Problem F
Divisor Swap

You are given a list of $N$ positive integers $a_1, a_2, \dots , a_N$. Your goal is to sort the list. In one move, you may swap two numbers in the list if one of them is a divisor of the other. In other words, you may swap $a_i$ and $a_j$ if $a_i \equiv 0 \pmod{a_j}$ or $a_j \equiv 0 \pmod{a_i}$. In many programming languages, you can check $a_i \equiv 0 \pmod{a_j}$ by testing whether $a_i \% a_j$ equals $0$ (i.e., the remainder of integer division is zero).

Input

The first line contains two integers $N$ and $X$ ($1 \leq N \leq 1000$, $0 \leq X \leq 1$), where $N$ is the number of elements in the list and $X$ is a flag indicating whether you need to output the sequence of moves.

The second line contains $N$ integers $a_1, a_2, \dots , a_N$ ($1 \leq a_i \leq 10^6$).

Output

If it is impossible to sort the list, output NEJ.

If it is possible to sort the list, first output JA on the first line. Then output an integer $M$ on a line, the number of moves you will make. This number must be at most $10^6$. Then output $M$ lines, each containing two integers $i, j$ ($1 \leq i,j \leq N$), indicating that you swap $a_i$ and $a_j$.

If $X = 0$, it suffices to output JA or NEJ correctly. You do not need to output the moves, and you will not be judged wrong if you do (even if the moves are incorrect).

Scoring

Your solution will be tested on a set of test groups, each worth a number of points. Each test group contains a set of test cases. To get the points for a test group you need to solve all test cases in the test group.

5 1
9 8 40 3 5

JA
3
2 3
2 5
1 4

2 1
9 5

NEJ

4 0
1 7 5 3

JA