P7596 "EZEC-8" Game Snake.

Little A and Little B are two snakes. They are playing a game on a special tree. The structure of this tree is as follows: first, there is a chain of length $n$, called the "main chain". The main chain consists of the $n$ nodes $1$ to $n$. On the main chain, adjacent numbered nodes are connected by an edge; otherwise, there is no edge. Each node on the main chain has another chain attached to it, called a "side chain". The length (number of nodes) of the side chain attached to the $i$-th node on the main chain is $x_i$. At the beginning, both Little A and Little B are on the main chain. Specifically, Little A's **tail** is at node $a$, and its **head** is at node $b$; Little B's **head** is at node $c$, and its **tail** is at node $d$. It satisfies $1\le a

The first line contains two positive integers $n,q$. The second line contains $n$ positive integers, representing $x_i$. The next $q$ lines each contain four positive integers, representing $a,b,c,d$ for this query.

Output a total of $q$ lines. For each query, output `A` or `B`, indicating the snake that will eventually win.

**This problem uses bundled testdata.** - Subtask 1 (10 points): $n,q \le500$. - Subtask 2 (10 points): $n\le10^5$, $q\le500$. - Subtask 3 (5 points): all $x_i$ are equal. - Subtask 4 (10 points): in all queries, the sum of the lengths of Little A and Little B does not exceed $5\times10^7$. - Subtask 5 (15 points): $x_i$ are randomly generated in $[1,10^9]$. - Subtask 6 (20 points): $n\le5\times10^3$. - Subtask 7 (30 points): no special constraints. For $100\%$ of the testdata, $1\le n,q\le5\times10^5$, $1\le x_i\le10^9$, $1\le a