RubbleRover

You have built a small robot named RubbleRover, which collects trash and has a radar. You want to use it for recycling. Here is what you need to know.

$*$ There are garbage blocks lined up In a row, with equal distance between them.

$*$ RubbleRover can tell if there is a garbage block at a certain distance from it$.$ If it finds a block, it moves to that block and collects it$.$

$*$ If RubbleRover cannot tell if the garbage is on its left or right, it will not go there to save energy and work efficiently.

$*$ RubbleRover will keep checking further if it is unsure about the garbage's location.

You are given the following:

The first line tells where RubbleRover starts, P$.$

The second line tells how many positions have

Garbage.

The third line has an array of $0$s and $15,$ where $1$ means there is garbage and $0$ means there is no garbage.

Your job is to figure out how many garbage blocks RubbleRover will recycle while being most efficient.

Input

$3$

$5$

$10111$

Output

$3$

Explanation: RubbleRover is located in the $3$rd position.

As the third line of the Input above shows, there is a garbage block at the $3$rd position, RubbleRover is sure about it$.$ So$,$ RubbleRover will recycle it$.$

RubbleRover knows that there is one garbage block at a distance $1$ from it$,$ but it cannot determine whether it should go to the left or right. So it will not check these positions.

RubbleRover starts checking further and sees that there are two garbage blocks at a distance of $2$ from It$.$ Since one position can have only one garbage block, RubbleRover is sure that one is to its left and the other is to the right. So it will recycle both of these garbage blacks.

The answer is $1+2=3.$ RubbleRover will recycle $3$

for input

Input

$4$

$4$

$0110$

Output

$2$

Explanation: RubbleRover is located in the $4$th position.

As the third line of the input above shows, there is no garbage block in the $4$th position.

There is one garbage block at a distance of $1$ from RubbleRover, and RubbleRover is sure that it is located to its left $($since there are only four garbage blocks$).$ RubbleRover will recycle that garbage block.

The same is true for a distance of $2$ from RubbleRover,

There is no garbage block at distance $3$ from RubbleRover.

The answeris $1+1=2$ RubbleRover will recycle $2$

Barbage blocks in this case

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