Multiset Query Operations

You are given an initial multiset of integers and need to perform a series of operations. The multiset supports the following five operations:

• D x: Delete one occurrence of \(x\) from the multiset. It is guaranteed that \(x\) exists in the multiset, and if there are multiple occurrences, only one is removed.
• B: Query the maximum value in the multiset.
• S: Query the minimum value in the multiset.
• M: Let \(a\) be the maximum value and \(b\) be the minimum value in the multiset. Compute \(a^b \bmod 317847191\) (present the formula in LaTeX as \(a^b \bmod 317847191\)).
• T: Query the product of all numbers in the multiset modulo \(317847191\).

For each querying operation, it is guaranteed that the multiset is non-empty. You are also given the initial multiset and a series of operations. Your task is to process the operations efficiently and output the answer for each query.

inputFormat

The first line contains two space-separated integers \(n\) and \(q\) (\(1 \le n, q \le 10^5\)), which represent the number of initial elements and the number of operations, respectively.

The second line contains \(n\) space-separated integers representing the initial multiset.

Each of the following \(q\) lines contains an operation in one of the following formats:

• D x
• B
• S
• M
• T

outputFormat

For each query operation (B, S, M, T), output the result on a separate line.

sample

5 5
1 2 3 4 5
B
S
M
T
D 3

5
1
5
120