An orchard has n bins, bin i holding a[i] ripe fruits. A single picker works an H-hour shift. Within any one hour the picker stays at exactly one bin and removes up to rate fruits from it (choosing the same whole-number rate for the entire shift). If a bin holds fewer than rate fruits when the picker arrives that hour, the picker still spends the whole hour there and simply empties it; leftover picking capacity in that hour is not carried to another bin.
So a bin of a[i] fruits takes ceil(a[i] / rate) hours to clear. Find the smallest whole-number rate (at least 1) that clears all bins within H hours in total.
Input format
Line 1: two integers n and H.
Line 2: n space-separated integers, the fruit counts per bin.
Output format
A single integer: the smallest picking rate that finishes within H hours.
Constraints
- 1 <= n <= 40
- n <= H <= 1000000000
- 1 <= each fruit count <= 100000