Recursive Queries

Description:

Input:

The first line contains two integers $$$n$$$ and $$$q$$$ ($$$1 \le n \le 10^6$$$, $$$1 \le q \le 10^6$$$) — the size of the permutation $$$p$$$ and the number of queries.

The second line contains $$$n$$$ pairwise distinct integers $$$p_1, p_2, \dots, p_n$$$ ($$$1 \le p_i \le n$$$, $$$p_i \neq p_j$$$ for $$$i \neq j$$$) — permutation $$$p$$$.

The third line contains $$$q$$$ integers $$$l_1, l_2, \dots, l_q$$$ — the first parts of the queries.

The fourth line contains $$$q$$$ integers $$$r_1, r_2, \dots, r_q$$$ — the second parts of the queries.

It's guaranteed that $$$1 \le l_i \le r_i \le n$$$ for all queries.

Output:

Print $$$q$$$ integers — the values $$$f(l_i, r_i)$$$ for the corresponding queries.

Sample Input:

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

Sample Output:

1 6 8 5 1 

Note:

Description of the queries:

1. $$$f(2, 2) = (2 - 2 + 1) + f(2, 1) + f(3, 2) = 1 + 0 + 0 = 1$$$;
2. $$$f(1, 3) = (3 - 1 + 1) + f(1, 2) + f(4, 3) = 3 + (2 - 1 + 1) + f(1, 0) + f(2, 2) = 3 + 2 + (2 - 2 + 1) = 6$$$;
3. $$$f(1, 4) = (4 - 1 + 1) + f(1, 2) + f(4, 4) = 4 + 3 + 1 = 8$$$;
4. $$$f(2, 4) = (4 - 2 + 1) + f(2, 2) + f(4, 4) = 3 + 1 + 1 = 5$$$;
5. $$$f(1, 1) = (1 - 1 + 1) + 0 + 0 = 1$$$.