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E. Roma and Poker

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputEach evening Roma plays online poker on his favourite website. The rules of poker on this website are a bit strange: there are always two players in a hand, there are no bets, and the winner takes 1 virtual bourle from the loser.

Last evening Roma started to play poker. He decided to spend no more than *k* virtual bourles — he will stop immediately if the number of his loses exceeds the number of his wins by *k*. Also Roma will leave the game if he wins enough money for the evening, i.e. if the number of wins exceeds the number of loses by *k*.

Next morning Roma found a piece of paper with a sequence on it representing his results. Roma doesn't remember the results exactly, and some characters in the sequence are written in a way such that it's impossible to recognize this character, so Roma can't recall whether he won *k* bourles or he lost.

The sequence written by Roma is a string *s* consisting of characters W (Roma won the corresponding hand), L (Roma lost), D (draw) and ? (unknown result). Roma wants to restore any valid sequence by changing all ? characters to W, L or D. The sequence is called valid if all these conditions are met:

- In the end the absolute difference between the number of wins and loses is equal to
*k*; - There is no hand such that the absolute difference before this hand was equal to
*k*.

Help Roma to restore any such sequence.

Input

The first line contains two numbers *n* (the length of Roma's sequence) and *k* (1 ≤ *n*, *k* ≤ 1000).

The second line contains the sequence *s* consisting of characters W, L, D and ?. There are exactly *n* characters in this sequence.

Output

If there is no valid sequence that can be obtained from *s* by replacing all ? characters by W, L or D, print NO.

Otherwise print this sequence. If there are multiple answers, print any of them.

Examples

Input

3 2

L??

Output

LDL

Input

3 1

W??

Output

NO

Input

20 5

?LLLLLWWWWW?????????

Output

WLLLLLWWWWWWWWLWLWDW

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