The Ravagers, a group of space mercenaries, have discovered information about several treasure vaults across the galaxy. Yondu needs to assign his crew members to raid these vaults efficiently.
There are n treasure vaults and m crew members. Each vault has a security level represented in a 0-indexed integer array v, with the ith vault requiring vi skill to break into. The skill level of each crew member is stored in a 0-indexed integer array r, with the jth crew member having rj skill level. Each crew member can only be assigned to a single vault and must have a skill level greater than or equal to the vault's security level (i.e., rj≥vi).
Yondu also has b special tech boosters that will increase a crew member's skill by e. He can decide which crew members receive these boosters; however, each crew member may receive at most one booster.
Given the 0-indexed integer arrays v and r and the integers b and e, return the maximum number of vaults that can be raided.
Input Format:
The first line of input contains two integers n and m(1≤n≤105 and 1≤m≤105), the number of vaults and ravagers respectively.
The second line contains two integers: the number of b(0≤b≤m) and e(1≤e≤109).
The third line contains n integers v1,v2,…,vn representing the vaults. (1≤vi<109)
The fourth line contains m integers r1,r2,…,rm representing the ravagers. (1≤ri≤109)
Output Format:
Output a single integer representing the maximum number of vaults that can be raided.