Pilot

Rar the Cat has finally fulfilled his childhood dream of becoming a pilot, and wants to take his friend Dinosaur on a few scenic flights. Rar lives on a linear world, which can be described as a series of N integers, where the ith integer $H_i$ is the height of the ith mountain from the leftmost edge of his world.

For example, the world described by $N = 6$, $H = \{1, 3, 2, 4, 1, 2\}$ looks like this:

Rar has a total of Q planes that he wants to show off, where the ith plane has a maximum cruising altitude of $Y_i$ metres. Each flight starts at the sth mountain and ends at the eth mountain. We may assume that $s \le e$, i.e. Rar always flies toward the right. Since each of his planes has a maximum cruising altitude, he cannot fly across, take off from, or land on a mountain whose height is greater than its cruising altitude, i.e. Rar can fly over the ith mountain with the jth plane only if $H_i \le Y_j$.

For the ith plane, help Rar determine the total number of different flights he can take, i.e. the total number of pairs (s, e) such that $s \le e$ and no mountain between s and e inclusive has height greater than $Y_i$.

Your program must read from standard input.

The first line of input contains two integers, N and Q.

The second line of input contains N integers, $H_1, \dots, H_N$.

The third line of input contains Q integers, $Y_1, \dots, Y_Q$.

Your program must print to standard output.

The output contains Q lines with one integer each, where the number on the ith line is the total number of different flights Rar can take with his ith plane.

• $1 \le N, Q, H_i, Y_i \le 10^6$