2017-09-02 02:38


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Have you ever heard about the story "a man is dug out of a well"? It said that some people dug a well near their house so that they didn't have to bring water far away. They were very happy because the man in charge of carrying water now had time to do other things. However, when this news spread apace one by one. The people far away deemed that a man was dug out of a well! There are many famous stories about hearsays, which sound very surprising.

What may even consciousless misunderstandings result in? You are required to write a programme to find out this.

Suppose the information to be spread is just a number. Take 27 as an instance. After one day, the datum is rounded to 30. Another day later, somebody may think this number must have been rounded, so he concluded the original was 34, and another guy took this as the exact datum. One more day later, one thought that 34 is so similar with 35 that the datum became 35.
Suppose there are three kinds of operations which can be applyed on the datum:

Rounding, which can take place at any position.
Deem that the datum had been rounded and tell a more "resonable" integer.
Increase by one.

The poor datum is transforming through any one of the three operations above every day. Floating-point number is out of our consideration.

What we want to know is what the number could be after d days.


Two unsigned integers: the original datum n and the days passed d, one pair per line.

There are many test cases through to the end of file.


For each pair of input, output the largest datum we could get after d days in one line.

If the number is more than or equals to 100 times of the original datum, print "Aoao~~" after it.

The output must be the exact number. But when it is larger than or equals to 10, you should use scientific format, such as 1E1. "E" must be capital letter and no "+" is needed.

Sample Input

37 4
36 28

Sample Output

4.499E3 Aoao~~

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