How can I make my code better and decrease the time which is used in my code?

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C#

Hello. I am attending one course which is about Data Structures and Algorithms. Now I am learning about Divide and Conqure algorithms which are more about recursive functions.

But now in the below practice, I get this error:

Error Message:
    Test 'SolveTest_Q5OrganizingLottery' exceeded execution timeout period.

Here is the problem description:

Task. You are given a set of points on a line and a set of segments on a line. The goal is to compute, for each point, the number of segments that contain this point.

Input Format. The first line contains two non-negative integers 𝑠 and 𝑝 defining the number of segments and the number of points on a line, respectively. The next 𝑠 lines contain two integers 𝑎𝑖, 𝑏𝑖 defining the 𝑖-th segment [𝑎𝑖, 𝑏𝑖]. The next line contains 𝑝 integers defining points 𝑥1, 𝑥2, . . . , 𝑥𝑝.

Constraints. 1 ≤ 𝑠, 𝑝 ≤ 50000; −108 ≤ 𝑎𝑖 ≤ 𝑏𝑖 ≤ 108 for all 0 ≤ 𝑖 < 𝑠; −108 ≤ 𝑥𝑗 ≤ 108 for all 0 ≤ 𝑗 < 𝑝.

Output Format. Output 𝑝 non-negative integers 𝑘0, 𝑘1, . . . , 𝑘𝑝−1 where 𝑘𝑖 is the number of segments which
contain 𝑥𝑖. More formally,      𝑘𝑖 = |{𝑗 : 𝑎𝑗 ≤ 𝑥𝑖 ≤ 𝑏𝑗}| .

For example:

Sample 1.
Input:
2 3
0 5
7 10
1 6 11
Output:
1 0 0
Here, we have two segments and three points. The first point lies only in the first segment while the remaining two points are outside of all the given segments.

Sample 2.
Input:
1 3
-10 10
-100 100 0
Output:
0 0 1

Sample 3.
Input:
3 2
0 5
-3 2
7 10
1 6
Output:
2 0

What I have tried:

My function has to get 3 parameters. The first one is for starts, the second one for ends, and the third one for points.
First I sort both the arrays which are for starts and end then I define an array which length is equal to the length of points. Second in a for loop, I define some conditions. I think the first if is obvious. but the second and third are used when the element point[i] does not exist in the starts or ends arrays.


Here is my code for Binary Search:

private static long BinarySearch(long[] a, long l, long h, long key)
{
    if (h < l)
    {
        return -1;
    }
    long mid = (l + h) / 2;
    if (key == a[mid])
    {
        return mid;
    }
    else if (key < a[mid])
    {
        return BinarySearch(a, l, mid - 1, key);
    }
    else
    {
        return BinarySearch(a, mid + 1, h, key);
    }
}

And this is my main function:

public static long[] OrganizingLottery(long[] starts,long[] ends, long[] points)
{
    long s_length = starts.Length;
    long e_length = ends.Length;
    Array.Sort(starts);
    Array.Sort(ends);
    long[] res = new long[points.Count()];
    long count = 0;
    for (long i = 0; i < points.Length; i++)
    {
        if (points[i] < starts.Min() || points[i] > ends.Max())
        {
            count = 0;
            continue;
        }
        long index_in_s = BinarySearch(starts, 0, s_length - 1, points[i]);
        long index_in_e = BinarySearch(ends, 0, e_length - 1, points[i]);
        if (index_in_s == -1)
        {
            long s_instead = starts.Where(x => x < points[i]).Max();
            index_in_s = BinarySearch(starts, 0, s_length - 1, s_instead);
        }
        if (index_in_e == -1)
        {
            long e_instead = ends.Where(y => y > points[i]).Min();
            index_in_e = BinarySearch(ends, 0, e_length - 1, e_instead);
        }
        count = index_in_s - index_in_e + 1;
        res[i] = count;
    }
    return res;
}

I know that I have used many LINQ functions 😅, but actually I did not have any other idea for solving this problem.
I will be grateful for any help and advice.
Thanks.