Taxi drivers and Lyft

Description:

Input:

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n,m \le 10^5$$$) — number of riders and taxi drivers.

The second line contains $$$n + m$$$ integers $$$x_1, x_2, \ldots, x_{n+m}$$$ ($$$1 \le x_1 < x_2 < \ldots < x_{n+m} \le 10^9$$$), where $$$x_i$$$ is the coordinate where the $$$i$$$-th resident lives.

The third line contains $$$n + m$$$ integers $$$t_1, t_2, \ldots, t_{n+m}$$$ ($$$0 \le t_i \le 1$$$). If $$$t_i = 1$$$, then the $$$i$$$-th resident is a taxi driver, otherwise $$$t_i = 0$$$.

It is guaranteed that the number of $$$i$$$ such that $$$t_i = 1$$$ is equal to $$$m$$$.

Output:

Print $$$m$$$ integers $$$a_1, a_2, \ldots, a_{m}$$$, where $$$a_i$$$ is the answer for the $$$i$$$-th taxi driver. The taxi driver has the number $$$i$$$ if among all the taxi drivers he lives in the $$$i$$$-th smallest coordinate (see examples for better understanding).

Sample Input:

3 1
1 2 3 10
0 0 1 0

Sample Output:

3 

Sample Input:

3 2
2 3 4 5 6
1 0 0 0 1

Sample Output:

2 1 

Sample Input:

1 4
2 4 6 10 15
1 1 1 1 0

Sample Output:

0 0 0 1 

Note:

In the first example, we have only one taxi driver, which means an order from any of $$$n$$$ riders will go to him.

In the second example, the first taxi driver lives at the point with the coordinate $$$2$$$, and the second one lives at the point with the coordinate $$$6$$$. Obviously, the nearest taxi driver to the rider who lives on the $$$3$$$ coordinate is the first one, and to the rider who lives on the coordinate $$$5$$$ is the second one. The rider who lives on the $$$4$$$ coordinate has the same distance to the first and the second taxi drivers, but since the first taxi driver has a smaller coordinate, the call from this rider will go to the first taxi driver.

In the third example, we have one rider and the taxi driver nearest to him is the fourth one.