Problem Statement

You are given $a permutation P=(P_1,P_2,\cdots,P_N)$ of $(1,2,\cdots,N)$.
Additionally, you are given an integer K.
You can perform the following operation zero or more times:

• Choose integers l and $r (1 \leq l < r \leq N).$ Here, the pair (l,r) must satisfy all of the following conditions:
• $K \leq r-l$.
• P_l > P_r at the time of the operation.

• The pair (l,r) has never been chosen before.

• Then, swap the values of P_l and P_r.

You want to maximize the number of operations.
Find one way to achieve this.

Input

The input is given from Standard Input in the following format:
N K
$P_1 P_2 \cdots P_N$

Output

Print the answer in the following format:
m
l_1 r_1
l_2 r_2
$\vdots$
l_m r_m

Here, m is the maximum number of operations, and l_i and r_i are the values of l and r chosen in the i-th operation, respectively.
If multiple solutions exist, you can print any of them.

Constraints

• $2 \leq N \leq 500$
• $1 \leq K \leq N-1$
• $(P_1,P_2,\cdots,P_N)$ is a permutation of $(1,2,\cdots,N)$.
• All input values are integers.

Sample Input 1

3 1
3 2 1

Sample Output 1

3
2 3
1 3
1 2

In this example, the maximum number of operations is 3.
The operations in the sample output proceed as follows:

• 1st operation: Choose (l,r)=(2,3). We have $1 \leq 3-2$ and P_2 > P_3, and (2,3) has not been chosen before, so the conditions are satisfied. Swap P_2 and P_3, resulting in P=(3,1,2).
• 2nd operation: Choose (l,r)=(1,3). We have $1 \leq 3-1$ and P_1 > P_3, and (1,3) has not been chosen before, so the conditions are satisfied. Swap P_1 and P_3, resulting in P=(2,1,3).
• 3rd operation: Choose (l,r)=(1,2). We have $1 \leq 2-1$ and P_1 > P_2, and (1,2) has not been chosen before, so the conditions are satisfied. Swap P_1 and P_2, resulting in P=(1,2,3).

Sample Input 2

5 4
1 4 3 2 5

Sample Output 2

0

Sample Input 3

4 2
4 1 2 3

Sample Output 3

2
1 4
1 3

Sample Input 4

10 5
8 7 6 10 9 3 1 5 2 4

Sample Output 4

15
3 8
2 8
3 10
3 9
1 8
2 10
2 9
2 7
1 10
5 10
1 9
4 10
4 9
1 7
1 6

见题面 Input 部分

见题面 Output 部分