HackerEarth Remove the element problem solution

In this HackerEarth Remove the element problem You are given an integer array A of size N. You can perform an operation exactly N number of times. In the operation, you can remove one element from array A and the operation will cost Ai units if ith is removed from the array. The operation will take 1 second.

Elements of array A will keep on increasing every second until it is removed. Let ith element is Ai at jth second. Then the ith element will increase by (j + 1) * Ai and the element will become Ai + (j + 1) * Ai at (j + 1)th second.

Your task is to find the minimum cost to remove all the elements from array A. As the answer can be very large, print the answer module 10^9 + 7.

#include <bits/stdc++.h>

using namespace std;

typedef long long int ll;
typedef pair<ll, ll> pll;
typedef vector<ll> vll;
typedef vector<int> vi;

#define pb push_back

const ll INF=1e18;

const int mod=1000000007;

ll arr[100005], fact[100005];

int main()
{
    ll t,n,m,i,j,k;

    fact[0]=1;

    for (i=1;i<100005;++i)
        fact[i]=(i*fact[i-1])%mod;

    scanf ("%lld",&t);

    while (t--)
    {
        scanf ("%lld",&n);
        for (i=1;i<=n;++i)
            scanf ("%lld",&arr[i]);
        sort(arr+1,arr+n+1,[](ll x, ll y)
        {
            return x>y;
        });

        ll ans=0;

        for (i=1;i<=n;++i)
            ans=(ans+fact[i]*arr[i])%mod;

        printf ("%lldn",ans);
    }

    return 0;
}