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

Example Output

8

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