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

4 8
3 6 7 11

4

3 3
1 1 1

1