ADAGAME  Ada and Game
Ada the Ladybug is playing Game of Digits against her friend Velvet Mite Vinit. The game is played in following manner: At first, there is a fourdigit number and a number of moves. Both Ada and Vinit take turns alternately (beginning with Ada). Both of them must increase ANY digit of the number, but if the digit was 9 it will become 0.
For example number 3590 can be expanded to: 4590,3690,3500 or 3591. If after all turns the number is greater than the original number, Ada wins  otherwise Vinit is the winner. Both of them play optimaly  can you decide who is the winner?
PS: It is possible, that Ada will have one more turn (if number of turns is odd)
Input
First line of input will consist T ≤ 200 number of testcases. Each testcase will consist of four digit number 0 ≤ N < 10^{4} [the original number] and 0 ≤ M ≤ 100 [the number of turns].
Output
For each testcase, print the name of winner ("Ada" or "Vinit").
Example Input
5 0000 0 5566 3 3333 10 9999 9 1234 30
Example Output
Vinit Ada Ada Vinit Ada
hide comments
piuspbd:
20170327 00:37:54
Awesome! 

sharma96:
20161228 10:49:37
@morass , does this problem uses a known DP algorithm or it's just a logical question?


morass:
20161210 23:03:34
@kira28: That if there exists a move which leads to sure victory {if no mistake appear  and it won't appear} then the player will choose such move [i.e since none will make any mistake it is possible {for each state} to decide who will win] 

kira28:
20161210 17:27:58
@morass what does "both of them play optimally" stand for? 

morass:
20161210 15:45:29
@kira28: oh .. well hard to say... I can say that Vinit will win there is nothing Ada can do about it ... an example of "how it can end" is by number "0593"  but since it doesn't matter for Ada what steps she will do, the result can be as well "3590" 

kira28:
20161210 14:36:03
@morass after all 5 turns.what will be that number which we will compare with the orignal number , to decide the winner 

morass:
20161210 12:59:39
@kira28: You mean after one turn? 9590 (if aplied to first digit first digit) 

kira28:
20161210 11:36:29
question is not clear


morass:
20161206 19:41:59
@pandey333: Good day to you  sure, for example:


pandey333:
20161206 17:29:23
@morass

Added by:  morass 
Date:  20160906 
Time limit:  4.5s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 GOSU 