CF985D Sand Fortress

You are going to the beach with the idea to build the greatest sand castle ever in your head! The beach is not as three-dimensional as you could have imagined, it can be decribed as a line of spots to pile up sand pillars. Spots are numbered $ 1 $ through infinity from left to right. Obviously, there is not enough sand on the beach, so you brought $ n $ packs of sand with you. Let height $ h_{i} $ of the sand pillar on some spot $ i $ be the number of sand packs you spent on it. You can't split a sand pack to multiple pillars, all the sand from it should go to a single one. There is a fence of height equal to the height of pillar with $ H $ sand packs to the left of the first spot and you should prevent sand from going over it. Finally you ended up with the following conditions to building the castle: - $ h_{1}

The only line contains two integer numbers $ n $ and $ H $ ( $ 1

Print the minimum number of spots you can occupy so the all the castle building conditions hold.

Here are the heights of some valid castles: - $ n=5,H=2,[2,2,1,0,...],[2,1,1,1,0,...],[1,0,1,2,1,0,...] $ - $ n=6,H=8,[3,2,1,0,...],[2,2,1,1,0,...],[0,1,0,1,2,1,1,0...] $ (this one has $ 5 $ spots occupied) The first list for both cases is the optimal answer, $ 3 $ spots are occupied in them. And here are some invalid ones: - $ n=5,H=2,[3,2,0,...],[2,3,0,...],[1,0,2,2,...] $ - $ n=6,H=8,[2,2,2,0,...],[6,0,...],[1,4,1,0...],[2,2,1,0,...] $