CF1408B Arrays Sum

You are given a non-decreasing array of non-negative integers $ a_1, a_2, \ldots, a_n $ . Also you are given a positive integer $ k $ . You want to find $ m $ non-decreasing arrays of non-negative integers $ b_1, b_2, \ldots, b_m $ , such that: - The size of $ b_i $ is equal to $ n $ for all $ 1 \leq i \leq m $ . - For all $ 1 \leq j \leq n $ , $ a_j = b_{1, j} + b_{2, j} + \ldots + b_{m, j} $ . In the other word, array $ a $ is the sum of arrays $ b_i $ . - The number of different elements in the array $ b_i $ is at most $ k $ for all $ 1 \leq i \leq m $ . Find the minimum possible value of $ m $ , or report that there is no possible $ m $ .

The first line contains one integer $ t $ ( $ 1 \leq t \leq 100 $ ): the number of test cases. The first line of each test case contains two integers $ n $ , $ k $ ( $ 1 \leq n \leq 100 $ , $ 1 \leq k \leq n $ ). The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 0 \leq a_1 \leq a_2 \leq \ldots \leq a_n \leq 100 $ , $ a_n > 0 $ ).

For each test case print a single integer: the minimum possible value of $ m $ . If there is no such $ m $ , print $ -1 $ .

In the first test case, there is no possible $ m $ , because all elements of all arrays should be equal to $ 0 $ . But in this case, it is impossible to get $ a_4 = 1 $ as the sum of zeros. In the second test case, we can take $ b_1 = [3, 3, 3] $ . $ 1 $ is the smallest possible value of $ m $ . In the third test case, we can take $ b_1 = [0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2] $ and $ b_2 = [0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2] $ . It's easy to see, that $ a_i = b_{1, i} + b_{2, i} $ for all $ i $ and the number of different elements in $ b_1 $ and in $ b_2 $ is equal to $ 3 $ (so it is at most $ 3 $ ). It can be proven that $ 2 $ is the smallest possible value of $ m $ .