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.

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.

Constraints

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

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).

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).

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.

Sample Input 4

6 123 321
10 100 1000 10000 100000 1000000

Sample Output 4

90688

见题面 Input 部分

见题面 Output 部分