Wizard and wolves

Once, while walking, you met n wolves. Each wolf has its own power parameter - health. When meeting with wolves, the i-th wolf has h[i] health units. If the wolf's health drops to 0 or lower, then he dies.

Luckily, you are a wizard who can create explosions. With these explosions you can reduce the health of wolves. In one blast, the health of wolves can be reduced in the following ways:

Selecting any live wolf, you explode next to it. In this case, the health of the selected wolf is reduced by a units, and all others by b units. a and b are given to you initially.

What is the minimum number of explosions needed to make to kill all the wolves?

Input

First line contains three integers n (1 ≤ n ≤ 10^5), a and b (1 ≤ b < a ≤ 10^9). Each of the next n lines contains number h[i] (1 ≤ h[i] ≤ 10^9) - the health of the i-th volf.

Output

Print the minimum number of explosions needed to kill all the wolves.

Examples

Note

Test 1.

• Let's create an explosion next to a wolf with health 8. After the explosion, the health of the wolves will be respectively 3, 4, 1, -1.

• We will produce the second explosion next to a wolf with a health equal to 4. After the second explosion, all the wolves will die.

Test 2.

• To kill all the wolves, it is necessary next to each of them produce 2 explosions, overall 4 explosions.It's impossible to kill all wolves with a smaller number of explosions.