Gabriella has been instructed to organize a renowned wine tasting event which will be attended by \(m\) critics. On display, there will be \(n\) different varieties of wine, each of which can either be a red wine or a white wine.
The wines will come in \(n\) bottles arranged in a line on the table, and, for convenience, each critic will sip from a contiguous interval of bottles: that is, he/she will taste exactly the bottles at position \(a, \, a + 1, \, \dots, \, b\) for some \(1 \le a \le b \le n\). The interval depends on the critic, who will select it on the spot according to their preferences. In fact, the \(i\)-th critic (\(1 \le i \le m\)) has requested that he/she wants to taste exactly \(r_i\) red wines and \(w_i\) white wines.
Gabriella has yet to choose how many bottles of red wine and white wine there will be, and in what order they will appear. Help her find an arrangement (that is, a sequence of \(n\) bottles of either red or white wine) that satisfies the requests of all the critics, or state that no such arrangement exists.
Output
For each test case, if at least one solution exists, print a string of length \(n\) made up of the characters R and W, where the \(j\)-th character (\(1 \le j \le n\)) denotes the type of the wine in the \(j\)-th bottle of the arrangement (R for red and W for white). If there are multiple solutions, print any.
If no solution exists, print the string IMPOSSIBLE.
Note
In the first test case, there are \(n = 5\) bottles of wine to be arranged and \(m = 3\) critics. The arrangement RWRRW satisfies the requests of all three critics. Indeed:
- the first critic can choose the interval \([3, \, 3]\), which contains exactly one bottle of red wine (note that \([1, \, 1]\) and \([4, \, 4]\) are other valid choices);
- the second critic can choose the interval \([1, \, 5]\), which contains \(3\) bottles of red wine and \(2\) bottles of white wine;
- the third critic can choose the interval \([2, \, 5]\), which contains \(2\) bottles of red wine and \(2\) bottles of white wine.
Примеры
| № | Входные данные | Выходные данные |
|
1
|
3
5 3
1 0
3 2
2 2
4 3
2 1
1 1
0 3
3 2
0 2
0 3
|
RWRRW
IMPOSSIBLE
WWW
|