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B. Case of Fugitive

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAndrewid 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 [*l*_{i}, *r*_{i}], besides, *r*_{i} < *l*_{i + 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 *l*_{i} ≤ *x* ≤ *r*_{i}, *l*_{i + 1} ≤ *y* ≤ *r*_{i + 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* ≤ 2·10^{5}) and *m* (1 ≤ *m* ≤ 2·10^{5}) — the number of islands and bridges.

Next *n* lines each contain two integers *l*_{i} and *r*_{i} (1 ≤ *l*_{i} ≤ *r*_{i} ≤ 10^{18}) — the coordinates of the island endpoints.

The last line contains *m* integer numbers *a*_{1}, *a*_{2}, ..., *a*_{m} (1 ≤ *a*_{i} ≤ 10^{18}) — 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 *b*_{1}, *b*_{2}, ..., *b*_{n - 1}, which mean that between islands *i* and *i* + 1 there must be used a bridge number *b*_{i}.

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.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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