Problem Statement

You are given positive integers $a$ and $b$ such that $a\\leq b$, and a sequence of positive integers $A = (A_1, A_2, \\ldots, A_N)$.

On this sequence, you can perform the following operation any number of times (possibly zero):

• Choose distinct indices $i, j$ ($1\\leq i, j \\leq N$). Add $a$ to $A_i$ and subtract $b$ from $A_j$.

Find the maximum possible value of $\\min(A_1, A_2, \\ldots, A_N)$ after your operations.

Constraints

• $2\\leq N\\leq 3\\times 10^5$
• $1\\leq a\\leq b\\leq 10^9$
• $1\\leq A_i\\leq 10^{9}$

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Input

Input is given from Standard Input in the following format:

$N$ $a$ $b$ $A_1$ $A_2$ $\\ldots$ $A_N$

Output

Print the maximum possible value of $\\min(A_1, A_2, \\ldots, A_N)$ after your operations.

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Sample Input 1

3 2 2
1 5 9

Sample Output 1

5

Here is one way to achieve $\\min(A_1, A_2, A_3) = 5$.

• Perform the operation with $i = 1, j = 3$. $A$ becomes $(3, 5, 7)$.
• Perform the operation with $i = 1, j = 3$. $A$ becomes $(5, 5, 5)$.

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Sample Input 2

3 2 3
11 1 2

Sample Output 2

3

Here is one way to achieve $\\min(A_1, A_2, A_3) = 3$.

• Perform the operation with $i = 1, j = 3$. $A$ becomes $(13, 1, -1)$.
• Perform the operation with $i = 2, j = 1$. $A$ becomes $(10, 3, -1)$.
• Perform the operation with $i = 3, j = 1$. $A$ becomes $(7, 3, 1)$.
• Perform the operation with $i = 3, j = 1$. $A$ becomes $(4, 3, 3)$.

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Sample Input 3

3 1 100
8 5 6

Sample Output 3

5

You can achieve $\\min(A_1, A_2, A_3) = 5$ by not performing the operation at all.

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Sample Input 4

6 123 321
10 100 1000 10000 100000 1000000

Sample Output 4

90688