No surrender! 2

Input

The first line of the input contains three non-negative integers: $n$, $c$, and $k$ (0 \leq n \leq 1000, 0 \leq c \leq 1000, 1 \leq k \leq 1000000000). The next line contains $n$ integers a_1, a_2, ..., a_n (1 \leq a_i \leq 1000), representing the denominations of the bills in the order they appear in Vanya's wallet.

Output

On the first line of the output, print a single integer $m$ - the minimum number of bills Vanya can use to make the exact amount. On the second line, print $m$ integers - the indices of the bills Vanya should use, listed in ascending order.

If it's impossible to make the exact amount without change, print $-1$.

Vanya is interested in how to make the exact amount using his favorite number $k$. If a solution exists, you must output the $k$-th solution in lexicographical order. Lexicographical order here means sorting solutions by the index of the first bill used, and if those are equal, by the second, and so on. It is guaranteed that if a solution exists, $k$ does not exceed the total number of solutions. Solutions are numbered starting from $1$, and solutions that differ only in the order of bills are considered the same (you should always output the indices in ascending order). If no solution exists, there are no restrictions on the value of $k$ in the input.

Examples

Note

In the first example, all possible solutions sorted in lexicographical order are:

• $12$ (the first and second bills, i.e., bills with denominations $1$ and $4$)

• $25$ (the second and fifth bills, i.e., bills with denominations $4$ and $1$)

• $34$ (the third and fourth bills, i.e., bills with denominations $2$ and $3$)

According to the problem, the second option is the one we need.