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 n integers k_1,k_2,\dots,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

$1 \le n \le 2$ \cdot 10^5$

$1 \le t \le 10^9$

$1 \le k_i \le 10^9$

Example

Input

3 7
3 2 5

Output

8

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