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We always hope things in our lives will run smoothly, and having smooth arrays may help. An array $A$ of $N$ non-negative integers is $K_S$-smooth if the sum of every set of $K$ consecutive integers is exactly $S$. Unfortunately, not all arrays are $K_S$-smooth. In fact, all $K_S$-smooth arrays must contain a repeating pattern of length $K$.
Any array can be made $K_S$-smooth by changing its elements. In each change one element may be modified to any integer between $0$ and $S$, inclusive. You want to make all of your arrays smooth, but you don’t want to make any more changes than necessary. So the question is: What is the minimum number of changes you have to make so that a given array would become $K_S$-smooth?
The first line of input will consist of three integers of the form:
$N\;\; K\;\; S$
where $N$ is the size of the array.
The remainder of the file will consist of $N$ integers, $a_n\in A$, separated by white space.
All input will be within the following constraints:
Your program must output a single integer specifying the minimum number of changes that must be made in order to make the array $K_S$ smooth.
3 3 5 1 2 3
6 3 5 1 2 3 3 2 1
5 1 5 1 2 3 4 5