The kingdom of Zokoria is under attack! The invaders wish to capture the Queen and conquer Zokoria. Aware of the danger, Heldorf , the captain of the Zokorian army must devise an exit strategy for the Queen.
In order to do so, the invaders must be kept at bay for a period of time. There are invaders who must be engaged in fight for as long as possible. The army has soldiers, with each having the capability to fight for a total of seconds. The soldiers can fight against any invader at any time i.e. they can move to fight with another invader by dropping the current fight.
Heldorf wants you to find out how long does he have to help the Queen escape. You have to find the maximum possible time for which all the invaders can be kept busy?
Input Format
The first line of input contains two numbers and - the number of invaders and the number of soldiers respectively.
The next line contains numbers, each integer representing the time for which the respective soldier can engage in a fight.
Constraints
- The time for which each solider can fight, , lies between and .
Output Format
Print the maximum possible time for which the invaders can be engaged in a fight. The number should be accurate up to absolute precision.
Sample Input 0
3 4
1000 100 100 100
Sample Output 0
150.000000000
Explanation 0
- Soldier can fight invader from time to time .
- Soldier can fight invader from time to time .
- Soldier can fight invader from time to time .
- Soldier can fight invader from time to time .
- Soldier can fight invader from time to .
Sample Input 1
3 4
10 15 10 100
Sample Output 1
17.500000000
Explanation 1
- Soldier can fight invader from time to time .
- Soldier can fight invader from time to time .
- Soldier can fight invader from time to time .
- Soldier can fight invader from time to time .
- Soldier can fight invader from time to time .