A13030. The Parade
编程题
普及/提高-
知识点
题目描述
The Berland Army is preparing for a large military parade. It is already decided that the soldiers participating in it will be divided into $k$ rows, and all rows will contain the same number of soldiers.
Of course, not every arrangement of soldiers into $k$ rows is suitable. Heights of all soldiers in the same row should not differ by more than $1$ . The height of each soldier is an integer between $1$ and $n$ .
For each possible height, you know the number of soldiers having this height. To conduct a parade, you have to choose the soldiers participating in it, and then arrange all of the chosen soldiers into $k$ rows so that both of the following conditions are met:
- each row has the same number of soldiers,
- no row contains a pair of soldiers such that their heights differ by $2$ or more.
Calculate the maximum number of soldiers who can participate in the parade.
Of course, not every arrangement of soldiers into $k$ rows is suitable. Heights of all soldiers in the same row should not differ by more than $1$ . The height of each soldier is an integer between $1$ and $n$ .
For each possible height, you know the number of soldiers having this height. To conduct a parade, you have to choose the soldiers participating in it, and then arrange all of the chosen soldiers into $k$ rows so that both of the following conditions are met:
- each row has the same number of soldiers,
- no row contains a pair of soldiers such that their heights differ by $2$ or more.
Calculate the maximum number of soldiers who can participate in the parade.
输入格式
The first line contains one integer $t$ ( $1 \le t \le 10000$ ) — the number of test cases. Then the test cases follow.
Each test case begins with a line containing two integers $n$ and $k$ ( $1 \le n \le 30000$ , $1 \le k \le 10^{12}$ ) — the number of different heights of soldiers and the number of rows of soldiers in the parade, respectively.
The second (and final) line of each test case contains $n$ integers $c_1$ , $c_2$ , ..., $c_n$ ( $0 \le c_i \le 10^{12}$ ), where $c_i$ is the number of soldiers having height $i$ in the Berland Army.
It is guaranteed that the sum of $n$ over all test cases does not exceed $30000$ .
Each test case begins with a line containing two integers $n$ and $k$ ( $1 \le n \le 30000$ , $1 \le k \le 10^{12}$ ) — the number of different heights of soldiers and the number of rows of soldiers in the parade, respectively.
The second (and final) line of each test case contains $n$ integers $c_1$ , $c_2$ , ..., $c_n$ ( $0 \le c_i \le 10^{12}$ ), where $c_i$ is the number of soldiers having height $i$ in the Berland Army.
It is guaranteed that the sum of $n$ over all test cases does not exceed $30000$ .
输出格式
For each test case, print one integer — the maximum number of soldiers that can participate in the parade.
输入输出样例
输入 #1
5 3 4 7 1 13 1 1 100 1 3 100 2 1 1000000000000 1000000000000 4 1 10 2 11 1
输出 #1
16 100 99 2000000000000 13
说明/提示
Explanations for the example test cases:
1. the heights of soldiers in the rows can be: $[3, 3, 3, 3]$ , $[1, 2, 1, 1]$ , $[1, 1, 1, 1]$ , $[3, 3, 3, 3]$ (each list represents a row);
2. all soldiers can march in the same row;
3. $33$ soldiers with height $1$ in each of $3$ rows;
4. all soldiers can march in the same row;
5. all soldiers with height $2$ and $3$ can march in the same row.
1. the heights of soldiers in the rows can be: $[3, 3, 3, 3]$ , $[1, 2, 1, 1]$ , $[1, 1, 1, 1]$ , $[3, 3, 3, 3]$ (each list represents a row);
2. all soldiers can march in the same row;
3. $33$ soldiers with height $1$ in each of $3$ rows;
4. all soldiers can march in the same row;
5. all soldiers with height $2$ and $3$ can march in the same row.