The Winter holiday will be here soon. Mr. Chanek wants to decorate his house's wall with ornaments. The wall can be represented as a binary string $$$a$$$ of length $$$n$$$. His favorite nephew has another binary string $$$b$$$ of length $$$m$$$ ($$$m \leq n$$$).

Mr. Chanek's nephew loves the non-negative integer $$$k$$$. His nephew wants exactly $$$k$$$ occurrences of $$$b$$$ as substrings in $$$a$$$.

However, Mr. Chanek does not know the value of $$$k$$$. So, for each $$$k$$$ ($$$0 \leq k \leq n - m + 1$$$), find the minimum number of elements in $$$a$$$ that have to be changed such that there are exactly $$$k$$$ occurrences of $$$b$$$ in $$$a$$$.

A string $$$s$$$ occurs exactly $$$k$$$ times in $$$t$$$ if there are exactly $$$k$$$ different pairs $$$(p,q)$$$ such that we can obtain $$$s$$$ by deleting $$$p$$$ characters from the beginning and $$$q$$$ characters from the end of $$$t$$$.

Input

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \leq m \leq n \leq 500$$$) — size of the binary string $$$a$$$ and $$$b$$$ respectively.

The second line contains a binary string $$$a$$$ of length $$$n$$$.

The third line contains a binary string $$$b$$$ of length $$$m$$$.

Output

Output $$$n - m + 2$$$ integers — the $$$(k+1)$$$-th integer denotes the minimal number of elements in $$$a$$$ that have to be changed so there are exactly $$$k$$$ occurrences of $$$b$$$ as a substring in $$$a$$$.

Note

For $$$k = 0$$$, to make the string $$$a$$$ have no occurrence of 101, you can do one character change as follows.

100101011 $$$\rightarrow$$$ 100100011

For $$$k = 1$$$, you can also change a single character.

100101011 $$$\rightarrow$$$ 100001011

For $$$k = 2$$$, no changes are needed.

Holiday Wall Ornaments

Examples