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D - Widespread

Score : $400$ points

Problem Statement

You are going out for a walk, when you suddenly encounter $N$ monsters. Each monster has a parameter called health, and the health of the $i$-th monster is $h_i$ at the moment of encounter. A monster will vanish immediately when its health drops to $0$ or below.

Fortunately, you are a skilled magician, capable of causing explosions that damage monsters. In one explosion, you can damage monsters as follows:

• Select an alive monster, and cause an explosion centered at that monster. The health of the monster at the center of the explosion will decrease by $A$, and the health of each of the other monsters will decrease by $B$. Here, $A$ and $B$ are predetermined parameters, and $A > B$ holds.

At least how many explosions do you need to cause in order to vanish all the monsters?

Constraints

• All input values are integers.
• $1 ≤ N ≤ 10^5$
• $1 ≤ B < A ≤ 10^9$
• $1 ≤ h_i ≤ 10^9$

Input

Input is given from Standard Input in the following format:

$N$ $A$ $B$

$h_1$

$h_2$

$:$

$h_N$

Output

Print the minimum number of explosions that needs to be caused in order to vanish all the monsters.

4 5 3
8
7
4
2

2

You can vanish all the monsters in two explosion, as follows:

• First, cause an explosion centered at the monster with $8$ health. The healths of the four monsters become $3$, $4$, $1$ and $-1$, respectively, and the last monster vanishes.
• Second, cause an explosion centered at the monster with $4$ health remaining. The healths of the three remaining monsters become $0$, $-1$ and $-2$, respectively, and all the monsters are now vanished.

2 10 4
20
20

4

You need to cause two explosions centered at each monster, for a total of four.

5 2 1
900000000
900000000
1000000000
1000000000
1000000000

800000000