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.

Input

The first line contains two integers $*n*$ and $*d*$ ($2 ≤ *n* ≤ 100$, $1 ≤ *d* ≤ *n* - 1$) — 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.

Output

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 $1$.

Note

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.