G. Recursive Queries
time limit per test
4 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a permutation $$$p_1, p_2, \dots, p_n$$$. You should answer $$$q$$$ queries. Each query is a pair $$$(l_i, r_i)$$$, and you should calculate $$$f(l_i, r_i)$$$.

Let's denote $$$m_{l, r}$$$ as the position of the maximum in subsegment $$$p_l, p_{l+1}, \dots, p_r$$$.

Then $$$f(l, r) = (r - l + 1) + f(l, m_{l,r} - 1) + f(m_{l,r} + 1, r)$$$ if $$$l \le r$$$ or $$$0$$$ otherwise.

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.

Example
Input
4 5
3 1 4 2
2 1 1 2 1
2 3 4 4 1
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. $$$f(1, 1) = (1 - 1 + 1) + 0 + 0 = 1$$$.