Doctor Nefario is planning a trip after spending a lot of time doing research in his lab. During the trip he needs to cross a river. Fortunately there are N rocks in the river lying on a straight line across the river that may be used to make the crossing. The width of the river (i.e., the total distance that needs to be crossed) is L.</p>

Doctor Nefario’s scooter can hover in the air, but to make the river crossing he wants to build a rocket booster that can make longer jumps. The cost of a rocket booster depends on its quality. More precisely, a rocket booster that can boost jumps up to distance R costs R². The booster may be used multiple times, but each jump costs an additional amount C.

For example, if Doctor Nefario builds a rocket booster that can boost jumps up to distance 10 and uses it to make 5 jumps, the total cost would be 10² + 5 × C = 100 + 5C.

Given the width of the river L, the cost of each jump C, and the location of N rocks, your goal is to find the minimum cost M for Doctor Nefario to cross the river, the number of jumps J needed, and the range R selected for the rocket booster.

For instance, in the figure above Doctor Nefario needs to cross a river of width 6. There are 4 rocks at distances 1, 2, 3, and 5. One possible solution is to build a rocket booster with range 3, which would allow the scooter to cross the river with two jumps.

The parameters of this problem may be quite large: 1 ≤ L ≤ 10⁹, 0 ≤ C ≤ 10⁶, and 0 ≤ N < 1000. Your implementation should represent these values using long instead of int. Exhaustively checking all possible values for range R will not work in the time allowed.

입력 형식

The input consists of multiple test cases. The first line of each test contains three integers L, C and, N: the width of the river, cost of each jump, and the number of rocks, respectively. Each of the next N lines contains an integer specifying the distance of a rock. The input terminates with a line containing just 0.

출력 형식

For each test case, print the minimum cost of crossing the river in the following format: Minimum cost M achieved with J jumps of range R

예제 입력

6 2 4
1
2
3
5
6 20 4
1
2
3
5
0

예제 출력

Minimum cost 12 achieved with 4 jumps of range 2 
Minimum cost 49 achieved with 2 jumps of range 3