Born This Way
Description
Arkady bought an air ticket from a city A to a city C. Unfortunately, there are no direct flights, but there are a lot of flights from A to a city B, and from B to C.
There are $n$ flights from A to B, they depart at time moments $a_1$, $a_2$, $a_3$, ..., $a_n$ and arrive at B $t_a$ moments later.
There are $m$ flights from B to C, they depart at time moments $b_1$, $b_2$, $b_3$, ..., $b_m$ and arrive at C $t_b$ moments later.
The connection time is negligible, so one can use the $i$-th flight from A to B and the $j$-th flight from B to C if and only if $b_j \ge a_i + t_a$.
You can cancel at most $k$ flights. If you cancel a flight, Arkady can not use it.
Arkady wants to be in C as early as possible, while you want him to be in C as late as possible. Find the earliest time Arkady can arrive at C, if you optimally cancel $k$ flights. If you can cancel $k$ or less flights in such a way that it is not possible to reach C at all, print $-1$.
The first line contains five integers $n$, $m$, $t_a$, $t_b$ and $k$ ($1 \le n, m \le 2 \cdot 10^5$, $1 \le k \le n + m$, $1 \le t_a, t_b \le 10^9$) — the number of flights from A to B, the number of flights from B to C, the flight time from A to B, the flight time from B to C and the number of flights you can cancel, respectively.
The second line contains $n$ distinct integers in increasing order $a_1$, $a_2$, $a_3$, ..., $a_n$ ($1 \le a_1 < a_2 < \ldots < a_n \le 10^9$) — the times the flights from A to B depart.
The third line contains $m$ distinct integers in increasing order $b_1$, $b_2$, $b_3$, ..., $b_m$ ($1 \le b_1 < b_2 < \ldots < b_m \le 10^9$) — the times the flights from B to C depart.
If you can cancel $k$ or less flights in such a way that it is not possible to reach C at all, print $-1$.
Otherwise print the earliest time Arkady can arrive at C if you cancel $k$ flights in such a way that maximizes this time.
Input
The first line contains five integers $n$, $m$, $t_a$, $t_b$ and $k$ ($1 \le n, m \le 2 \cdot 10^5$, $1 \le k \le n + m$, $1 \le t_a, t_b \le 10^9$) — the number of flights from A to B, the number of flights from B to C, the flight time from A to B, the flight time from B to C and the number of flights you can cancel, respectively.
The second line contains $n$ distinct integers in increasing order $a_1$, $a_2$, $a_3$, ..., $a_n$ ($1 \le a_1 < a_2 < \ldots < a_n \le 10^9$) — the times the flights from A to B depart.
The third line contains $m$ distinct integers in increasing order $b_1$, $b_2$, $b_3$, ..., $b_m$ ($1 \le b_1 < b_2 < \ldots < b_m \le 10^9$) — the times the flights from B to C depart.
Output
If you can cancel $k$ or less flights in such a way that it is not possible to reach C at all, print $-1$.
Otherwise print the earliest time Arkady can arrive at C if you cancel $k$ flights in such a way that maximizes this time.
Samples
4 5 1 1 2
1 3 5 7
1 2 3 9 10
11
2 2 4 4 2
1 10
10 20
-1
4 3 2 3 1
1 999999998 999999999 1000000000
3 4 1000000000
1000000003
Note
Consider the first example. The flights from A to B depart at time moments $1$, $3$, $5$, and $7$ and arrive at B at time moments $2$, $4$, $6$, $8$, respectively. The flights from B to C depart at time moments $1$, $2$, $3$, $9$, and $10$ and arrive at C at time moments $2$, $3$, $4$, $10$, $11$, respectively. You can cancel at most two flights. The optimal solution is to cancel the first flight from A to B and the fourth flight from B to C. This way Arkady has to take the second flight from A to B, arrive at B at time moment $4$, and take the last flight from B to C arriving at C at time moment $11$.
In the second example you can simply cancel all flights from A to B and you're done.
In the third example you can cancel only one flight, and the optimal solution is to cancel the first flight from A to B. Note that there is still just enough time to catch the last flight from B to C.