Summing the Sum
Submissions: 1660   Accuracy:

17.81%

  Difficulty: Easy   Marks: 2

Ishaan was playing with numbers. He knew how to calculate the sum of numbers. He defined a function for his use which calculates the twice sum of first N natural numbers as sum(N).
But being curious, he modified his function to calculate something more complex. He defined his function to be sumX(N,M,K).
Now this function calculates :
sum( K + sum( K + sum( K + ...sum(K + N)...))) , continuing for M terms (Refer example for explanation).
Given N, M and K, calculate the value of sumX(N,M,K). 
Since the answer can be very large, print the answer in modulo 10^9 + 7.

Input : 
First line of input contains a single integer T denoting the number of test cases.
The only line of each test case contains 3 space-separated integers N, M and K.

Output : 
For each test case, print the required answer in a new line.

Constraints : 
1 <= T <= 200
1 <= N <= 1000
1 <= M <= 1000
1 <= K <= 1000

Example : 
Input : 

3
1 2 3
2 2 2
3 3 2
Output : 
552
506
1120422

Explanation : 
Case 1 : 
sum(3 + sum(3 + 1) ) = sum(3 + 20) = 552

Case 2 : 
sum(2 + sum(2 + 2) ) = sum(2 + 20) = 506

Case 3 : 
sum(2 + sum(2 + sum(2 + 3) ) ) = sum(2 + sum( 2 + 30 ) ) = sum(2 + 1056) = 1120422

 

** For More Input/Output Examples Use 'Expected Output' option **

Author: goyalanubhav11


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