A. MEXanized Arraytime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given three non-negative integers n, k, and x. Find the maximum possible sum of elements in an array consisting of non-negative integers, which has n elements, its MEX is equal to k, and all its elements do not exceed x. If such an array does not exist, output -1.The MEX (minimum excluded) of an array is the smallest non-negative integer that does not belong to the array. For instance:  The MEX of [2,2,1] is 0, because 0 does not belong to the array.  The MEX of [3,1,0,1] is 2, because 0 and 1 belong to the array, but 2 does not.  The MEX of [0,3,1,2] is 4, because 0, 1, 2 and 3 belong to the array, but 4 does not. InputThe first line contains a single integer t (1 \leq t \leq 1000) — the number of test cases. Then follows the description of the test cases.The only line of each test case contains three integers n, k, and x (1 \leq n, k, x \leq 200).OutputFor each test case, output a single number — the maximum sum of elements in a valid array, or -1, if such an array does not exist.ExampleInput
95 3 34 7 54 2 2812 10 657 51 122200 1 2002 2 13 2 14 7 10Output
7
-1
57
-1
2007
39800
1
2
-1
NoteIn the first test case, the maximum sum is 7, and one of the valid arrays is [0, 1, 2, 2, 2].In the second test case, there are no valid arrays of length n.In the third test case, the maximum sum is 57, and one of the valid arrays is [0, 1, 28, 28].
95 3 34 7 54 2 2812 10 657 51 122200 1 2002 2 13 2 14 7 10
7 -1 57 -1 2007 39800 1 2 -1 
['constructive algorithms', 'greedy', 'math', '*800']