| <p> | |
| Facebook HQ -- a mysterious place full of magical code and trade secrets. | |
| If outsiders were ever to breach the walls of the compound, which are | |
| protected by a legion of security foxes, the entire company could well | |
| be brought to its knees! | |
| </p> | |
| <p> | |
| Hmmm. Actually, campus tours are given regularly. | |
| </p> | |
| <p> | |
| The compound consists of <b>N</b> buildings, with <b>M</b> walkways running amongst them. | |
| The <i>i</i>th walkway connects buildings <b>A<sub>i</sub></b> and <b>B<sub>i</sub></b>, (<b>A<sub>i</sub></b> != <b>B<sub>i</sub></b>) | |
| and no two buildings are | |
| directly connected by more than one walkway. There are no other ways to | |
| move from building to building. | |
| </p> | |
| <p> | |
| Over a period of <b>D</b> days, some events will occur at Facebook HQ. One | |
| of two types of events will happen on the <i>i</i>th day, indicated by a character | |
| <b>E<sub>i</sub></b>. If <b>E<sub>i</sub></b> = 'T', then a tour will take place. Otherwise, <b>E<sub>i</sub></b> = 'S', and a | |
| security sweep of one building will take place. | |
| </p> | |
| <p> | |
| If a tour is given on the <i>i</i>th day, visitors will plan to enter the compound at | |
| building <b>X<sub>i</sub></b>, and leave from building <b>Y<sub>i</sub></b> (<b>X<sub>i</sub></b> != <b>Y<sub>i</sub></b>). If it turns out that | |
| these two buildings are not actually connected by any sequence of walkways, | |
| then the tour will be cancelled, and the unfortunate visitors will be | |
| given Facebook T-shirts on the way out. Otherwise, a large number of people | |
| will be led from building <b>X<sub>i</sub></b> to building <b>Y<sub>i</sub></b> along various routes. No route | |
| will involve travelling along the same walkway multiple times (even in | |
| different directions), but a route might revisit the same building repeatedly, | |
| including buildings <b>X<sub>i</sub></b> and <b>Y<sub>i</sub></b>. Along the way some visitors will inevitably | |
| get themselves "lost", and fail to rejoin the tour group. In total, <b>O<sub>i</sub></b> new | |
| outsiders will be left behind in each building which could possibly be part of | |
| any valid tour route from building <b>X<sub>i</sub></b> and building <b>Y<sub>i</sub></b>. Good thing they'll no | |
| doubt have brought cameras to amuse themselves with while they wait to be | |
| found. | |
| </p> | |
| <p> | |
| On the other hand, if a security sweep is conducted on the <i>i</i>th day, then the | |
| security foxes will carefully search building <b>Z<sub>i</sub></b> for any trespassers | |
| remaining from previous tours, and kindly escort them out. | |
| </p> | |
| <p> | |
| Since Facebook likes data, you've been hired to record how many outsiders | |
| were found in each sweep. | |
| </p> | |
| <h3>Input</h3> | |
| <p> | |
| Input begins with an integer <b>T</b>, the number of test cases. Each test case | |
| begins with a line containing three integers, <b>N</b>, <b>M</b>, and <b>D</b>. | |
| The next <b>M</b> lines contain two integers <b>A<sub>i</sub></b> and <b>B<sub>i</sub></b>. | |
| The next <b>D</b> lines contain a character <b>E<sub>i</sub></b>, followed by either three integers | |
| <b>X<sub>i</sub></b>, <b>Y<sub>i</sub></b>, <b>O<sub>i</sub></b> if <b>E<sub>i</sub></b> = 'T', or a single integer <b>Z<sub>i</sub></b> if <b>E<sub>i</sub></b> = 'S'. | |
| </p> | |
| <h3>Output</h3> | |
| <p> | |
| For each test case <i>i</i>, output "Case #i: " followed by the total number of visitors the foxes escort off the campus. Since this number may be quite large, output it modulo 1,000,000,007. | |
| </p> | |
| <h3>Constraints</h3> | |
| <p> | |
| 1 ≤ <b>T</b> ≤ 20 <br/> | |
| 1 ≤ <b>N</b> ≤ 10<sup>5</sup> <br/> | |
| 1 ≤ <b>M</b> ≤ 10<sup>6</sup> <br/> | |
| 1 ≤ <b>D</b> ≤ 10<sup>6</sup> <br/> | |
| 1 ≤ <b>O<sub>i</sub></b> ≤ 1,000 <br/> | |
| 1 ≤ <b>A<sub>i</sub></b>, <b>B<sub>i</sub></b>, <b>X<sub>i</sub></b>, <b>Y<sub>i</sub></b>, <b>Z<sub>i</sub></b> ≤ <b>N</b> <br/> | |
| </p> | |
| <h3>Explanation of Sample</h3> | |
| <p> | |
| In the first sample case: | |
| </p> | |
| <p> | |
| On the first day, a tour is given from building 1 to building 2. The only | |
| valid route consists of simply crossing the walkway between these two | |
| buildings. As such, by the end of the day, 5 outsiders are left hiding in each | |
| of buildings 1 and 2. | |
| </p> | |
| <p> | |
| On the second day, the tour cannot take place. | |
| </p> | |
| <p> | |
| On the third and fourth days, security sweeps of buildings 2 and 6 are carried | |
| out, with 5 and 0 outsiders found respectively. | |
| </p> | |
| <p> | |
| On the fifth day, a tour is given from building 2 to building 3. There are | |
| exactly three valid routes (2, 3), (2, 3, 4, 5, 3), (2, 3, 5, 4, 3). As such, | |
| one new outsider remains behind in each of buildings 2, 3, 4, and 5. | |
| </p> | |
| <p> | |
| On the sixth day, the valid tour routes are (5, 3) and (5, 4, 3), so 14 new | |
| outsiders take up residence in each of buildings 3, 4, and 5. | |
| </p> | |
| <p> | |
| Finally, security sweeps of buildings 1, 2, and 4 are conducted evicting 5, 1, | |
| and 15 people respectively, for a grand total of 26. | |
| </p> | |