Fake scoreboard

As you know, after the SWERC award ceremony, it is customary to publish a complete scoreboard with detailed information on submissions and verdicts. However, due to issues with the contest management system, most of the relevant data may not be recorded. Such a situation does not meet the high standards we strive for, so the judges decide to reconstruct the missing data based on whatever information remains, hoping that contestants cannot notice the difference. To further simplify the process, you are asked to provide a solution, or else today's scoreboard will remain forever a mystery (even the fake one).

What is known at the end of the contest is the number of teams $T$, the number of problems $P$, and the number of problems solved by each team. From the number and color of balloons, it is possible to deduce how many teams solved each problem. Your task is to determine which teams solved which problems.

If the information does not add up, your program should detect that the input data is impossible (see sample input $1$). Otherwise, you should output one possible solution as a sequence of $T$ lines, each with $P$ characters. Both problems and teams are numbered from $1$ to $P$ and $1$ to $T$, respectively. For team number $i$ (1 \leq i \leq T), write a string on the alphabet N, Y such that its $j$-th (1 \leq j \leq P) character is Y if the team solved problem $j$, and N otherwise. For example, the following three lines are a possible solution to the second sample case, where the scores for each of three teams are $2$, $1$, $2$ and the number of accepted submissions for each of three problems is $1$, $2$, $2$:

NYY NNY YYN

There is at least one other solution, namely:

NYY NYN YNY

When multiple solutions are possible, you must output the lexicographically smallest string obtained by concatenating the $T$ lines in order. In the example above, the first solution is preferred since NYYNNYYYN comes before NYYNYNYNY in lexicographical order. (A string $S$ comes before S' in lexicographical order if the first differing character between them is N in $S$ and Y in S'.)