Navi is at the Beer Bar where he has ordered N beers. After seeing his love with the beers, Bar's Manager has decided to make as much money as they can by asking Navi to pay K * i³ Rupees for the i^th beer. But Navi has only M Rupees in his purse. So you are required to lent him some money so that he can still be able to pay for all of the N beers.

Input:

• First line will contain T (No. of test cases).
• Each test case will contain only one line having three space separated integers : N, K and M

Output:

• For every test case, print the required answer in a new line.

• 1 ≤ T ≤ 10⁵
• 1 ≤ N, K ≤ 10³
• 1 ≤ M ≤ 10⁶

Sample Code:

  #include 
    using namespace std;

    int main()
    {
        //taking input for number of test cases, T.
        cin>>T;

        //For every test case, taking input for N , K and M.
        cin>>N>>K>>M;


        //let the answer be in variable **Ans**
        cout << Ans << endl; //print your answer for every test case.
        return 0;
    }