Mo, the jumper has found an extraordinary tree in the woods. He absolutely loves it. He already has made quite a few jumps from one branch to another. After a while, being bored, he wonders what would be the minimum time to reach a vertex from another.
Formally, a tree is a connected graph with bidirectional edges and there exists only one path between two vertices. The tree Mo found is rooted at $1$ and has $N$ vertices numbered from $1$ to $N$. Every vertex $i$ has some color $c_i$. It takes him $d$ seconds to go from vertex $u$ to $v$ if $u, ~v$ are adjacent. Also, Mo can jump from a vertex $u$ to vertex $v$ if the colors of those two vertices are same, i.e. $c_u = c_v$. These jumps take him $f_{c_u}$ seconds.
For two vertices $s$ and $t$, find out the minimum time needed for Mo to reach $t$ from $s$.
Input
First line contains an integer $T$.
There are $T$ test cases. For each test case ---
- First line contains two integers
$N, ~d$, giving the number of vertices in the tree and the time needed to move between adjacent vertices. The vertices are numbered from$1$to$N$. - Next line follows with
$N-1$integers, the$i$th of which denotes the parent of vertex$i+1$. - The next line contains
$N$integers, the$i$th integer denotes the color of vertex$i$,$c_i$. - The following line contains another
$N$integers, the$i$th integer denotes$f_{c_i}$. It is guaranteed that for any$i, ~j$, if$c_i = c_j$then$f_{c_i} = f_{c_j}$. - The last line contains two integers
$s$and$t$, the source and the destination.
Scoring
Subtask 1 (20 points):
$1 \leq T \leq 5$,$2 \leq N \leq 10^3$,$1 \leq c_i, s, t \leq N$,$0 \leq d, f_{c_i} \leq 10^4$.
Subtask 2 (30 points):
$1 \leq T \leq 10$,$2 \leq N \leq 10^5$,$1 \leq c_i, s, t \leq N$,$0 \leq d, f_{c_i} \leq 10^7$,$d = f_{c_i}$for every$c_i$.
Subtask 3 (50 points):
$1 \leq T \leq 10$,$2 \leq N \leq 10^5$,$1 \leq c_i, s, t \leq N$,$0 \leq d, f_{c_i} \leq 10^7$.
Output
For each test case, output the minimum time needed in seconds to reach $t$ from $s$.
Sample
| Input | Output |
|---|---|
1 8 10 1 2 2 4 4 1 6 3 2 4 4 3 2 1 4 12 20 14 14 12 20 5 14 7 8 | 44 |
Mo walks 7-1 in d=10 seconds. 1-2 in another 10 seconds. Then he goes to 3 via 2-3 causing another 10 seconds. Then he jumps from vertex-3 to vertex-8 since they are the same color. This jump takes him 14 seconds. Total time: 44 seconds. | |
Large input file. Please use faster I/O. (e.g. scanf(), printf() in C/C++)
