Yes. I got it accepted using bitmask DP. My code

One thing you gotta take care is that how are subproblems dependent on each other.
Lets say if you can choose string indexed $$$x$$$ after choosing string $$$i$$$. Then
$$$dp[i][mask]$$$ is dependent on $$$dp[x][mask2]$$$, where
$$$mask2$$$ is a value with one lesser number of set bits that $$$mask$$$.
Hence doing a bottom up DP is hard.

I did it using top down memorized DP.

Edit — I just realized that you also did memoized DP.

Probably, but I did a complete search dfs. Here is my submission: https://atcoder.jp/contests/abc278/submissions/36632674

Say you have answer of $$$(k,l)$$$
What information do you need to keep track of, to be able to get answer of $$$(k, l+1)$$$ from answer of $$$(k,l)$$$?

Also Notice that $$$N \le 300$$$. So keeping frequency count isn't that hard.

Move the block ($$${w * h}$$$) in the following form.

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so on..

You can move the block by one step in $$${O(max(w, h))}$$$ so you may solve this problem in $$${O(H * W * max(h, w))}$$$. use map or unordered_map for counting distinct element and update them in each step of block.

++

My solution(but didn't manage to get AC for now) was to consider two cases: when $$$l \neq r$$$ then first player always has winning strategy erasing cards in the middle to obtain two equal parts and then having the symmetric strategy. When $$$l = r$$$ then you can solve the problem in quadratic time using grundy values.

Edit: got AC now.

gcc9 does not support c++20.

What are built-in features of c++20 which can be helpful in cp. I am very much interested in learning about that. Can you share them or is there any blog or something?

Since you are creating a vector of size n(which in the worst case can be 10^9), you encounter an RE verdict.