Best I can come up with at 3 am.
(Python3)

from functools import reduce

MOD = 1_000_000_007

def _value_of_S_reduce(x:int,y:int)->int:
    return (x+y+x*y) % MOD

def value_of_S(l:list)->int:
    return reduce(_value_of_S_reduce,l)
    
if __name__=='__main__':
    _ = input()
    print(value_of_S(list(map(int,input().split()))))

my simple c solution***

include

include

include

include

int main() { int n; scanf("%d",&n); long long int a[n]; int i; for(int i=0;i

return 0;

}

We have to get an average, which is sum(entries)/num(entries). So, ostensibly, we need sum(f(each permutation))/nPn. But the key is to realize that the operations are commutative, associative, and distributive.

So we'll always get the same value S. That means that means our expression reduces to nPn*f(one permutation)/nPn = f(one permutation)

We may as well choose the original permutation. The other thing to help speed up runtime is (a+b)%m = (a%m + b%m)%m

We can expect lots of explanation with examples from various apparel manufacturers topics of maths from here. I think this site offers lots of solved examples from each of the topic. I am looking for further updates from here. Keep up the good work.

My simple solution

https://github.com/joy-mollick/Problem-Solving-Solutions-Math-Greedy-/blob/master/HackerRank-Tell%20the%20Average.cpp