A factory has \(n\) machines which can be used to make products. Your goal is to make a total of \(t\) products.

For each machine, you know the number of seconds it needs to make a single product. The machines can work simultaneously, and you can freely decide their schedule.

What is the shortest time needed to make \(t\) products?

Input

• The first input line has two integers \(n\) and \(t\): the number of machines and products.
• The next line has \(n\) integers \(k_1, k_2, \ldots, k_n\): the time needed to make a product using each machine.

Output

• Print one integer: the minimum time needed to make \(t\) products.

Constraints

• \(1 \leq n \leq 2 \cdot 10 ^ 5\)
• \(1 \leq t \leq 10 ^ 9\)
• \(1 \leq k_i \leq 10 ^ 9\)

Example

Sample input

3 7  
3 2 5

Sample output

8

Note

Machine \(1\) makes two products, machine \(2\) makes four products and machine \(3\) makes one product.