Meal Delivery

Snuke lives at position x on a number line. On this line, there are two stores A and B, respectively at position a and b, that offer food for delivery.

Snuke decided to get food delivery from the closer of stores A and B. Find out which store is closer to Snuke's residence.

Here, the distance between two points s and t on a number line is represented by |s-t|.

Constraints

• 1 \leq x \leq 1000
• 1 \leq a \leq 1000
• 1 \leq b \leq 1000
• x, a and b are pairwise distinct.
• The distances between Snuke's residence and stores A and B are different.

Input

Input is given from Standard Input in the following format:

x a b

Output

If store A is closer, print A; if store B is closer, print B.

Examples

Input

5 2 7

Output

B

Input

1 999 1000

Output

A

inputFormat

Input

Input is given from Standard Input in the following format:

x a b

outputFormat

Output

If store A is closer, print A; if store B is closer, print B.

Examples

Input

5 2 7

Output

B

Input

1 999 1000

Output

A

样例

1 999 1000

A