There is a tree (an undirected connected graph with no cycles) consisting of $N$ vertices. The vertices are numbered from $1$ to $N$, and each vertex is colored either black or white.

Write a program that processes the following query:

• $X$: Toggle the color of vertex $X$ (white $\to$ black, black $\to$ white). After that, output the sum of the LCA (lowest common ancestor) levels over all distinct pairs of white vertices $(a, b)$.

The root vertex is vertex $1$. The level of the root is $0$, and the level of any other vertex is defined as (level of its parent) $+ 1$.

Input

The first line contains two integers $N$ and $Q$, the number of vertices and the number of queries.

The second line contains $N$ integers $t_1, t_2, \cdots, t_N$ representing the colors of vertices $1, 2, \cdots, N$. For each $1 \le i \le N$, $t_i = 0$ means black and $t_i = 1$ means white.

The third line contains $N-1$ integers $P_2, P_3, \cdots, P_N$, representing the parent of vertices $2, 3, \cdots, N$.

The next $Q$ lines each contain an integer $X$ representing a query.

Output

The first line outputs the answer for the initial state.

The next $Q$ lines each output the answer for the corresponding query.

Examples

Input 1

5 5
1 0 0 1 1
1 1 3 2
5
3
5
4
2

Output 1

0
0
1
1
0
1

Input 2

10 10
1 0 0 1 1 0 1 0 1 0
1 2 1 4 5 6 1 4 1
8
4
4
4
10
9
2
1
5
3

Output 2

7
7
4
7
4
4
2
2
2
0
1

Input 3

20 20
1 0 1 0 1 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0
1 2 3 4 2 2 1 3 2 4 4 3 3 3 8 14 11 7 7
5
12
19
5
10
18
17
13
10
5
5
13
10
4
11
8
14
13
19
15

Output 3

26
16
26
21
33
39
26
38
51
44
31
44
32
38
53
71
71
55
70
79
97