Card Game Strategy

Alice and Bob play a card game. There are $n$ cards, and card $i$ has the integer $x_i$ written on it. The game runs in this order.

1. Alice picks an integer between $a$ and $b$, inclusive. Call that integer $t$. Alice tells Bob the value of $t$.
2. Bob picks $k$ of the $n$ cards. Call the sum of the integers on the $k$ cards Bob picks $u$.

Alice wants $|t - u|$ to be as large as possible, and Bob wants it to be as small as possible.

Before the game starts, both players know $n$, $k$, $a$, $b$ and the integer on every card. Both play optimally. In particular, Alice picks $t$ knowing that Bob will then make $|t - u|$ as small as possible for the announced $t$. If several values of $t$ are equally good, Alice picks the smallest of them.

Find the value of $t$ Alice picks, and the $k$ cards Bob picks for that $t$.

The first line contains the integers $n$, $k$, $a$, $b$ ($1 \le k \le n \le 600$, $0 \le a \le b \le 180000$).

The second line contains the integers $x_1, \dots, x_n$ ($0 \le x_i \le 300$), where $x_i$ is written on card $i$.

On the first line, print the value of $t$ Alice picks.

On the second line, print the numbers of the $k$ cards Bob picks in increasing order. When several sets of $k$ cards make $|t - u|$ as small as possible, print the set whose increasing sequence of card numbers is lexicographically smallest.