Molly is trying to steal some candy from her best friend FatalWhale. Unfortunately, FatalWhale is very organized and will immediately notice if the total sweetness of candies Molly takes is not a multiple of ~P~. Help Molly determine which candies out of the ~N~ FatalWhale has in order to take the maximum sweetness!
- ~N, P \le 4096~
- You will receive ~20\%~ of the points if you find just the maximum sweetness, but in order to receive these points, you must correctly follow the output specification.
- Molly will always take at least one candy.
On the first line of input you will find two space-separated integers, ~N~ and ~P~.
On the second line of input you will find the sweetness of the ~N~ candies, as space-separated integers ~s_i~. (~0 \le s_i \le 500\,000~)
On the first line you will print the maximum sweetness.
On the second line you will print the number of the candies that Molly takes in order to take the maximum sweetness.
On the third line, you will print the indices of the candies Molly takes.
7 6 178 25 123 34 56 79 100
570 6 1 3 4 5 6 7
Sample Output [for 20% of points]
570 1 1