Power Variety

By Kay Akashi

Time: 1000 ms

Memory: 256000 kB

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Problem Statement

Given two integers $x$ and $y$ , identify the name of the variable that gives the largest value: $a = x^{x}$ , $b = y^{y}$ , $c = x^{y}$ , $d = y^{x}$ . If there're multiple largest answers, print $e$ instead of answering with one of the four symbols, $a$ , $b$ , $c$ , or $d$ .

Constraints

$1 \leq x, y \leq 5 × 10^{5}$ .

Input

The input contains two integers, $x$ and $y$ in a single line.

Output

Output one alphabetical letter, $a$ , $b$ , $c$ , $d$ ,or $e$ .

Examples

Input

3 5

Output

Explanation

Values of $a$ , $b$ , $c$ , and $d$ are as follows: $27$ , $3125$ , $243$ , and $125$ . Amongst those, $b$ is apparently the largest one and there's no pair that gives identical largest value. Hence the answer is $b$ .

Input

1 1

Output

Explanation

Values of $a$ , $b$ , $c$ , and $d$ are as follows: $1$ , $1$ , $1$ , and $1$ . In this case, $1$ is the largest value but there're multiple answers. Thus, output $e$ .

Power Variety

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