Observation: at any time, the state can be described by $$$0\le L\le R\le N$$$, where the first $$$L$$$ letters are R, the last $$$N-R$$$ letters are B, while the other letters are the same as initial state.

First consider subtask 5: $$$L=R=t$$$, note that pressing button $$$A$$$ would change $$$t$$$ into $$$(t+[t \lt A]+A)\bmod (N+1)$$$, one can solve this subtask by processing queries offline and maintaining such changes using BST. Complexity $$$O(N+(M+Q)\log Q)$$$. (There exists other solutions.)

Now we are interested in simulating a bunch of presses to make $$$L=R$$$. Note that the influence of several presses in the prefix or suffix can be simply summed (sum of their distances to borders), and a press in the middle part doubles the length of either prefix or suffix, so there's only $$$O(\log N)$$$ such presses. You can find them quickly in $$$O(\log M)$$$ time each, giving $$$O(\log N \log M)$$$ complexity per query.

I found a O(RClogN) solution and a O(RC) solution.

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