Once upon a time, there was a magical land with n artifacts. Each artifact has a mysterious power of a$[$i$].$

These artifacts are protected by a spell such that they can only be used in groups of a particular size. The spell is encoded in an array b of length m and with values, indicating the length of each group.

You should divide the artifacts into m non$-$overlapping contiguous subarrays, with the first subarray having a length of b$[1],$ the second subarray having a length of b$[2],$ and so on$,$ and use each group of artifacts independently. It is guaranteed that the sum of all the elements in b is exactly n$.$

Let's say that you sort the powers of a group of artifacts a$[$L$,$R$]$ in ascending order.

Then, the power of the artifact with the k$-$th smallest value where k is the number of distinct powers in that group of artifacts is considered to be its magic value

You are told that a group of artifacts provides you with a level up factor equivalent to the sum of magic value of all m subarray's of artifacts.

You are allowed to reorder the elements in b in any way you want.

Find the maximum possible value of level up factor.

Input Format

$1)$ The first line contains an integer, n$,$ denoting the number of elements in a$.$

$2)$ The next line contains an integer, m$,$ denoting the length of the array b described in the problem.

$3)$ Each line i of the n subsequent lin$$s $($where $0<=$ i $<$ n$)$ contains an integer describing a$[$i$].$ It is given that a$[$i$]$ describes the power of artifact i$.$

$4)$ Each line i of the m subsequent lines $($where $0<=$ i $<$ m$)$ contains an integer describing b$[$i$].$ contains an integer describing a$[$i$].$ It is given that b$[$i$]$ describes the length of the ith set of artifacts to be used together.

Given function:

int GetAnswer$($int n$,$ int m$,$ vector a$,$ vector b$)\{$

$\}$

Example:

Sample input $1$:

$1)$ n$=5,$ m$=2,$ a$=[1,1,2,2,2],$ b$=[2,3]$

Sample output $1$:

$1)3$

Explanation $1$:

In this sample, if we leave the array b as it is b$=[2,3],$ we divide the array a into a$[1,2]=[1,1]$ and a$=[3,5]=[2,2,2]$ where the number of the distinct elements k in both of them is $1,$ so we will take the first element from each of them after we sort each one of them $($they are initially sorted$)$ as k$=1,$ thus the answer $1+2=3$ and if we also take b$=[3,2]$ then we will obtain the same answer.

Sample input $2$:

$1)$ n$=7,$m$=3,$ a$=[2,2,3,4,4,5,5],$ b$=[2,2,3]$

Sample output $2$:

$1)11$

Sample input $3$:

$1)$ n$=10,$ m$=4,$ a$=[1,2,3,3,3,3,3,3,3,3],$ b$=[3,3,3,1]$

Sample output $3$:

$1)12$

Explanation $3$:

in this sample, each permutation of array b will give the maximum possible answer except for b$=[1,3,3,3]$