Minimum Lights to Activate

There is a corridor in a Jail which is N units long. Given an array A of size N. The i^th index of this array is 0 if the light at i^th position is faulty otherwise it is 1.

All the lights are of specific power B which if is placed at position X, it can light the corridor from [ X-B+1, X+B-1].

Initially all lights are off.

Return the minimum number of lights to be turned ON to light the whole corridor or -1 if the whole corridor cannot be lighted.

1 <= N <= 100000

1 <= B <= 10000

First argument is an integer array A where A[i] is either 0 or 1.

Second argument is an integer B.

Return the minimum number of lights to be turned ON to light the whole corridor or -1 if the whole corridor cannot be lighted.

Input 1:

A = [ 0, 0, 1, 1, 1, 0, 0, 1].
B = 3

Input 2:

A = [ 0, 0, 0, 1, 0].
B = 3

Output 1:

2

Output 2:

-1

Explanation 1:

In the first configuration, Turn on the lights at 2nd and 7th index. 
Light at 2nd index covers from [ 1, 5] and light at 7th index covers [6, 8].

Explanation 2:

In the second configuration, there is no light which can light the first corridor.