Yunny's Trip

Yunny enters Uniworld, her virtual world, to take a short break. Uniworld is an infinite two-dimensional grid, and Yunny is currently standing at $(0, 0)$. To reach her destination $(E_x, E_y)$, Yunny can repeat the following two kinds of actions.

1. Move one cell to an adjacent cell. That is, change the $x$ coordinate by $1$ or change the $y$ coordinate by $1$. This action consumes $1$ stamina.
2. Use one of the items she is carrying. Each item is given as $(a_i, b_i)$. Using it increases her $x$ coordinate by $a_i$ and her $y$ coordinate by $b_i$. So if she is at $(x, y)$, using the item moves her to $(x+a_i, y+b_i)$. This action does not consume the item, so the same item can be used many times. It consumes $2$ stamina.

If her stamina drops below $0$, she returns to the real world, so she keeps her stamina at $0$ or above. Yunny is frail, so her initial stamina does not exceed $5$. Determine whether she can reach the destination. If she can, find the minimum stamina she must spend to get there.

The first line contains the number of items $N$ and Yunny's initial stamina $K$, separated by a space. ($1 \le N \le 2 \times 10^5$; $1 \le K \le 5$)

Each of the next $N$ lines contains $a_i$ and $b_i$ for one item, separated by a space. ($-10^{12} \le a_i, b_i \le 10^{12}$)

The last line contains the destination $E_x$ and $E_y$, separated by a space. ($-10^{12} \le E_x, E_y \le 10^{12}$)

No item or destination is $(0, 0)$, and no item is given more than once.

Print the minimum stamina that must be spent to reach the destination. If Yunny cannot reach the destination with her initial stamina $K$, print -1.