Problem Statement

There are $2$ variables $x,y$, and initially $(x,y)=(a,b)$.

You may perform the following operations in any order, up to $1000$ times in total (possibly $0$ times).

• Operation $1$ : Choose an integer $k\ (-10^9 \le k \le 10^9)$ and add $k \times y$ to $x$.
• Operation $2$ : Choose an integer $k\ (-10^9 \le k \le 10^9)$ and add $k \times x$ to $y$.

Determine whether it is possible to make $(x,y)=(c,d)$ by the above operations, and if it is possible, show one such sequence of operations.

Constraints

• $-10^8 \le a,b,c,d \le 10^8$
• All inputs are integers.

Input

The input is given from standard input in the following format.

$a\ \ b\ \ c\ \ d$

Output

If it is impossible to make $(x,y)=(c,d)$, print $-1$.

If it is possible to make $(x,y)=(c,d)$, print such a sequence of operations in the following format (if there are multiple sequences of operations satisfying the conditions, you may print any of them).

$N$
$t_1\ \ k_1$
$t_2\ \ k_2$
$\vdots$
$t_N\ \ k_N$

• $0 \le N\le 1000$
• $t_i=1$ or $t_i=2$
• $-10^9\le k_i \le 10^9$

Sample

5 1 -10 19

4
1 3
2 1
1 -2
2 -1

0 0 1 -1

-1

123 456 123 456

0