| Piggy gives Turtle three sequences $a_1, a_2, \ldots, a_n$, $b_1, b_2, \ldots, b_n$, and $c_1, c_2, \ldots, c_n$. | |
| Turtle will choose a subsequence of $1, 2, \ldots, n$ of length $m$, let it be $p_1, p_2, \ldots, p_m$. The subsequence should satisfy the following conditions: | |
| * $a_{p_1} \le a_{p_2} \le \cdots \le a_{p_m}$; * All $b_{p_i}$ for all indices $i$ are pairwise distinct, i.e., there don't exist two different indices $i$, $j$ such that $b_{p_i} = b_{p_j}$. | |
| Help him find the maximum value of $\sum\limits_{i = 1}^m c_{p_i}$, or tell him that it is impossible to choose a subsequence of length $m$ that satisfies the conditions above. | |
| Recall that a sequence $a$ is a subsequence of a sequence $b$ if $a$ can be obtained from $b$ by the deletion of several (possibly, zero or all) elements. | |
| The first line contains two integers $n$ and $m$ ($1 \le n \le 3000$, $1 \le m \le 5$) — the lengths of the three sequences and the required length of the subsequence. | |
| The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le n$) — the elements of the sequence $a$. | |
| The third line contains $n$ integers $b_1, b_2, \ldots, b_n$ ($1 \le b_i \le n$) — the elements of the sequence $b$. | |
| The fourth line contains $n$ integers $c_1, c_2, \ldots, c_n$ ($1 \le c_i \le 10^4$) — the elements of the sequence $c$. | |
| Output a single integer — the maximum value of $\sum\limits_{i = 1}^m c_{p_i}$. If it is impossible to choose a subsequence of length $m$ that satisfies the conditions above, output $-1$. | |
| In the first example, we can choose $p = [1, 2]$, then $c_{p_1} + c_{p_2} = 1 + 4 = 5$. We can't choose $p = [2, 4]$ since $a_2 > a_4$, violating the first condition. We can't choose $p = [2, 3]$ either since $b_2 = b_3$, violating the second condition. We can choose $p = [1, 4]$, but $c_1 + c_4 = 4$, which isn't maximum. | |
| In the second example, we can choose $p = [4, 6, 7]$. | |
| In the third example, it is impossible to choose a subsequence of length $3$ that satisfies both of the conditions. |