Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Memory for Arrays

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou get to work and turn on the computer. You start coding and give little thought to the RAM role in the whole process. In this problem your task is to solve one of the problems you encounter in your computer routine.

We'll consider the RAM as a sequence of cells that can contain data. Some cells already contain some data, some are empty. The empty cells form the so-called memory clusters. Thus, a memory cluster is a sequence of some consecutive empty memory cells.

You have exactly *n* memory clusters, the *i*-th cluster consists of *a*_{i} cells. You need to find memory for *m* arrays in your program. The *j*-th array takes 2^{bj} consecutive memory cells. There possibly isn't enough memory for all *m* arrays, so your task is to determine what maximum number of arrays can be located in the available memory clusters. Of course, the arrays cannot be divided between the memory clusters. Also, no cell can belong to two arrays.

Input

The first line of the input contains two integers *n* and *m* (1 ≤ *n*, *m* ≤ 10^{6}). The next line contains *n* integers *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 10^{9}). The next line contains *m* integers *b*_{1}, *b*_{2}, ..., *b*_{m} (1 ≤ 2^{bi} ≤ 10^{9}).

Output

Print a single integer — the answer to the problem.

Examples

Input

5 3

8 4 3 2 2

3 2 2

Output

2

Input

10 6

1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0

Output

6

Note

In the first example you are given memory clusters with sizes 8, 4, 3, 2, 2 and arrays with sizes 8, 4, 4. There are few ways to obtain an answer equals 2: you can locate array with size 8 to the cluster with size 8, and one of the arrays with size 4 to the cluster with size 4. Another way is to locate two arrays with size 4 to the one cluster with size 8.

In the second example you are given 10 memory clusters with size 1 and 6 arrays with size 1. You can choose any 6 clusters and locate all given arrays to them.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/24/2019 02:40:54 (d2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|