A garage has n mechanics working in parallel. A mechanic of rank r takes r * c * c minutes to personally repair c cars (the more cars one mechanic handles, the slower each additional car). So within T minutes a rank-r mechanic can finish the largest whole number c of cars with r * c * c <= T.
The garage must repair a total of C cars. Find the fewest whole minutes T such that the mechanics together can finish at least C cars.
Input format
Line 1: two integers n and C.
Line 2: n space-separated integers, the mechanic ranks.
Output format
A single integer: the minimum number of minutes to repair C cars.
Constraints
- 1 <= n <= 20
- 1 <= C <= 100000
- 1 <= each rank <= 100