G. Zimpha Fan Club
time limit per test
12 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

One day, Zimpha casually came up with a problem. As a member of "Zimpha fan club", you decided to solve that problem.

You are given two strings $s$ and $t$ of length $n$ and $m$, respectively. Both strings only consist of lowercase English letters, - and *.

You need to replace all occurrences of * and -, observing the following rules:

• For each -, you must replace it with any lowercase English letter.
• For each *, you must replace it with a string of any (possibly, zero) length which only consists of lowercase English letters.

Note that you can replace two different instances of - with different characters. You can also replace each two different instances of * with different strings.

Suppose $s$ and $t$ have been transformed into $s'$ and $t'$. Now you're wondering if there's a replacement that makes $s'=t'$.

Input

The first line of input contains two integers $n$ and $m$ ($1 \leq n, m \leq 2 \cdot 10^6$) — the length of the strings $s$ and $t$, respectively.

The second line contains the string $s$ of length $n$. It is guaranteed that $s$ only consists of lowercase English letters, - and *.

The third line contains the string $t$ of length $m$. It is guaranteed that $t$ only consists of lowercase English letters, - and *.

Output

For each test case, output "Yes" if there is a replacement that makes $s'=t'$, and output "No" otherwise.

You can output "Yes" and "No" in any case (for example, strings "yEs", "yes", "Yes" and "YES" will be recognized as a positive response).

Examples
Input
10 10justmonikaj-stsayori
Output
No
Input
7 8ttk-wxx*tt-l-xx
Output
Yes
Input
13 11asoulwangziji-soulg*z-y-
Output
No
Input
7 3abc*cbaa*c
Output
No
Input
20 18bulijiojio-dibuliduo*li*ji-*ox*i*-du*-
Output
Yes
Note

In the second test case, we can transform both strings into ttklwxx. In $s$, - will be replaced with l. In $t$, * will be replaced by the empty string with the first and second - will be replaced with k and w respectively.

In the fifth test case, we can transform both strings into bulijiojioxdibuliduo.