Circular Board Game

A board game called Expo is played on a circular board with $N$ cells numbered $1$ to $N$. Cell $N$ is followed by cell $1$ again, so a token that passes the end keeps going from the start.

A player rolls a die, reads the number $S$ on the top face and moves the token one cell forward $\operatorname{expo}(S)$ times, where

$\operatorname{expo}(S) = S^{(S-1)^{(S-2)^{\,\cdots^{\,2^{1}}}}}$

So $\operatorname{expo}(1) = 1$, $\operatorname{expo}(2) = 2^{1} = 2$, $\operatorname{expo}(3) = 3^{2^{1}} = 9$ and $\operatorname{expo}(4) = 4^{9} = 262144$. A player starts on cell $1$ and wins by standing exactly on cell $N$ once a move is complete. Passing cell $N$ in the middle of a move does not count.

Brad and Pete are playing this game. Once $S$ grows even a little, moving the token $\operatorname{expo}(S)$ times takes longer than a lifetime. Their grandfathers never finished the game they started in their youth the traditional way, so the two of them play on their behalf. Given the number $S$ on the die and the cell $M$ the token stands on, report the cell the token stands on when the move is finished.

The first line contains one integer $T$ ($1 \le T \le 256$), the number of test cases.

Each of the next $T$ lines contains three space separated integers $S$, $M$ and $N$ ($1 \le S \le 10^{9}$, $1 \le M \le N \le 10^{9}$): the number on the die, the cell the token stands on, and the number of cells on the board.

For each test case print one line with the number of the cell the token stands on after moving $\operatorname{expo}(S)$ cells forward from cell $M$.