Little beaver planted n flowers in a row on his windowsill and started waiting for them to grow. However, after some time the beaver noticed that the flowers stopped growing.So he decided to come up with some solutions.
There are $m$ days left .The height of the $i$th flower (assume that the flowers in the row are numbered from 1 to n from left to right) is equal to $a[i]$ at the moment. At each of the remaining $m$ days the beaver can take a special watering and water $w$ contiguous flowers (he can do that only once at a day).
At that each watered flower grows by one height unit on that day. The beaver wants the height of the smallest flower be as large as possible in the end. What maximum height of the smallest flower can he get?
Example : Let $n=6 ,m=2$ and $w=3$ and heights are : $[2, 2, 2, 2, 1, 1]$ then answer is $2.$
Explanation : Beaver can water the last $3$ flowers at the first day. On the next day he may not to water flowers at all. In the end he will get the following heights: $[2, 2, 2, 3, 2, 2].$ The smallest flower has height equal to $2.$ It's impossible to get height $3$ in this test.