CF1408B.Arrays Sum

普及/提高-

通过率：0%

AC君温馨提醒

该题目为【codeforces】题库的题目，您提交的代码将被提交至codeforces进行远程评测，并由ACGO抓取测评结果后进行展示。由于远程测评的测评机由其他平台提供，我们无法保证该服务的稳定性，若提交后无反应，请等待一段时间后再进行重试。

题目描述

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 $m$ .

输入格式

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 $a_1, a_2, \ldots, a_n$ ( $0 \leq a_1 \leq a_2 \leq \ldots \leq a_n \leq 100$ , $a_n > 0$ ).

输出格式

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

输入输出样例

输入#1

6
4 1
0 0 0 1
3 1
3 3 3
11 3
0 1 2 2 3 3 3 4 4 4 4
5 3
1 2 3 4 5
9 4
2 2 3 5 7 11 13 13 17
10 7
0 1 1 2 3 3 4 5 5 6

输出#1

说明/提示

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 $m$ .

首页