Prerequisites?

Freddie the freshman has chosen to take $k$ courses. To meet the degree requirements, he must take at least a minimum number of courses from each of several categories. Given Freddie's course selection, determine whether he will be able to graduate.

The input consists of several test cases.

For each test case, the first line contains two integers $k$ and $m$ ($1 \le k \le 100$, $0 \le m \le 100$): the number of courses Freddie has chosen and the number of categories.

One or more following lines contain the $k$ four-digit course numbers that Freddie selected.

Each of the $m$ categories is then described by $c$, $r$, and the $c$ course numbers belonging to it, where $1 \le c \le 100$ is the number of courses in the category and $0 \le r \le c$ is the minimum number of them Freddie must take. Every course number is a four-digit integer.

The same course may count toward several categories. Within Freddie's selection, and within any single category, all course numbers are distinct.

A line containing a single $0$ follows the last test case.

For each test case, output a single line containing yes if Freddie's selection meets all of the degree requirements, or no otherwise.