We take a line segment of length on a one-dimensional plane and bend it to create a circle with circumference that's indexed from to . For example, if :
We denote a pair of points, and , as . We then plot pairs of points (meaning a total of individual points) at various indices along the circle's circumference. We define the distance between points and in pair as .
Next, let's consider two pairs: and . We define distance as the minimum of the six distances between any two points among points , , , and . In other words:
For example, consider the following diagram in which the relationship between points in pairs at non-overlapping indices is shown by a connecting line:
Given pairs of points and the value of , find and print the maximum value of , where , among all pairs of points.
The first line contains two space-separated integers describing the respective values of (the number of pairs of points) and (the circumference of the circle).
Each line of the subsequent lines contains two space-separated integers describing the values of and (i.e., the locations of the points in pair ).
Print a single integer denoting the maximum , , where .
Sample Input 0
5 80 42 61 53 74 4
Sample Output 0
In the diagram below, the relationship between points in pairs at non-overlapping indices is shown by a connecting line:
As you can see, the maximum distance between any two pairs of points is , so we print as our answer.
Sample Input 1
2 10000 1010 20
Sample Output 1
In the diagram below, we have four individual points located at three indices:
Because two of the points overlap, the minimum distance between the two pairs of points is . Thus, we print as our answer.