Hey .. here is a problem I saw somewhere on net. Can anyone give me
some ideas on its algo ?

There is a tray that contains a row of "s" slots where biscuits may be
placed. You can have atmost one biscuit per slot. You and your friend
play a game with it. Each of you get to pick biscuits in turns. You
can pick atmost "b" biscuits in a single turn provided they are in
consecutive slots with no gaps (empty slots) in between (but you have
to pick atleast one in your turn). Whoever picks the last biscuit wins
the game.

You are given a snapshot of the game and its your turn. Assuming that
from this point onwards, both the players play optimally. Find out if
you can win the game. And if yes, what is your next move? If there are
multiple options for the next move, choose the one where you pick the
highest number of biscuits in the next turn. If still there are
multiple options, choose the one where you take the leftmost biscuit
among them.

As input, you will be given 't' which indicates the number of test
cases. For each case, you will be given s ( 1<=s<=2000 ), b
( 1<=b<=20 ) seperated by space and the next line will contain s
characters that are either '0' or '1' representing each of the s
slots. '0' indicates that a biscuit is not present at that particular
slot and '1' indicates that a biscuit is present.

As output, print "yes" or "no" indicating if you can win and if the
answer is yes, print a string of s characters of either '0' or '1'
that indicates whether a biscuit is absent or present at the
particular slot after you have played your turn.

Sample input:
3
3 2
111
8 3
10110111
8 4
11111111

Sample output:
yes 101
no
yes 11000011

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