Apple Picking with Limited Energy

TaoTao's apple tree has produced $n$ apples this autumn. He now has a stool with height $a$ centimeters. When he cannot reach an apple with his bare arms (with maximum reach $b$ centimeters), he stands on the stool and tries again. However, due to previous efforts, his remaining energy is limited to $s$. Each apple requires a certain amount of energy $y_i$ to pick. The apples lie on the ground at heights $x_i$. Note that TaoTao can only pick an apple if its height $x_i$ satisfies $$x_i \leq b \quad \text{or} \quad (b < x_i \leq a+b).$$ In other words, an apple is reachable if $$x_i \leq a+b.$$ Among all reachable apples, each one costs $y_i$ energy to pick. TaoTao wishes to pick as many apples as possible before his energy falls below zero. Determine the maximum number of apples he can pick so that the total energy consumed does not exceed $s$.

inputFormat

The first line contains four integers $n$, $a$, $b$, and $s$, where $n$ is the number of apples, $a$ is the height of the stool, $b$ is the maximum reach of TaoTao when standing normally, and $s$ is the available energy. The second line contains $n$ integers $x_1, x_2, \dots, x_n$, representing the heights (in centimeters) at which the apples lie on the ground. The third line contains $n$ integers $y_1, y_2, \dots, y_n$, where $y_i$ is the energy required to pick the $i$-th apple.

outputFormat

Output a single integer representing the maximum number of apples that TaoTao can pick without his energy dropping below zero.

sample

5 10 5 10
3 10 15 20 14
1 2 3 4 5

3