Election Night

The nation of Cicoci elects its president with a winner-take-all electoral system. There are $N$ states, and each state casts exactly one electoral vote. A state's electoral vote goes to the candidate who wins the most popular votes in that state. The candidate who collects the most electoral votes becomes president. If two or more candidates are tied for the most electoral votes, no president is elected.

As the returns come in, the winner of some states is already decided, while others are still too close to call: in such a state, any one of several candidates could still win. Considering every way the undecided states might turn out, determine for each candidate whether that candidate is guaranteed to become president, could still become president, or cannot become president any more.

Formally, an outcome assigns to every state exactly one of the candidates who can still win that state (a state whose winner is already decided keeps that winner). For each candidate, report one of three verdicts:

• the candidate becomes president in every possible outcome;
• the candidate becomes president in at least one outcome, but not in every outcome;
• the candidate becomes president in no outcome.

The input contains several test cases. The first line of a test case has two positive integers $N$ and $C$: the number of states and the number of candidates. Neither exceeds $100$. Each of the next $N$ lines describes one state: it starts with an integer $k$, the number of candidates who might still win that state, followed by the $k$ identifiers of those candidates. Candidates are numbered with consecutive integers from $1$ to $C$.

The input ends with a line containing two zeros ($0$ $0$), which is not a test case and must not be processed.

For each test case, consider the candidates in ascending order of their number. For candidate $X$, print exactly one of the following lines, whichever applies:

Candidate X will become president.
Candidate X may become president.
Candidate X will not become president.

Print will when the candidate becomes president in every possible outcome, may when the candidate becomes president in some but not all outcomes, and will not when the candidate can never become president. Separate the output of consecutive test cases with a blank line.