Problem Statement

Let $\mathrm{popcount}(n)$ be the number of $1$s in the $2$-ary representation of $n$. For example, $\mathrm{popcount}(11)=3,\ \mathrm{popcount}(64)=1$.

For a sequence of positive integers $A_1,A_2,\dots,A_K$, define $f(A)$ as follows.

• The number of pairs of positive integers $(i,j)$ such that $1 \le i,j \le K$ and $\mathrm{popcount}(A_i \times A_j) \equiv 0 \pmod 2$

Construct a pair of sequences of positive integers $(X_1,X_2,\dots,X_P),(Y_1,Y_2,\dots,Y_Q)$ satisfying the following. If no such pair exists, report that.

• $X,Y$ is a pair of sequences obtained by splitting $(1,2,3,\dots,N)$ into $2$ sequences. Formally, the following hold.
• $0 \le P,Q$
• $P+Q=N$
• $1 \le X_i \le N$
• $1 \le Y_j \le N$
• If $i \neq j$, then $X_i \neq X_j$
• If $i \neq j$, then $Y_i \neq Y_j$
• $X_i \neq Y_j$
• $f(X)-f(Y)=M$

Input

$N\ M$

• All inputs are integers.
• $2 \le N \le 300$
• $0 \le M \le N^2$

Output

If no pair of sequences of positive integers $(X_1,X_2,\dots,X_P),(Y_1,Y_2,\dots,Y_Q)$ satisfying the conditions exists, print $-1$.

If a pair of sequences of positive integers $(X_1,X_2,\dots,X_P),(Y_1,Y_2,\dots,Y_Q)$ satisfying the conditions exists, print $1$ solution in the following format.

If there are multiple solutions, you may print any of them.

$P\ Q$
$X_1\ X_2\ \dots\ X_P$
$Y_1\ Y_2\ \dots\ Y_Q$

Sample

5 1

3 2
1 2 5
3 4

6 7

-1

19 43

11 8
13 12 10 18 14 6 5 8 3 16 4 
19 9 17 1 15 7 11 2