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

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 schedules.

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.