F. Squarestime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere 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,\dots,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:  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.  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.InputThe first line contains two integers n, q (1\le n,q\le 2 \cdot 10^5)  — the number of squares and the number of rounds.The second line contains n distinct integers p_1,p_2,\dots,p_n (1\le p_i\le n). It is guaranteed that the sequence p_1,p_2,\dots,p_n forms a permutation.The third line contains n integers a_1,a_2,\ldots,a_n (-10^9\le a_i\le 10^9).The fourth line contains n integers b_1,b_2,\dots,b_n (-10^9\le b_i\le 10^9).Then q lines follow, i-th of them contains a single integer x_i (1\le x_i\le n). If x_i was in the set S on the (i-1)-th round you should remove it, otherwise, you should add it.OutputPrint q lines, each of them should contain a single integer  — the minimum cost you should pay to end the corresponding round.ExamplesInput
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
NoteLet'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\to 3\to 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\to 2\to 3\to T and its cost is 8.
3 2
2 1 3
10 -5 4
3 -2 3
1
2

6 8 
['constructive algorithms', 'data structures', 'dp', 'graphs', 'trees', '*3300']