| 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! | |
| Hmmm. Actually, campus tours are given regularly. | |
| The compound consists of **N** buildings, with **M** walkways running amongst | |
| them. The _i_th walkway connects buildings **Ai** and **Bi**, (**Ai** != | |
| **Bi**) and no two buildings are directly connected by more than one walkway. | |
| There are no other ways to move from building to building. | |
| Over a period of **D** days, some events will occur at Facebook HQ. One of two | |
| types of events will happen on the _i_th day, indicated by a character **Ei**. | |
| If **Ei** = 'T', then a tour will take place. Otherwise, **Ei** = 'S', and a | |
| security sweep of one building will take place. | |
| If a tour is given on the _i_th day, visitors will plan to enter the compound | |
| at building **Xi**, and leave from building **Yi** (**Xi** != **Yi**). 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 **Xi** to building **Yi** 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 **Xi** and **Yi**. Along the way some visitors | |
| will inevitably get themselves "lost", and fail to rejoin the tour group. In | |
| total, **Oi** new outsiders will be left behind in each building which could | |
| possibly be part of any valid tour route from building **Xi** and building | |
| **Yi**. Good thing they'll no doubt have brought cameras to amuse themselves | |
| with while they wait to be found. | |
| On the other hand, if a security sweep is conducted on the _i_th day, then the | |
| security foxes will carefully search building **Zi** for any trespassers | |
| remaining from previous tours, and kindly escort them out. | |
| Since Facebook likes data, you've been hired to record how many outsiders were | |
| found in each sweep. | |
| ### Input | |
| Input begins with an integer **T**, the number of test cases. Each test case | |
| begins with a line containing three integers, **N**, **M**, and **D**. The | |
| next **M** lines contain two integers **Ai** and **Bi**. The next **D** lines | |
| contain a character **Ei**, followed by either three integers **Xi**, **Yi**, | |
| **Oi** if **Ei** = 'T', or a single integer **Zi** if **Ei** = 'S'. | |
| ### Output | |
| For each test case _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. | |
| ### Constraints | |
| 1 ≤ **T** ≤ 20 | |
| 1 ≤ **N** ≤ 105 | |
| 1 ≤ **M** ≤ 106 | |
| 1 ≤ **D** ≤ 106 | |
| 1 ≤ **Oi** ≤ 1,000 | |
| 1 ≤ **Ai**, **Bi**, **Xi**, **Yi**, **Zi** ≤ **N** | |
| ### Explanation of Sample | |
| In the first sample case: | |
| 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. | |
| On the second day, the tour cannot take place. | |
| On the third and fourth days, security sweeps of buildings 2 and 6 are carried | |
| out, with 5 and 0 outsiders found respectively. | |
| 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. | |
| 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. | |
| Finally, security sweeps of buildings 1, 2, and 4 are conducted evicting 5, 1, | |
| and 15 people respectively, for a grand total of 26. | |