Problem #300
Being the CR
You are the CR of your class. One day, 5000 students of your class gathered in a row. The professor assigned you to arrange the students in increasing order of their enrollment number.
For rearranging students you follow the given strategy:
1. Start from the beginning of the row.
2. Inspect the first two students' enrollment numbers and swap them if second student’s enrollment number < first student’s enrollment number.
3. Repeat Step 2 for (2^{nd} student ,3^{rd} student), (3^{rd} student, 4^{th} student) and so on.
You decide to follow the above strategy 2022 times.
Find the number of different initial arrangements of students that will lead to a sorted sequence after the whole process.Report the answer modulo 1000000007.