Problem Statement

You are presented with two primary strings: S and T, and a target string X of the same length as S, initially filled entirely with the character #. Your task is to determine if it's possible to transform X into S by repeatedly overlaying the string T onto X.

Constraints

• The string S is composed of letters and has a length N.
• The string T also consists of letters and has a length M, where M is less than or equal to N.
• X is a string of length N filled entirely with the character #.
• You can overlay T on any part of X, replacing M consecutive characters, as many times as you want.
• Given lengths: $1 ≤ N ≤ 2×10^5$ and $1 ≤ M ≤ min(N, 5)$.

Input

The input is given from Standard Input in the following format:

N M
S
T

Output

Print Yes if it is possible to make X match S; print No otherwise.

Sample Input 1

5 3
ABCBC
ABC

Sample Output 1

Yes

Below, let $X[l:r]$ denote the part from the $l$-th through the $r$-th character of $X$.

You can make $X$ match $S$ by operating as follows.

1. Replace $X[3:5]$ with $T$. $X$ becomes ##ABC.
2. Replace $X[1:3]$ with $T$. $X$ becomes ABCBC.

Sample Input 2

7 3
ABBCABC
ABC

Sample Output 2

No

it's impossible to make $X$ match $S$.

Sample Input 3

12 2
XYXXYXXYYYXY
XY

Sample Output 3

Yes