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 $k_1,k_2,\dots ,k_n$​: 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

• $1\le n\le 2\cdot {10}^5$
• $1\le t\le {10}^9$
• $1\le k_i\le {10}^9$

3 7
3 2 5

8

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