St Andrews Online Judge

Power Variety

By Kay Akashi

Time: 1000 ms
Memory: 256000 kB

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Problem Statement

Given two integers xx and yy, identify the name of the variable that gives the largest value: a=xxa = x^{x}, b=yyb = y^{y}, c=xyc = x^{y}, d=yxd = y^{x}. If there're multiple largest answers, print ee instead of answering with one of the four symbols, aa, bb, cc, or dd.

Constraints

1x,y5×1051 \leq x, y \leq 5 × 10^{5}.

Input

The input contains two integers, xx and yy in a single line.

Output

Output one alphabetical letter, aa, bb, cc, dd,or ee.

Examples

Input

3 5

Output

b

Explanation

Values of aa, bb, cc, and dd are as follows: 2727, 31253125, 243243, and 125125. Amongst those, bb is apparently the largest one and there's no pair that gives identical largest value. Hence the answer is bb.

Input

1 1

Output

e

Explanation

Values of aa, bb, cc, and dd are as follows: 11, 11, 11, and 11. In this case, 11 is the largest value but there're multiple answers. Thus, output ee.