Pepero Gifts

There are $N$ people on a circle of circumference $L$. The number $N$ is even. Person $i$ is at clockwise coordinate $X_i$ from a fixed origin. Repeat the following action until no people remain.

• Choose a remaining person $a$.
• Choose a nearest other remaining person $b$. Distance is the shortest distance along the circumference. Ties may be broken arbitrarily.
• Person $a$ travels this shortest distance to give Pepero to $b$, and both people are removed.

Other people's positions do not change. The distance between $a$ and $b$ is $\min(|X_a-X_b|,L-|X_a-X_b|)$. Find the minimum total distance and output an action sequence attaining it.

The input is given in the following format:

$N\ L$ $X_1\ X_2\ \cdots\ X_N$

Print the minimum total distance on the first line. On each of the next $N/2$ lines, print the original indices $a,b$ chosen in that action, in execution order. Indices range from $1$ to $N$. Both people must still be present, and $b$ must be a nearest other remaining person to at that moment. If there are multiple solutions, print any of them.

• $2 \leq N \leq 2000$.
• $N$ is even.
• $N \leq L \leq 10^9$.