Notice

Problem Statement

Sonia is going to buy $N$ types of cosmetics. Each of the $N$ types of cosmetics is sold by both Company A and Company B.

For each type of cosmetic, Sonia has decided to buy exactly one of "Company A's product" or "Company B's product" (she cannot choose to buy neither).

For the $i$-th type of cosmetic, if she buys "Company A's product", Sonia gains $A_i$ happiness, and if she buys "Company B's product", Sonia gains $B_i$ happiness (each of these may be negative).

Here, among the $N$ types of cosmetics, Sonia wants to buy "Company A's product" for exactly $K$ types and "Company B's product" for exactly $N-K$ types.

Among the ways of buying cosmetics that satisfy Sonia's request, find one way of buying the $N$ types of cosmetics that maximizes the total happiness gained.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq K \leq N$
• $|A_i|, |B_i| \leq 10^9$
• All inputs are integers

Input

$N$ $K$
$A_1$ $\cdots$ $A_N$
$B_1$ $\cdots$ $B_N$

Output

The output consists of a string $S$ of $N$ characters. For the $i$-th type of cosmetic, set $S[i]=$A if buying Company A's product, and $S[i]=$B if buying Company B's product. Also, do not forget the newline.

If there are multiple ways of buying that maximize the total happiness gained, you may output any one of them.

Sample

3 1
2 7 4
3 5 8

BAB

5 2
1 1 1 1 1
2 2 2 2 2

ABBBA

6 3
-31 -41 -59 -26 -53 -59
-27 -18 -28 -18 -28 -46

ABBABA