A12511. Born This Way

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.

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.