| You are the King of Byteland, which now consists of **K** rival states. The | |
| national day of Byteland is approaching, and it is a day of great merriment. | |
| Each of the **K** states is throwing its own party. Fortunately your kingdom | |
| also has **N** rich and famous entertainers, numbered from **0** to **N-1**. | |
| Its your job to allocate to each state, some non empty set of entertainers. | |
| Note that the same entertainer cannot be allocated to two different states. | |
| Some entertainers may be unallocated. Also to each allocated entertainer, you | |
| must pay **C** coins to hire him. | |
| The trouble is, some of the entertainers are fond of some others, and refuse | |
| to spend the national day without their friends, meaning they insist on being | |
| allocated to the same state if they are allocated). Under this constraint, you | |
| find out that allocating entertainers to the states becomes impossible. So you | |
| appeal to them to relax their requirements, and they ask you to donate more | |
| money to the entertainment industry. More formally, you will be provided with | |
| a 2-dimensional array **R**. If the total amount of money you donate is less | |
| than **R[u][v]**, for **u** not equal to **v**, then entertainer **#u** will | |
| NOT agree to spend the national day without the company of entertainer **#v**. | |
| Note that if you do not allocate entertainer **#u**, then you can safely | |
| ignore his restrictions. **R[u][v]** need not be equal to **R[v][u]**. | |
| You are free to donate any non-negative amount of coins as you see fit. Find | |
| out the minimum expenditure you must make to satisfy all entertainers and all | |
| states. Note that your total expenditure is : (the amount of money you donate | |
| + **C** * the number of allocated entertainers). | |
| ## Input: | |
| The first line contains **T**, the number of test cases. Each test contains 3 | |
| lines. | |
| * The first line contains 3 integers **N**, **K**, **C**. | |
| * The second line contains 4 integers **x1**, **a1**, **b1**, **m1** | |
| * The third line contains 4 integers **x2**, **a2**, **b2**, **m2** | |
| * Using these values, the array **R** can be generated as follows: | |
| * Let **f1**[0] = **x1**, **f2**[0] = **x2**; | |
| * **f1**[**i**] = (**a1** * **f1**[**i**-1] + **b1**) % **m1** for **i** ≥ 1 | |
| * **f2**[**i**] = (**a2** * **f2**[**i**-1] + **b2**) % **m2** for **i** ≥ 1 | |
| * If **i** > **j**, **R**[**i**][**j**] = **f1**[ **i** * (**i**-1) / 2 + **j** ] | |
| * If **i** < **j**, **R**[**i**][**j**] = f2[ **j** * (**j**-1) / 2 + **i** ] | |
| * Note that **R**[**i**][**j**] is not defined for **i** = **j**. | |
| ## Output: | |
| For test case numbered **i**, output "Case #i: " followed by the minimum | |
| number of coins you must spend to satisfy everybody. | |
| ## Constraints: | |
| * **T** ≤ 20 | |
| * 1 ≤ **N** ≤ 1111 | |
| * 1 ≤ **K** ≤ **N** | |
| * 1 ≤ **C** ≤ 1,000,000,000 | |
| * 0 ≤ **x1**, **a1**, **b1** ≤ 1,000,000,000 | |
| * 0 ≤ **x2**, **a2**, **b2** ≤ 1,000,000,000 | |
| * 1 ≤ **m1**, **m2** ≤ 1,000,000,000 | |
| ## Explanation of Sample Cases: | |
| In case 1, we get R[1][0] = 20 and R[0][1] = 8. The optimal choice is to | |
| donate 8 coins, and allocate entertainer #0 to the only state. | |
| In case 2, R[1][0] = 20 and R[0][1] = 12. The optimal choice here is to donate | |
| 0 coins, and allocate both entertainers to the only state. | |
| * In case 5, the matrix R look like this: | |
| * \--- 800 1600 | |
| * 400 --- 400 | |
| * 800 1200 --- | |
| * The optimal choice is to donate 1,600 coins, and allocate one entertainer to each state. | |