100-days-of-rust/Week-09/Day-62_Funny-Plant

Funny plant

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 needs 1 week to grow, so each weak you can harvest it fruits. Also the plant gives 1 fruit more than the week before and to get more plants you need to plant a fruit.

Now you need to calculate after how many weeks, you can support a group of x people, given y fruits to start with.

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
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.

Examples

input: 200, 15
output: 5

input: 50000, 1
output: 14

input: 150000, 250
output: 9