No.197 Magic Trick
タグ : / 解いたユーザー数 334
作問者 :
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Problem Statement
A-kun is practicing a magic trick. The trick goes as follows.
Three hats are lined up, each of which either contains one coin or contains no coin.
First, A-kun shows for every hat whether it contains a coin or not.
One operation swaps either the left two hats or the right two hats, along with their contents.
A-kun asks a customer to perform exactly $N$ operations in any way they like.
(The number of operations is known, but how they were performed cannot be seen.)
If the state is impossible when A-kun opens all the hats, the trick is a success.
Tell A-kun "SUCCESS" if his trick succeeded, and "FAILURE" if it failed.
Input
$S_{before}$
$N$
$S_{after}$
$S_{before}$ is a string of 3 characters, each of which is 'o' or 'x'.
$S_{before}$ represents, in order from the left hat, whether each hat initially contains a coin or not.
'o' means the hat contains a coin. 'x' means the hat does not contain a coin.
$N$ is the number of operations the customer performs. $0 \le N \le 2000000000$.
$S_{after}$ is a string of 3 characters, each of which is 'o' or 'x'.
$S_{after}$ represents, in order from the left hat, whether each hat contains a coin or not after the $N$ operations.
'o' means the hat contains a coin. 'x' means the hat does not contain a coin.
Output
Print "SUCCESS" if A-kun's trick is a success, or "FAILURE" if it is a failure, on one line.
Do not forget the newline at the end.
Sample
Sample 1
Input
xxo 1 oxx
Output
SUCCESS
There are three hats.
The rightmost hat contains a coin.
After one operation, the coin has moved to the leftmost hat.
Neither swapping the left two hats nor swapping the right two hats produces this state.
Since this is impossible, A-kun's trick is a success.
Sample 2
Input
xoo 2 oox
Output
FAILURE
There are three hats.
The middle hat and the rightmost hat contain coins.
After two operations, the coins have moved to the middle hat and the leftmost hat.
This state is possible by first swapping the left two hats and then swapping the right two hats.
Therefore, there is nothing mysterious about it, and A-kun's trick is a failure.
Sample 3
Input
ooo 0 xxx
Output
SUCCESS
By performing 0 operations (that is, doing nothing), all the coins in the hats have disappeared.
The trick is a success.
Sample 4
Input
oxo 2000000000 oxo
Output
FAILURE
This is possible. It is a failure.
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