This problem is a Mooshak version of a CSES problem.

[PC007] Factory Machines

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 nn integers \(k_1, k_2, \ldots, k_n\)​: the time needed to make a product using each machine.

Output

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

Constraints

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

3 7
3 2 5

8

Explanation: Machine 1 makes two products, machine 2 makes four products and machine 3 makes one product.