No surrender! 1

Input

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

Output

On the first line of the output, print a single number $m$ — the minimum number of bills Vanya can use to make the exact payment. On the second line, print $m$ numbers — the indices of the bills Vanya should use, in ascending order, as he must take the bills sequentially from his wallet.

If it is impossible to gather the exact amount without requiring change, print $-1$.

Vanya is not concerned with how the exact amount is gathered, so if there are multiple solutions, any valid one can be provided. The number $k$ can be ignored in your solution.

Examples

Note

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

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

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

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

Any of these options can be output.