Uolevi owns a factory that has $n$ machines which can be used to make cars. He is now pondering how much unpaid overtime his employees should do so that the quarterly quota of $t$ cars is met.

For each machine, you know the number of seconds it needs to make a single car. The machines can work simultaneously, and you can freely decide their schedule.

What is the shortest time needed to make $t$ cars?

Input

The first input line has two integers $n$ and $t$: the number of machines and cars.

The next line has $n$ integers $k_1,k_2,\dots,k_n$: the time needed to make a car using each machine.

Output

Output one integer which is the minimum time needed to make $t$ cars.

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 cars, machine 2 makes four cars and machine 3 makes one car.