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 four-digit 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 optimally - 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 test-cases. Each testcase will consist of four digit number 0 ≤ N < 10⁴ [the original number] and 0 ≤ M ≤ 100 [the number of turns].

Output

For each test-case, 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