MCOINS  Coins Game
English  Vietnamese 
Asen and Boyan are playing the following game. They choose two different positive integers K and L, and start the game with a tower of N coins. Asen always plays first, Boyan – second, after that – Asen again, then Boyan, and so on. The boy in turn can take 1, K or L coins from the tower. The winner is the boy, who takes the last coin (or coins). After a long, long playing, Asen realizes that there are cases in which he could win, no matter how Boyan plays. And in all other cases Boyan being careful can win, no matter how Asen plays.
So, before the start of the game Asen is eager to know what game case they have. Write a program coins which help Asen to predict the game result for given K, L and N.
INPUT
The input describes m games.
The first line of the standard input contains the integers K, L and m, 1 < K < L < 10, 3 < m < 50. The second line contains m integers N1, N2, …, Nm, 1 ≤ Ni ≤ 1 000 000, i = 1, 2, …., m, representing the number of coins in each of the m towers
SAMPLE INPUT
2 3 5
3 12 113 25714 88888
OUTPUT
The standard output contains a string of length m composed of letters A and B. If Asen wins the ith game (no matter how the opponent plays), the ith letter of the string has to be A. When Boyan wins the ith game (no matter how Asen plays), the ith letter of the string has to be B.
SAMPLE OUTPUT
ABAAB
Problem for kid  Please, think like kid.
hide comments
manishjoshi394:
20181125 06:56:44
If you can't figure out what to do, try reading Topcoder tutorial on 'Algorithm games'. Here is the link, https://www.topcoder.com/community/competitiveprogramming/tutorials/algorithmgames/ 

manishjoshi394:
20181125 06:55:46
Even my memoization solution passed easily in first go. If you are getting RTE with Memoization, check if you are handling function calls with negative and zero values. 

masterchef2209:
20181013 11:17:59
good one


jmr99:
20181004 19:56:54
AC!!.


slinky:
20180708 16:50:02
for somebody stuck on case 10, if no. of coins are less than l, you can only pick 1 or k coins and if coins less than k only 1 coin. 

ameyanator:
20180203 17:03:29
Initially I got a WA on test case 10. Couldn't find what's wrong with my code so looked through the comments. Seems like no one had a problem with test case 10 :/. Coded the same logic that I had again a bit more clearer this time and AC! :) 

dunjen_master:
20171228 21:03:57
so weak in dp that solving this problem gave me pleasure...btw think that you can win only if u bring the other player in a situation from where he looses 

chetan4060:
20171220 18:11:21
make a table up to some numbers and see repetitions


lazyfellow:
20171016 06:18:04
ac in one go!


rohit9934:
20170904 08:57:12
beginner dp+game theory. For a given set {1,L,K}, A will win anyway at 1,L,K and loses at K+1.If at any point n>K, if A can jump to any losing position then n is the winning position or vice versa.

Added by:  ~!(*(@*!@^& 
Date:  20090217 
Time limit:  0.216s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  BOI For Kid 08 