Not able to Memoize this Recursive Code into Top Down DP

I got this problem on one of my tests. I wrote a Recursive solution for it (I tried it on a few test cases, it seems to be working fine). I am trying to memoize this code, but am not able to do that.

The problem statement goes like this,

You are playing Fantasy Cricket on IPL11 App. The game is a bit different from other Fantasy Cricket Apps. Here you are given two lists of players. Both lists contain n players each. The list is denoted based on the value they provide.

You need to select exactly n players out of these 2*n players.

The selection needs to be done based on the following rules.

• You can select either from the end of list1 or end of list2
• Once you select a player, he is removed from that list.
• To get access to better players, you also have an option to discard a player and remove them from the end of the list. You can do the discard operation at most k times.

Naturally, you would want to get the maximum value possible in your team. Find the maximum value that you can get after selecting n players from the 2 lists based on the above rules.

Example

n: 6
list1: [10, 13, 31, 12, 12, 18]
list2: [34, 12, 3, 23, 11, 13]
k: 2

O/P: 112

Explanation:

* Select 18 (list1)
* Select 13 (list2)
* Skip 11 (list2)
* Select 23 (list2)
* Select 12 (list1)
* Skip 3 (list2)
* Select 12 (list2)
* Select 34 (list2)

My Recursive Solution,

public static int helper(int[] list1, int[] list2, int n1, int n2, int k, int count) {
        if(count == n) return 0;
        int chooseFromList1 = Integer.MIN_VALUE;
        int chooseFromList2 = Integer.MIN_VALUE;
        if(n1 > 0) {
            chooseFromList1 = list1[n1-1]+helper(list1, list2, n1-1, n2, k, count+1);
        }
        if(n2 > 0) {
            chooseFromList2 = list2[n2-1]+helper(list1, list2, n1, n2-1, k, count+1);
        }
        int temp = Integer.MIN_VALUE;
        if(k > 0) {
            int skipList1 = helper(list1, list2, n1-1, n2, k-1, count);
            int skipList2 = helper(list1, list2, n1, n2-1, k-1, count);
            temp = Math.max(skipList1, skipList2);
        }
        return Math.max(Math.max(chooseFromList1, chooseFromList2), temp);
    }

What I did is, I took 4 choices in this recursive code,

• Take last element from list1 if n1 > 0
• Take last element from list2 if n2 > 0
• Skip last element from list1 if k > 0
• Skip last element from list2 if k > 0

I want to convert it to Top Down DP, but not able to write the code for it.