Problem: E: Red Black Balloons

Story

Homura-chan's dream comes true. It means ICPC Asia regional contest 20xx will be held in Sapporo! Homura-chan has been working hard for the preparation. And finally, it's the previous day of the contest. Homura-chan started to stock balloons to be delivered to contestants who get accepted. However, she noticed that there were only two colors of balloons: red and black.

Problem Statement

ICPC Asia regional contest in Sapporo plans to provide N problems to contestants. Homura-chan is a professional of contest preparation, so she already knows how many contestants would get acceptance for each problem (!!), a_i contestants for the i-th problem. You can assume the prediction is perfectly accurate. Ideally, Homura-chan would assign a distinct color of a balloon to each problem respectively. But you know, she has only two colors red and black now. Thus, Homura-chan comes up with the idea to differentiate the size of balloons in K levels, that is, each problem has a balloon with a distinct pair of (color, size).

Homura-chan now has r_i red balloons with size i (1 \leq i \leq K) and b_j black balloons with size j (1 \leq j \leq K). Suppose we assign a pair (c_i, s_i) of a color c_i (red or black) and a size s_i to the i-th problem, for each i. As noted, we have to assign distinct pairs to each problem, more precisely, (c_i, s_i) \neq (c_j, s_j) holds for i \neq j. Moreover, the number of balloons with (c_i, s_i) must be no less than a_i. In the case that there are no such assignments, Homura-chan can change the size of balloons by her magic power. Note that Homura-chan doesn't know magic to change the color of balloons, so it's impossible.

Your task is to write a program computing the minimum number of balloons whose size is changed by Homura-chan's magic to realize an assignment satisfying the above-mentioned conditions. If there is no way to achieve such an assignment even if Homura-chan changes the size of balloons infinitely, output `-1` instead.

Input


N K
a_1 ... a_N
r_1 ... r_K
b_1 ... b_K


Constraints

* 1 \leq N,K \leq 60
* N \leq 2K
* 1 \leq a_i \leq 50 (1 \leq i \leq N)
* 1 \leq r_j,b_j \leq 50 (1 \leq j \leq K)
* Inputs consist only of integers.



Output

Output the minimum number of balloons whose size is changed to achieve an assignment in a line. If there are no ways to achieve assignments, output `-1` instead.

Sample Input 1


3 2
6 5 4
8 1
7 1


Output for Sample Input 1


3

Homura-chan changes the size of three red balloons from 1 to 2. Then she can assign (black,1) to the problem 1, (red,1) to the problem 2, and (red,2) to the problem 3.

Sample Input 2


2 1
50 50
2
3


Output for Sample Input 2


-1

Sample Input 3


4 3
3 10 28 43
40 18 2
26 7 11


Output for Sample Input 3


5





Example

Input

3 2
6 5 4
8 1
7 1


Output

3

Solution (in CPP):

Solution:
#include<iostream>
#include<algorithm>
#include<vector>
using namespace std;
typedef long long ll;
#define mod 1000000007
#define chmin(a,b) a=min(a,b)
ll f[66][66][3333];
ll n,k,v[66],va[66],vb[66];
int main(){
  cin>>n>>k;
  for(int i=0;i<n;i++)cin>>v[i];
  sort(v,v+n,greater<ll>());
  for(int i=0;i<k;i++)cin>>va[i];
  sort(va,va+k,greater<ll>());
  for(int i=0;i<k;i++)cin>>vb[i];
  sort(vb,vb+k,greater<ll>());
  for(int i=0;i<=k;i++)for(int j=0;j<=k;j++){
      for(int p=0;p<3333;p++)f[i][j][p]=1e17;
  }
  
  ll sum=0;
  for(int i=0;i<n;i++)sum+=v[i];
  ll sa=0;
  for(int i=0;i<k;i++)sa+=va[i];
  ll sb=0;
  for(int i=0;i<k;i++)sb+=vb[i];
  ll ans=1e17;
  
  f[0][0][0]=0;
  for(int i=0;i<=k;i++)for(int j=0;j<=k&&i+j<=n;j++){
      for(int p=0;p<3333;p++){
	  if(i+j==n){
	      if(p<=sa&&sum-p<=sb){
		  chmin(ans,f[i][j][p]);
	      }
	      continue;
	  }
	  if(f[i][j][p]==1e17)continue;
	  //cout<<i<<" "<<j<<" "<<p<<" "<<f[i][j][p]<<endl;
	  if(i<k){
	      chmin(f[i+1][j][p+v[i+j]],f[i][j][p]+max(0LL,v[i+j]-va[i]));
	  }
	  if(j<k){
	      chmin(f[i][j+1][p],f[i][j][p]+max(0LL,v[i+j]-vb[j]));
	  }
      }
  }
  if(ans==1e17)ans=-1;
  cout<<ans<<endl;
  return 0;
}