Hemose was shopping with his friends Samez, AhmedZ, AshrafEzz, TheSawan and O_E in Germany. As you know, Hemose and his friends are problem solvers, so they are very clever. Therefore, they will go to all discount markets in Germany. Hemose has an array of nn integers. He wants Samez to sort the array in the non-decreasing order. Since it would be a too easy problem for Samez, Hemose allows Samez to use only the following operation:

Hemose Shopping solution codeforces

Hemose was shopping with his friends Samez, AhmedZ, AshrafEzz, TheSawan and O_E in Germany. As you know, Hemose and his friends are problem solvers, so they are very clever. Therefore, they will go to all discount markets in Germany.

Hemose has an array of nn integers. He wants Samez to sort the array in the non-decreasing order. Since it would be a too easy problem for Samez, Hemose allows Samez to use only the following operation:

  • Choose indices ii and jj such that 1i,jn1≤i,j≤n, and |ij|x|i−j|≥x. Then, swap elements aiai and ajaj.

Can you tell Samez if there’s a way to sort the array in the non-decreasing order by using the operation written above some finite number of times (possibly 00)?

Hemose Shopping solution codeforces

Each test contains multiple test cases. The first line contains the number of test cases tt (1t105)(1≤t≤105). Description of the test cases follows.

The first line of each test case contains two integers nn and xx (1xn105)(1≤x≤n≤105).

The second line of each test case contains nn integers a1,a2,...,ana1,a2,…,an (1ai109)(1≤ai≤109).

It is guaranteed that the sum of nn over all test cases doesn’t exceed 21052⋅105.

Hemose Shopping solution codeforces

For each test case, you should output a single string.

If Samez can sort the array in non-decreasing order using the operation written above, output “YES” (without quotes). Otherwise, output “NO” (without quotes).

You can print each letter of “YES” and “NO” in any case (upper or lower).

Example

Hemose Shopping solution codeforces

Copy
4
3 3
3 2 1
4 3
1 2 3 4
5 2
5 1 2 3 4
5 4
1 2 3 4 4

output

Copy
NO
YES
YES
YES

Hemose Shopping solution codeforces

In the first test case, you can’t do any operations.

In the second test case, the array is already sorted.

In the third test case, you can do the operations as follows:

  • [5,1,2,3,4][5,1,2,3,4]swap(a1,a3)swap(a1,a3)
  • [2,1,5,3,4][2,1,5,3,4]swap(a2,a5)swap(a2,a5)
  • [2,4,5,3,1][2,4,5,3,1]swap(a2,a4)swap(a2,a4)
  • [2,3,5,4,1][2,3,5,4,1]swap(a1,a5)swap(a1,a5)
  • [1,3,5,4,2][1,3,5,4,2]swap(a2,a5)swap(a2,a5)
  • [1,2,5,4,3][1,2,5,4,3]swap(a3,a5)swap(a3,a5)
  • [1,2,3,4,5][1,2,3,4,5]

(Here swap(ai,aj)swap(ai,aj) refers to swapping elements at positions iijj).

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