Problem:
Score : 300 points

Problem Statement

There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.

On this sequence, Snuke can perform the following operation:

Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.

Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times.
Find the minimum number of operations required.
It can be proved that, Under the constraints of this problem, this objective is always achievable.

Constraints

2 \leq K \leq N \leq 100000

A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 ... A_N

Output

Print the minimum number of operations required.

Sample Input 1

4 3
2 3 1 4

Sample Output 1

2

One optimal strategy is as follows:

In the first operation, choose the first, second and third elements. The sequence A becomes 1, 1, 1, 4.

In the second operation, choose the second, third and fourth elements. The sequence A becomes 1, 1, 1, 1.

Sample Input 2

3 3
1 2 3

Sample Output 2

1

Sample Input 3

8 3
7 3 1 8 4 6 2 5

Sample Output 3

4

Solution in Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

program main
	implicit none
	integer N, K, i, m, n1, l1, S, l, S1, S2
	integer, allocatable :: A(:)
	read(*, *) N, K
	allocate(A(1: N))
	read(*, *) A(1: N)
	S = 0
	S1 = 0
	S2 = 0
	do i = 1, N
		if(A(i) == 1) then
			l = i
			exit
		end if
	end do
	m = 1
	do i = 1, K
		if((l-K+i) == 1) then
			m = -K+i
		end if
	end do
	n1 = -1
	do i = 1, K
		if((l+K-i) == 1) then
			n1 = K-i
		end if
	end do
	if(n1-m+1==N) then
		write(*, *) 1
	else if(m /= 1 .or. n1 /= -1) then
		do i = 1, 10000000
			N = N - K + 1
			S = S + 1
			if(N < 2) then
				write(*, *) S
				exit
			end if
		end do
	else  
	l1 = l
		do i = 1, 10000000
			l1 = l1 - K + 1
			S1 = S1 + 1
			if(N < 2) then
				exit
			end if
		end do
		l = (N-l+1)
		do i = 1, 10000000
			l = (N-l+1) - K + 1
			S2 = S2 + 1
			if(N < 2) then
				exit
			end if
		end do
		write(*, *) S1+S2
	end if
end program main