Moon finds himself on a 2D plane, but he can only walk on the line $y=0$ at a speed not exceeding $v_c$ m/s (he can move back and forth). At this moment, it starts to pour with rain. There are $n$ raindrops in total. The $i$-th ($1 \le i \le n$) raindrop starts falling at a constant speed of $v_g$ m/s from $(x_i, y_i)$. At the same time, a strong wind starts blowing at a speed of $v_w$ m/s in the positive direction of the $x$-axis. It can be assumed that each raindrop acquires the same horizontal velocity as the wind, and the wind does not affect Moon's walking speed.

Moon loves getting rained on. For simplicity, both each raindrop and Moon are treated as points. Moon can only be hit by a raindrop if the raindrop reaches the $x$-axis at the exact same time and position as Moon. Now, given $q$ queries, where the $i$-th ($1 \le i \le q$) query provides an initial position $(s_i, 0)$, Moon wants to know the maximum number of raindrops he can be hit by, starting from $(s_i, 0)$ and moving throughout the entire process.

Input

The first line contains five integers $n, q, v_g, v_w, v_c$.

The next $n$ lines each contain two integers $x_i, y_i$.

The next $q$ lines each contain an integer $s_i$.

Output

For each query, output a single integer representing the maximum number of raindrops Moon can be hit by.

Constraints

For all data, $1 \le n, q \le 10^5$, $1 \le v_w, v_g, v_c, y_i \le 10^6$, $-10^6 \le x_i, s_i \le 10^6$.

For 30% of the data, $1 \le n, q \le 100$.

For another 30% of the data, $1 \le q \le 5$.

Examples

Input 1

4 4 1 1 5
-3 2
4 1
0 4
2 3
-4
1
-2
0

Output 1

2
3
2
3