Time Limit: 2 Seconds
Memory Limit: 65536 KB
The bored Bob is playing a number game. In the beginning, there are n numbers. For each turn, Bob will take out two numbers from the remaining numbers, and get the product of them. There is a condition that the sum of two numbers must be not larger than k.
Now, Bob is curious to know what the maximum sum of products he can get, if he plays at most m turns. Can you tell him?
The first line of input contains a positive integer T, the number of test cases. For each test case, the first line is three integers n, m(0≤ n, m ≤100000) and k(0≤ k ≤20000). In the second line, there are n numbers ai(0≤ ai ≤10000, 1≤ i ≤n).