Solve the programming task below in a Python markdown code block.
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Chef is having a candlelit dinner with his girlfriend at his place. Currently, it is time $0$, Chef just managed to light a candle, but he is out of matchsticks.

Since Chef has an infinite supply of (unlit) candles, he can use the following strategy: each second (starting at time $0$), he takes one lit candle and lights up $X$ other candles using it. This process takes $1$ unit of time to complete, i.e. if Chef starts lighting up $X$ candles at a time $t_{1}$, he is able to finish at the time $t_{1} + 1$.

However, since candle wax is limited, a candle can only burn for $Y$ units of time and then it is extinguished.

Chef's girlfriend arrives at a time $A$ — specifically, after all the candles that were supposed to get extinguished at time $A$ have been extinguished and after Chef lights up all the candles that he was lighting up since time $A-1$. Now Chef wants to know the maximum number of candles which can be lit at the time $A$ to impress his girlfriend.

------  Input ------
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 $A$, $Y$ and $X$.

------  Output ------
For each test case, print a single line containing one integer — the maximum number of lit candles Chef can impress his girlfriend with.

------  Constraints ------
$1 ≤ T ≤ 10^{5}$
$1 ≤ A, Y, X ≤ 10^{9}$

------  Subtasks ------
Subtask #1 (40 points): $A ≥ Y$

Subtask #2 (60 points): original constraints

----- Sample Input 1 ------ 
3

1 1 1

1 2 1

2 2 1
----- Sample Output 1 ------ 
1

2

2
----- explanation 1 ------ 
Example case 1: At the time $0$, there is one lit candle, using which we light $1$ more candle. At the time $1$, the starting candle gets extinguished and the candle which we started lighting up at the time $0$ is lit, so we have only $1$ candle lit up when Chef's girlfriend arrives.

Example case 2: At the time $0$, there is one lit candle, using which we light $1$ more candle. At the time $1$, the candle which we started lighting up at the time $0$ and the starting candle are both lit.

Example case 3: At the time $0$, there is one lit candle, using which we light $1$ more candle. At the time $1$, the candle which we started lighting up at time $0$ is lit, and we start lighting up one more candle. At the time $2$, the starting candle gets extinguished and the candle which we started lighting up at the time $1$ is lit. In total, we have $2$ lit candles when Chef's girlfriend arrives.