Squares

There are n squares drawn from left to right on the floor. The i-th square has three integers p_i,a_i,b_i, written on it. The sequence p_1,p_2,...,p_n forms a permutation.

Each round you will start from the leftmost square 1 and jump to the right. If you are now on the i-th square, you can do one of the following two operations:

1. Jump to the i+1-th square and pay the cost a_i. If i=n, then you can end the round and pay the cost a_i.
2. Jump to the j-th square and pay the cost b_i, where j is the leftmost square that satisfies j > i, p_j > p_i. If there is no such j then you can end the round and pay the cost b_i.

There are q rounds in the game. To make the game more difficult, you need to maintain a square set S (initially it is empty). You must pass through these squares during the round (other squares can also be passed through). The square set S for the i-th round is obtained by adding or removing a square from the square set for the (i-1)-th round.

For each round find the minimum cost you should pay to end it.

Input

The first line contains two integers n, q (1≤ n,q≤ 2 ⋅ 10^5) — the number of squares and the number of rounds.

The second line contains n distinct integers p_1,p_2,...,p_n (1≤ p_i≤ n). It is guaranteed that the sequence p_1,p_2,...,p_n forms a permutation.

The third line contains n integers a_1,a_2,…,a_n (-10^9≤ a_i≤ 10^9).

The fourth line contains n integers b_1,b_2,...,b_n (-10^9≤ b_i≤ 10^9).

Then q lines follow, i-th of them contains a single integer x_i (1≤ x_i≤ n). If x_i was in the set S on the (i-1)-th round you should remove it, otherwise, you should add it.

Output

Print q lines, each of them should contain a single integer — the minimum cost you should pay to end the corresponding round.

Examples

Input

3 2 2 1 3 10 -5 4 3 -2 3 1 2

Output

6 8

Input

5 4 2 1 5 3 4 6 -5 3 -10 -1 0 3 2 7 2 1 2 3 2

Output

-8 -7 -7 -8

Note

Let's consider the character T as the end of a round. Then we can draw two graphs for the first and the second test.

In the first round of the first test, the set that you must pass through is {1}. The path you can use is 1→ 3→ T and its cost is 6.

In the second round of the first test, the set that you must pass through is {1,2}. The path you can use is 1→ 2→ 3→ T and its cost is 8.

inputFormat

Input

The first line contains two integers n, q (1≤ n,q≤ 2 ⋅ 10^5) — the number of squares and the number of rounds.

The second line contains n distinct integers p_1,p_2,...,p_n (1≤ p_i≤ n). It is guaranteed that the sequence p_1,p_2,...,p_n forms a permutation.

The third line contains n integers a_1,a_2,…,a_n (-10^9≤ a_i≤ 10^9).

The fourth line contains n integers b_1,b_2,...,b_n (-10^9≤ b_i≤ 10^9).

Then q lines follow, i-th of them contains a single integer x_i (1≤ x_i≤ n). If x_i was in the set S on the (i-1)-th round you should remove it, otherwise, you should add it.

outputFormat

Output

Print q lines, each of them should contain a single integer — the minimum cost you should pay to end the corresponding round.

Examples

Input

3 2 2 1 3 10 -5 4 3 -2 3 1 2

Output

6 8

Input

5 4 2 1 5 3 4 6 -5 3 -10 -1 0 3 2 7 2 1 2 3 2

Output

-8 -7 -7 -8

Note

Let's consider the character T as the end of a round. Then we can draw two graphs for the first and the second test.

In the first round of the first test, the set that you must pass through is {1}. The path you can use is 1→ 3→ T and its cost is 6.

In the second round of the first test, the set that you must pass through is {1,2}. The path you can use is 1→ 2→ 3→ T and its cost is 8.

样例

5 4
2 1 5 3 4
6 -5 3 -10 -1
0 3 2 7 2
1
2
3
2

-8
-7
-7
-8

</p>