Given integers ${b}$ and $a$, find the smallest integer ${h}$, such that there exists a triangle of height ${h}$, base ${b}$, having an area of at least $a$.

Example

$b=4$

${a=6}$

The minimum height ${h}$ is $3$. 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 $a$

Input Format

There are two space-separated integers ${b}$ and $a$, on a single line.

Constraints

$1\leq b\leq10^{6}$
$1\leq a\leq10^{6}$

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 $2$ and area at least $2$. It turns out, that there are triangles with height $2$, base $2$ and area $2$, for example a triangle with corners in the following points: $(1,1),(3,1),(1,3)$:

It can be proved that there is no triangle with integer height smaller than $2$, base $2$ and area at least $2$.

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 $17$ and area at least $100$.It turns out,that there are triangels with height $12$,base $17$ and area $102$ for example a triangle with corners in the following points: $(2,2),(19,2),(16,14)$.

It can be proved that there is no triangle with integer height smaller than $12$, base $17$ and area at least $100$

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