Red Black Balloons

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

inputFormat

outputFormat

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

样例

3 2
6 5 4
8 1
7 1

3