NY10B  NimB Sum
Note: This problem has nothing to do with siting sewage plants, power lines or wind farms. NIM is an ambigram.
The game of NIM is played with any number of piles of objects with any number of objects in each pile. At each turn, a player takes one or more (up to all) objects from one pile. In the normal form of the game, the player who takes the last object is the winner. There is a wellknown strategy for this game based on the nim2 sum.
The NimB sum (nim sum base B) of two nonnegative integers X and Y (written NimSum(B, X, Y)) is computed as follows:
 Write each of X and Y in base B.
 Each digit in base B of the NimB sum is the sum modulo B of the corresponding digits in the base B representation of X and Y.
For example:
NimSum(2, 123, 456) = 1111011 ¤ 111001000 = 110110011 = 435
NimSum(3, 123, 456) = 11120 ¤ 121220 = 102010 = 300
NimSum(4, 123, 456) = 1323 ¤ 13020 = 10303 = 307
The strategy for normal form Nim is to compute the Nim2 sum T of the sizes of all piles. If at any time, you end your turn with T = 0, you are guaranteed a WIN. Any opponent move must leave T not 0 and there is always a move to get T back to 0. This is done by computing NimSum(2, T, PS) for each pile; if this is less than the pile size (PS), compute the difference between the PS and the Nim2 sum and remove it from that pile as your next move.
Write a program to compute NimSum(B, X, Y).
Input
The first line of input contains a single integer P, (1P1000), which is the number of data sets that follow. Each data set is a single line that contains the data set number, followed by a space, followed by three space separated decimal integers, B, X and Y. 2B2000000, 0X2000000, 0Y2000000.
Output
For each data set there is one line of output. It contains the data set number followed by a single space, followed by N, the decimal representation of the Nim sum in base B of X and Y.
Sample Input
4
1 2 123 456
2 3 123 456
3 4 123 456
4 5 123 456
Sample Output
1 435
2 300
3 307
4 429
hide comments
DHEERAJ KUMAR:
20160321 04:11:54
What's the point of taking input of first number?? Should be moved to tutorial :P


Ankit!!:
20130621 06:11:48
more test cases plzzzz.. 

$!:D:
20130604 16:00:28
Last edit: 20130604 17:49:01 

Naman:
20120119 17:04:02
keep it simple.. Ignore unnecessary details... 

Santiago Palacio:
20110617 06:54:33
Weird, VERY weird, as every other testcase is correct, why would that be wrong...? 

Suprabh Shukla:
20110616 12:03:21
@Santiago: The answer for 4 is 429 just as the author has written. Maybe that case wasn't there in the test data if you got AC with answer as 427. 

Santiago Palacio:
20110613 05:52:13
int (32 bit) is enough?


jobless:
20110510 16:55:34
why am i getting wa??


Gurpreet Singh:
20110508 19:06:06
why there is so much unnecessary details in this question?? 

cegprakash:
20110409 11:47:27
@Rach: i too had that doubt first 
Added by:  egaeus 
Date:  20110323 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Greater New York Region 2010 