Necklaces

Bajtyna has $n$ beads numbered from 1 to $n$. All beads are distinct. Each bead has a value in bajtalars.

Bajtyna wants to make a necklace from some of her beads. There are many ways to do this. Two ways are different if the sets of beads they use are different. Bajtyna wants to sort all the ways using these rules:

1. A way with a smaller total value comes earlier.
2. If two ways have the same total value, compare the sorted lists of bead numbers they use in lexicographic order.∗

For example, suppose there are four beads with values 3, 7, 4, and 3, in order. Then a necklace can be made in 16 ways. The table below shows these ways in Bajtyna's order.

Bajtyna wants the necklace that is in position $k$ in this order. Find it.

∗ Sequence $i_1, ..., i_p$ is smaller than $j_1, ..., j_q$ if either the first sequence is a prefix of the second one (so $p < q$ and $i_1 = j_1, ..., i_p = j_p$), or at the first position $u$ where they differ, $i_u < j_u$ (with $i_1 = j_1, ..., i_{u-1} = j_{u-1}$).

The first line contains two positive integers $n$ and $k$, separated by a single space. Here $n$ is the number of beads, and $k$ is the position of the wanted way in the order described above.

The second line contains $n$ positive integers $a_1, a_2, ..., a_n$, separated by single spaces. Here $a_i$ is the value of bead $i$.

You may assume that Bajtyna did not make a mistake, so there are at least $k$ different ways to make her necklace.

Print one integer on the first line: the total value of the beads in the necklace you found.

Print the bead numbers used in the necklace on the second line, in increasing order, separated by single spaces.

• $n, k \le 10^6$
• $a_i \le 10^9$