Problem Description

Gug is having fun with barcodes! A barcode is a string of 0s and 1s. Gug will only be happy if the 1s in the barcode can be divided into consecutive sections of length X to Y. Note that 2 consecutive sections of 1 do not need to be divided by a 0 in between.

Gug is able to edit the barcode by changing 0 to 1 or 1 to 0 at chosen position(s) in the barcode. Given a barcode of length N, find the minimum operations it takes for Gug to be happy.

Input

The first line of input will contain a 3 integers, N, X, Y.

The second line of input will contain a string of length N, representing the barcode.

Output

The output should contain one integer representing the minimum number of operations it takes for Gug to be happy if he starts with the given barcode.

Limits

Subtask 1 (30%): 1 ≤ N ≤ 103, 0 ≤ X, Y ≤ N.

Subtask 2 (31%): 1 ≤ N ≤ 105, 0 ≤ X = Y ≤ N.

Subtask 3 (39%): 1 ≤ N ≤ 105, 0 ≤ X, Y ≤ N.

```8 3 4
01010101```

`2`

Explanation

Gug changes the barcode from 01010101 to 01110111, taking 2 operations.

```8 4 5
10001010```

`3`

Explanation

Gug changes the barcode from 10001010 to 00001111, taking 3 operations.