Two players (numbered and ) are playing a game of Tower Breakers! The rules of the game are as follows:
- Player always moves first.
- Initially there are towers of various heights.
- The players move in alternating turns. In each turn, a player must choose a tower of height and break it down into towers, each of height . The numbers and must satisfy and .
- If the current player is unable to make any move, they lose the game.
Given the value of and the respective height values for all towers, can you determine who will win, assuming both players always move optimally? If the first player wins, print ; otherwise, print .
The first line contains an integer, , denoting the number of test cases.
The subsequent lines define the test cases. Each test case is described by two lines:
- An integer, , denoting the number of towers.
- space-separated integers, , where each describes the height of tower .
For each test case, print a single integer denoting the winner (i.e., either or ) on a new line.
2 2 1 2 3 1 2 3
In the first test case, the first player simply breaks down the second tower of height into two towers of height and wins.
In the second test case, there are only two possible moves:
- Break the second tower into towers of height .
- Break the third tower into towers of height .
Whichever move player makes, player can make the other move and win the game.