Migrated from Lutece 1313 Game

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Description

Bob is playing a game with $n$ rounds.

He has $s$ points initially, and for every round, he will add $a$ points if he win, or subtract $b$ points if he lose.

If his score is less than zero after a round, the score will be changed to zero.

Bob is not honest always, so he may use a cheater to get an abnormal score.

Now you are given his final score $t$, and you should determine whether Bob cheat in the game.

If it is impossible to get $t$ points, print CHEATED.

Otherwise, print any possible sequence of game process.

Input

Five integers $n,s,t,a,b$.

$1\leq n\leq 10^6$

$0\leq s, t\leq 10^9$

$1\leq a, b\leq 10^9$

Output

If it is impossible to get $t$ points, print CHEATED.

Otherwise, print a string with $n$ characters, consisting of O and X. If $i^{th}$ character is O, Bob win in $i^{th}$ round; if $i^{th}$ character is X, Bob lose in $i^{th}$ round.

There may be multiple solutions, you can print any one of them.

Samples

4 2 3 3 3

XOXO

2 1 100 2 2

CHEATED

Resources

The 14th UESTC Programming Contest Final