In the country of Enelogonia, there is a problem: every year, the sea level rises. This has caused the country to be divided into islands. The government wants to know the number of islands the country will be divided into at the end of each year.
Initially, the country is a line divided into $$$n$$$ segments; each segment has a height of $$$a_{i}$$$ meters. At the beginning of the first year, the sea level is at $$$0$$$, and at the end of the i-th year, the level is at $$$m_{i}$$$. It holds that if $$$i \lt j$$$, then $$$m_{i} \lt m_{j}$$$.
Given the $$$n$$$ heights of the segments and the sea levels at the end of each year, determine how many islands there are at the end of each year.
When the i-th segment goes underwater, the (i+1)-th and (i-1)-th segments become part of different islands because they are separated by water (this is in case both segments are above sea level).
A segment goes underwater when the sea level is equal to or greater than its height.
The input consists of several cases.
Each case starts with a line containing the integers $$$n$$$ and $$$k$$$. On the second line, there are the $$$n$$$ integers $$$a_{i}$$$, and on the third line the $$$k$$$ integers $$$m_{i}$$$.
For each case, write a line with $$$k$$$ integers separated by a space, where the i-th integer is the number of islands at the end of the i-th year.
$$$1 \leq a_{i}, m_{i} \leq 1000000$$$
Case 1: 30 points
$$$1 \leq n \leq 1000$$$
$$$k = 1$$$
Case 2: 30 points
$$$1 \leq n \leq 1000$$$
$$$1 \leq k \leq 1000$$$
Case 3: 40 points
$$$1 \leq n \leq 100000$$$
$$$1 \leq k \leq 100000$$$
7 1 9 1 6 1 3 7 2 5 10 5 9 5 4 10 3 2 5 6 2 6 3 4 6 8 9
3 3 4 2 2 1
