A13701. Arrays Sum
编程题
普及/提高-
知识点
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 $m$ .
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 $a_1, a_2, \ldots, a_n$ ( $0 \leq a_1 \leq a_2 \leq \ldots \leq a_n \leq 100$ , $a_n > 0$ ).
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
-1 1 2 2 2 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 $m$ .
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 $m$ .