Factory Machines

A factory has $nn$ machines which can be used to make products. Your goal is to make a total of $tt$ 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 $tt$ products?

Input

The first input line has two integers $nn$ and $tt$: the number of machines and products.

The next line has $nn$ integers $k_1,k_2,\dots ,k_{n}k\_1,k\_2,\backslash dots,k\_n$: the time needed to make a product using each machine.

Output

Print one integer: the minimum time needed to make $tt$ products.