Scientist have discovered a new plant. The fruit of the plant can feed 1 person for a whole week and best of all, the plant never dies. Fruits take 1 week to grow. Each week the plant gives 1 fruit more than the week before. To get more plants you need to plant a fruit. Each week you will prioritise planting one fruit from each plant, and what is left over can be consumed.
You start with one plant. Now you need to calculate after how many weeks, you can support a group of x people, given y fruits to start with.
Input
15 1
Output
5
Input description
The input gives you 2 positive integers x and y, being x the number of people needed to be fed and y the number of fruits you start with.
Output description
The number of weeks before you can feed the entire group of people.
Explanation
Here you have a table that shows the growth when starting with 1 fruit. It shows when the plant came into existence (is planted) and how may fruit it bears each week
Plant 1 2 3 4 5 6 7 8 9 10 11 12 13 Total # of fruits in a harvest
0——————————-—0
10———————————0
210——————————-1
321000————————-3
432111000000—————6
543222111111
Week
1 0 - - - - - - - - - - - - 0
2 1 0 - - - - - - - - - - - 1
3 2 1 0 0 0 - - - - - - - - 3
4 3 2 1 1 1 0 0 0 0 0 0 0 0 8
5 4 3 2 2 2 1 1 1 1 1 1 1 1 21
At week 1 we have 1 plant giving 0 fruits, because it has just been planted.
When week 2 comes along we have 1 plant that gives off a fruit and then we use that fruit to plant plant 2.
Then in week 3 we have 2 fruits from plant 1, 1 from plant 2, so we can plant 3 new plants.
Challenge Input
200 15
50000 1
150000 250
Challenge Output
5
14
9