The Way to Home，一个不怎么明显的dp题。详见本文内容
A. The Way to Home
time limit per test: 1 second
memory limit per test: 256 megabytes
input: standard input
output: standard output
A frog lives on the axis $Ox$ and needs to reach home which is in the point $n$. She starts from the point $1$. The frog can jump to the right at a distance not more than $d$. So, after she jumped from the point $x$ she can reach the point $x+a$, where $a$ is an integer from $1$ to $d$.
For each point from $1$ to $n$ is known if there is a lily flower in it. The frog can jump only in points with a lilies. Guaranteed that there are lilies in the points $1$ and $n$.
Determine the minimal number of jumps that the frog needs to reach home which is in the point $n$ from the point $1$. Consider that initially the frog is in the point $1$. If the frog can not reach home, print $-1$.
The first line contains two integers $n$ and $d$ $(2 \le n \le 100, 1 \le d \le n-1)$ — the point, which the frog wants to reach, and the maximal length of the frog jump.
The second line contains a string $s$ of length $n$, consisting of zeros and ones. If a character of the string s equals to zero, then in the corresponding point there is no lily flower. In the other case, in the corresponding point there is a lily flower. Guaranteed that the first and the last characters of the string $s$ equal to one.
If the frog can not reach the home, print $-1$.
In the other case, print the minimal number of jumps that the frog needs to reach the home which is in the point $n$ from the point $1$.
In the first example the from can reach home in two jumps: the first jump from the point $1$ to the point $4$ (the length of the jump is three), and the second jump from the point $4$ to the point $8$ (the length of the jump is four).
In the second example the frog can not reach home, because to make it she need to jump on a distance three, but the maximum length of her jump equals to two.