A country has n city which are placed at 1km distance . You are given city data numbered from 1 to n. Ai = 1 means a water plant can be made in this (i-th) city. A power plant can serve the neighbouring k-1 cities both to the left and right. For example:
For the distribution 0 1 0 0 0 1 1 1 1 1 . The city which can have power plants are {2,6,7,8,9,10}
If k=3,a power plant at city 6 can serve cities {4,5,7,8}. Determine the minimum number of power pants to serve all the cities . If it is not possible print -1.
Input Format
The first line contains two space-separated integers n and k.
The second line contains n spaced-integers containing either 0 or 1;
Constraints
1<=k<=n<=105
Output Format
Print a single integer denoting the minimum number of plants . If this is not possible for the given value of k, print -1.
Sample Input 0
10 3 0 1 0 0 0 1 1 1 1 1
Sample Output 0
3
Explanation 0
One of Optimal soln will have plants at {2,6,10}
Sample Input 1
7 2 0 1 0 0 0 1 0
Sample Output 1
-1