You are given an integer array nums, an initial base integer p, and a $2$D integer array queries where each queries[i] = [val_i, k_i].

Process each query $i$ in order from $0$ to queries.length $- 1$:

1. Append val_i to nums.

2. Find the k_ith largest element in the updated array nums, denoted as $x$.

3. Update p to $(p^x) \bmod (10^9 + 7)$.

Return an array containing the value of p after each query is processed.

Constraints:

• $1 \leq$ nums.length $\leq 2 \times 10^4$

• $1 \leq$ nums[i] $\leq 10^6$

• $1 \leq$ p $\leq 10^6$

• $1 \leq$ queries.length $\leq 2 \times 10^4$

• $1 \leq$ val_i $\leq 10^6$

• $1 \leq$ k_i $\leq$ nums.length $+ i + 1$

• $|$ k_i $-$ k_{i - 1} $| < 10$ for $i > 0$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.