there is no info about mod here so should we take mod in each step as we cant stope 100! in a normal variable
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No there is no need to take mod, you don’t need to calculate 500 factorial. There is another way out.
I can give you a hint.
The task is to factor n! into a and b such that gcd(p,q)=1 and p<q. so we calculate the number of distinct primes in n!
Let prime factorisation of n!= (p1)^x1 * (p2)^x2 …(pk)^xk
now for each i, (pi)^xi can either go in p or q. hence 2^k ways. but as we want p<q. therefore only 2^(k-1) ways.
So just find primes upto n and think how you can use this hint.
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