
###############################################################################


def get_inputs(test_inputs=None):

    it = iter(test_inputs.split("\n")) if test_inputs else None

    def uinput():
        """ Unit-testable input function wrapper """
        if it:
            return next(it)
        else:
            return input()

    # Getting string inputs. Place all uinput() calls here
    num = [int(s) for s in uinput().split()]
    list = [[int(s) for s in uinput().split()] for i in range(num[0])]
    alist = [int(s) for s in uinput().split()]

    # Decoding inputs into a list
    inputs = [list, alist]

    return inputs


def calculate(test_inputs=None):
    """ Base class calculate method wrapper """
    return Fug(get_inputs(test_inputs)).calculate()


###############################################################################
# Unit Tests
###############################################################################


class unitTests(unittest.TestCase):

    def test_sample_tests(self):
        """ Quiz sample tests. Add \n to separate lines """

        # Sample test 1
        test = "4 4\n1 4\n7 8\n9 10\n12 14\n4 5 3 8"
        self.assertEqual(calculate(test), "Yes\n2 3 1")
        self.assertEqual(
            get_inputs(test),
            [[[1, 4], [7, 8], [9, 10], [12, 14]], [4, 5, 3, 8]])

        # My tests
        test = "5 5\n1 1\n2 7\n8 8\n10 10\n16 16\n1 1 5 6 2"
        self.assertEqual(calculate(test), "Yes\n1 2 5 4")

        # Other tests
        test = "2 2\n11 14\n17 18\n2 9"
        self.assertEqual(calculate(test), "No")

        # Other tests
        test = (
            "2 1\n1 1\n1000000000000000000 1000000000000000000" +
            "\n999999999999999999")
        self.assertEqual(calculate(test), "Yes\n1")

        test = ("5 9\n1 2\n3 3\n5 7\n11 13\n14 20\n2 3 4 10 6 2 6 9 5")
        self.assertEqual(calculate(test), "Yes\n1 6 3 2")

        size = 50000
        test = str(size) + " " + str(size) + "\n"
        x = size*1000
        for i in range(size):
            x += 2
            test += str(x) + " " + str(x+1) + "\n"
        for i in range(size):
            test += str(2) + " "
        self.assertEqual(calculate(test)[0], "Y")

    def test_Fug_class__basic_functions(self):
        """ Fug class basic functions testing """

        # Constructor test
        d = Fug([[[1, 5], [7, 8], [9, 10], [12, 14]], [4, 5, 3, 8]])
        self.assertEqual(d.list[0][0], 1)
        self.assertEqual(d.alist[0], 4)

        # Sort bridges
        self.assertEqual(d.asrt[0], (3, 2))

        # Sort Gaps
        self.assertEqual(d.gaps[0], (2, 7, 0))
        self.assertEqual(d.gsrt[0], (1, 3, 1))

        iter = d.iterate()
        next(iter)
        self.assertEqual(d.gmin, [1, 2, 2])
        self.assertEqual(d.heap, [(5, 2, 2), (7, 2, 0)])

if __name__ == "__main__":

    # Avoiding recursion limitaions
    sys.setrecursionlimit(100000)

    if sys.argv[-1] == "-ut":
        unittest.main(argv=[" "])

    # Print the result string
    print(calculate())

```