This problem is a programming version of Problem 148 from projecteuler.net
We can easily verify that none of the entries in the first seven rows of Pascal's triangle are divisible by 7:
However, if we check the first one hundred rows, we will find that only 2361 of the 5050 entries are not divisible by 7.
Find the number of entries which are not divisible by 7 in the first rows and first columns of Pascal's triangle. Here, "column" means a column when the triangle is written this way:
Since the answer can be very large, output it modulo .
The first line of input contains , the number of test cases.
Each test case consists of one line containing two integers, and , separated by a space.
Test files #01-#03:
Test files #04-#06:
Test files #07-#09:
Test files #10-#12:
Test files #13-#15: No additional constraints.
For each test case, output a single line containing a single integer, the answer for that test case.
In the first test case, the following are the entries in the first rows and first columns: (highlighted in bold)
There are entries all in all, and they are all not divisible by . Thus, the answer is .
The second test case is mentioned in the problem statement.