Description

You need to maintain a multiset that supports five operations:

• D x Delete $x$; it is guaranteed that $x$ exists. If there are multiple occurrences, delete only one.
• B Query the maximum value in the set.
• S Query the minimum value in the set.
• M Let the maximum be $a$ and the minimum be $b$; query $a^b \bmod 317847191$.
• T Query the product of all numbers, modulo $317847191$.

For all queries, the multiset is guaranteed to be non-empty.

Input Format

The first line contains two positive integers $n, m$, the initial multiset size and the number of operations.
The second line contains $n$ positive integers $a_i$, the initial multiset.
Then $m$ lines follow, each describing one operation.

Output Format

For each query, output one integer per line representing the answer.

3 6
2 6 9
M
D 9
B
S
M
T

81
6
2
36
12

Hint

Constraints
For partial testdata, $1 \le n \le 1000$, $1 \le m \le 100$, $1 \le a_i \le 400$.
For $100\%$ of the testdata, $1 \le n, m \le 10^6$, $1 \le a_i \le 10^8$.

Translated by ChatGPT 5