CF1870A MEXanized Array

You 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.

The 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 $ ).

For 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.

In 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] $ .