Virus

A new computer virus has been discovered, and you want to build a vaccine program to remove it. To build the vaccine you must know the virus code: the part that appears in common across all infected programs is suspected to be the virus. Each program's code is represented as a sequence of positive integers.

To avoid detection, the virus may insert its code in reverse. Therefore a code and its reversal are treated as the same virus code — for example, one program may contain it as A B C D while another contains it as D C B A.

Because parts of two programs' codes may match by coincidence, a common code is only suspected to be the virus when its length is at least $K$.

Given $N$ infected programs, write a program that decides whether there exists a contiguous code fragment of length at least $K$ that appears (forward or reversed) in every one of the programs.

The first line contains the number of infected programs $N$ and the minimum length $K$ required to suspect a virus code. ($2 \le N \le 100$, $4 \le K \le 1{,}000$)

From the second line, the information for each program is given in order. For each program, its code length $M_i$ is given on one line, and the next line contains the $M_i$ positive integers that make up the program's code, separated by spaces. ($10 \le M_i \le 1{,}000$, and each integer is between $1$ and $10{,}000$ inclusive.)

Print YES if a suspected virus code exists in all programs, and NO otherwise.