27041번 - Leapcow 다국어

문제

Like everyone else, the cows like to bury each other in sand while at the beach. On this beach, the cows are only buried on the integer coordinates of a one-dimensional number line. Bessie wants to travel from one end of the beach (i.e., coordinate 0) to the other end (coordinate E, 5 ≤ E ≤ 40,000) without stepping on any buried cows. Bessie travels only by leaps, each of which has some length in the range 1..L (3 ≤ L ≤ 50).

Given the locations (1..E-1) of the B (1 ≤ B ≤ 500) buried cows, figure out the least number of leaps Bessie can use to get from one side to the other. It is guaranteed that an answer exists.

입력

• Line 1: Three space-separated integers: E, L, and B.
• Lines 2..B+1: Each line contains a single integer telling the coordinate of a buried cow.

출력

A single line with an integer that is the smallest number of "legal" leaps that are required for Bessie to reach coordinate E.

제한

힌트

A single line with an integer that is the smallest number of "legal" leaps that are required for Bessie to reach coordinate E.

Here's a diagram of the beach and leaps:

# # c c # # <--- cow denoted by 'c'
0 1 2 3 4 5 <--- location numbers
 1 2 3 <--- where leaps 1, 2, and 3 end