codechef AUG17 T2 Chef and Mover

Chef and Mover Problem Code: CHEFMOVR

Chef's dog Snuffles has so many things to play with! This time around, Snuffles has an array A containing N integers: A₁, A₂, ..., A_N.

Bad news: Snuffles only loves to play with an array in which all the elements are equal.

Good news: We have a mover of size D!

A mover of size D is a tool which helps to change arrays. Chef can pick two existing elements A_i and A_j from the array, such that i + D = j and subtract 1 from one of these elements, and add 1 to the other element. In effect, a single operation of the mover, moves a value of 1 from one of the elements to the other.

Chef wants to find the minimum number of times she needs to use the mover of size D to make all the elements of the array A equal. Help her find this out.

Input

• The first line of the input contains an integer T, denoting the number of test cases. The description of T test cases follows.
• The first line of each test case contains two integers N and D, denoting the number of elements in the array and the size of the mover.
• The second line of each testcase contains N space-separated integers: A₁, A₂, ..., A_N, denoting the initial elements of the array.

Output

• For each test case, output a single line containing the minimum number of uses or -1 if it is impossible to do what Snuffles wants.

Constraints

• 1 ≤ T ≤ 10
• 2 ≤ N ≤ 10⁵
• 1 ≤ D < N
• 1 ≤ A_i ≤ 10⁹

Subtasks

• Subtask 1 (30 points) : N ≤ 10³
• Subtask 2 (70 points) : Original constraints

Example

Input:
3
5 2
1 6 5 0 3
3 1
0 3 0
4 2
3 4 3 5

Output:
5
2
-1

Explanation

Testcase 1:

Here is a possible sequence of usages of the mover:

• Move 1 from A₃ to A₁
• Move 1 from A₃ to A₁
• Move 1 from A₂ to A₄
• Move 1 from A₂ to A₄
• Move 1 from A₂ to A₄

At the end, the array becomes (3, 3, 3, 3, 3), which Snuffles likes. And you cannot achieve this in fewer moves. Hence the answer is 5.

Testcase 2:

Here is a possible sequence of usages of the mover:

• Move 1 from A₂ to A₁
• Move 1 from A₂ to A₃

At the end, the array becomes (1, 1, 1), which Snuffles likes. And you cannot achieve this in fewer moves. Hence the answer is 2.

Testcase 3:

It is impossible to make all the elements equal. Hence the answer is -1.

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这道题我居然WA了两次QAQ

其实题意就是给你n个数和一个d 相邻距离为d的数字可以进行你+1我-1的操作 求最少的操作次数使得全部的数相等

所以我们一开始就要把所有的数加起来得到sum 如果sum%n！=0 那么肯定不存在这么一个答案 

因为你无论怎么加减 总和都是不变的

然后再判断相邻d的所有数加起来是否为0 不如！=0 说明答案也不存在 这个也很好证明

最后统计答案的时候 我一开始想的是把所有的正数加起来 但是发现不行

比如这样一个例子 d=1时 4 1 1

按上面来算答案应该是2但是答案其实是3

因为你只能相邻交换 所以应该是4给第一个1 2 然后 第一个1给第二个1 1 

答案是3

所以我们统计答案的时候可以像均分纸牌一样 每次拿出第一个数（<=k)

他只能从下一个数拿 而下一个数不可能从这个数再拿回来 所以他只能从下一个拿

这样把值推过去再慢慢统计就好辣

这样这个问题就解决辣