Read problem statements in [Bengali], [Mandarin Chinese], [Russian], and [Vietnamese] as well.

Chef is trying to invent the light bulb that can run at room temperature without electricity. So he has N gases numbered from 0 to N - 1 that he can use and he doesn't know which one of the N gases will work but we do know it.

Now Chef has worked on multiple search algorithms to optimize search. For this project, he uses a modulo-based search algorithm that he invented himself. So first he chooses an integer K and selects all indices i in increasing order such that $i \bmod K = 0$ and test the gases on such indices, then all indices i in increasing order such that $i \bmod K = 1$, and test the gases on such indices, and so on.

Given N, the index of the gas p that will work, and K, find after how much time will he be able to give Chefland a new invention assuming that testing 1 gas takes 1 day.

For example, consider N = 5, p = 2 and K = 3.
On the $1^{st} day, Chef tests gas numbered 0 because 0 \bmod 3 = 0$.
On the $2^{nd} day, Chef tests gas numbered 3 because 3 \bmod 3 = 0$.
On the $3^{rd} day, Chef tests gas numbered 1 because 1 \bmod 3 = 1$.
On the $4^{th} day, Chef tests gas numbered 4 because 4 \bmod 3 = 1$.
On the $5^{th} day, Chef tests gas numbered 2 because 2 \bmod 3 = 2$.

So after 5 days, Chef will be able to give Chefland a new invention

------ Input Format ------

• The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
• The first and only line of each test case contains three space-separated integers N, p, and K.

------ Output Format ------

For each test case, print a single line containing one integer — after how much time Chef will be able to give Chefland a new invention assuming that testing 1 gas takes 1 day.

------ Constraints ------

$1 ≤ T ≤ 10^{5}$
$1 ≤ N, K ≤ 10^{9}$
$0 ≤ p < N$

------ subtasks ------

Subtask #1 (100 points): Original constraints

----- Sample Input 1 ------
4
10 5 5
10 6 5
10 4 5
10 8 5
----- Sample Output 1 ------
2
4
9
8
----- explanation 1 ------
Test case $1$: On the day $1$ Chef will test gas numbered $0$ and on the day $2$ Chef will test gas numbered $5$.

Test case $2$: On the day $1$ Chef will test gas numbered $0$, on the day $2$ Chef will test gas numbered $5$, on the day $3$ Chef will test gas numbered $1$, and on the day $4$ Chef will test gas numbered $6$.

Test case $3$: On the day $1$ Chef will test gas numbered $0$, on the day $2$ Chef will test gas numbered $5$, on the day $3$ Chef will test gas numbered $1$, on the day $4$ Chef will test gas numbered $6$, on the day $5$ Chef will test gas numbered $2$, on the day $6$ Chef will test gas numbered $7$, on the day $7$ Chef will test gas numbered $3$, on the day $8$ Chef will test gas numbered $8$, and on the day $9$ Chef will test gas numbered $4$.

Test case $4$: On the day $1$ Chef will test gas numbered $0$, on the day $2$ Chef will test gas numbered $5$, on the day $3$ Chef will test gas numbered $1$, on the day $4$ Chef will test gas numbered $6$, on the day $5$ Chef will test gas numbered $2$, on the day $6$ Chef will test gas numbered $7$, on the day $7$ Chef will test gas numbered $3$, and on the day $8$ Chef will test gas numbered $8$.

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