The Scratch Cat wants to be a cool coder. He searches for some coding desktop backgrounds, which naturally always contain `1`

s and `0`

s. The Scratch Cat prefers specifically balanced text consisting of `1`

s and `0`

s. He defines the *imbalance* function of string as , where is the frequency of `1`

s, is the frequency of `0`

s, and is the length of string . The function represents the percentage of that is extraneous.

The Scratch Cat determines the "coolness" of a background's text by the number of substrings of that have an *imbalance* between and , inclusive. The Scratch Cat asks you for help because you are the true cool coder.

#### Constraints

Each character of is either `1`

or `0`

.

##### Subtask 1 [10%]

##### Subtask 2 [40%]

##### Subtask 3 [50%]

No additional constraints.

#### Input Specification

The first line will contain two space-separated integers and , the minimum and maximum *imbalance*.

The second line will contain the string , the text in a desktop background. only consists of `1`

or `0`

.

#### Output Specification

Output the number of **non-empty** substrings with an *imbalance* in the range . Two substrings are distinct if they are from different segments of , even if the substrings themselves are identical.

Do not round the function .

#### Sample Input

```
33 100
1001
```

#### Sample Output

`7`

#### Explanation

Below are the *imbalances* for all substrings of `1001`

:

- :
`1`

**100** - :
`10`

**0** - :
`0`

**100** - :
`100`

**33.33...** - :
`00`

**100** - :
`0`

**100** - :
`1001`

**0** - :
`001`

**33.33...** - :
`01`

**0** - :
`1`

**100**

substrings have an *imbalance* between and .

## Comments