Problem Statement

$N$ skewers of yakitori are lined up in a row.

The deliciousness of the $i$-th yakitori from the left is $A_i$.

Each of these yakitori will be given a topping of either salt or tare sauce. Of the $N$ yakitori, $K$ will be topped with salt and $N - K$ will be topped with tare sauce.

Topping the $i$-th yakitori from the left with salt increases its deliciousness by $B_i$, and topping it with tare sauce increases its deliciousness by $C_i$.

Since sepa-kun wants to eat yakitori that is as delicious as possible, he decided to apply the toppings so as to maximize the total deliciousness.

Find the maximum possible value of the total deliciousness of the $N$ yakitori.

Constraints

• $1 \leq N \leq 2 \times 10^{5}$
• $0 \leq K \leq N$
• $1 \leq A_i \leq 10^{9}$
• $1 \leq B_i, C_i \leq 10^{9}$
• All input values are integers.

Input

The input is given from standard input in the following format.

$N$ $K$ 
$A_1$ $A_2$ ... $A_N$ 
$B_1$ $B_2$ ... $B_N$ 
$C_1$ $C_2$ ... $C_N$ 

Output

Output the answer to the problem on one line.

Sample

3 2
2 3 5
5 7 6
4 9 2

30

10 4
6 35 90 38 69 51 66 40 92 74
53 83 46 26 3 48 50 38 67 66
32 52 20 47 51 77 24 77 26 6

1131