Ranran has a set $s_v$ of $n$ vectors and an integer $d$. He is bored at Sunday so he decides to invent a new problem for you.

You need to give a set $s_p$ of points, size of which is $m$. You will pick up every point $(a_i, b_i)$ in $s_p$ and every vector $(x_j, y_j)$ in $s_v$. The pair $(a_i,b_i,x_j,y_j)$ is called good if and only if the line $(a_i + tx_j, b_i + ty_j), t\in \mathbb{R}$ visits exactly $d$ points in $s_p$. $s_p$ is good if and only if every pair satisfies the condition. You need to find out a good set of points.

Ranran thinks about it at a few sleepless nights thinking of Yangyang and solves it. Now he gives this problem to you. Can you solve it?

The first contains two integers $n$ and $d (1\leq n, d\leq 6)$.

Each of the next $n$ lines contains two integers $x_i, y_i (0\leq x_i, y_i\leq 6, x_i + y_i > 0)$.

Attention, it is not guarenteed that all vectors are pairwise different.

Output an integer $m$ in the first line.

Each of the next $m$ lines, output two integers $a_j, b_j$.

You should guarantee that $1\leq m\leq 10 ^ 5$, $a_j, b_j$ are 32-bit signed integers and points are pairwise different.

The conditions can be satisfied using only one point.