Given integers and , find the smallest integer , such that there exists a triangle of height , base , having an area of at least .
Example
The minimum height is . One example is a triangle formed at points (0, 0), (4, 0), (2, 3).
Function Description
Complete the lowestTriangle function in the editor below.
lowestTriangle has the following parameters:
- int b: the base of the triangle
- int a: the minimum area of the triangle
Returns
- int: the minimum integer height to form a triangle with an area of at least
Input Format
There are two space-separated integers and , on a single line.
Constraints
Sample Input 0
2 2
Sample Output 0
2
Explanation 0
The task is to find the smallest integer height of the triangle with base and area at least . It turns out, that there are triangles with height , base and area , for example a triangle with corners in the following points: :
It can be proved that there is no triangle with integer height smaller than , base and area at least .
Sample Input 1
17 100
Sample Output 1
12
Explanation 1
The task is to find the smallest integer height of the triangle with base and area at least . It turns out, that there are triangles with height , base and area , for example a triangle with corners in the following points: .
It can be proved that there is no triangle with integer height smaller than , base and area at least .