Rating Updates

Maintain the current rating $R$. Read the performances $P_i$ in order and update $R\leftarrow (3R+P_i)/4$ each time. Every updated rating is guaranteed to be an integer, so no rounding rule is needed.

Initially, $R=R_0$. If $R=R_i$ after processing the $i$-th performance, applying the given formula to the next performance makes $R=R_{i+1}$. By induction, after all contests $R=R_N$.

Because $R$ and $P_i$ are at most $5\cdot10^8$, the numerator $3R+P_i$ is at most $2\cdot10^9$. Thus, every calculation fits in a 32-bit signed integer.

The same method applies to subtask 1. Its condition $P_i\geq R_{i-1}$ means that the rating does not decrease, but the update formula is unchanged. Across either subtask, the total time complexity is $O(T+\sum N)$ and the extra space complexity is $O(1)$ when the input is streamed.

Solution written by GPT5