Jimmy loves playing with strings. He thinks string is *similar* to string if the following conditions are satisfied:

- Both strings have the same length (i.e., and ).
- For each valid pair of indices, , in the strings, and or and .

For example, string and are similar as for , and and for all other pairs as well as .

He has a string, , of size and gives you queries to answer where each query is in the form of a pair of integers . For each substring , find the number of substrings where substring is *similar* to substring and print this number on a new line.

**Note:** Substring is the contiguous sequence of characters from index to index . For example, if `abcdefgh`

, then `cdef`

.

**Input Format**

The first line contains two space-separated integers describing the respective values of and .

The second line contains string .

Each line of the subsequent lines contains two space-separated integers describing the respective values of and for query .

**Constraints**

**Output Format**

For each query, print the number of similar substrings on a new line.

**Sample Input**

```
8 4
giggabaj
1 1
1 2
1 3
2 4
```

**Sample Output**

```
8
6
2
1
```

**Explanation**

We perform the following sequence of queries:

- Strings with length are all similar, so our answer is .
`gi`

,`ig`

,`ga`

,`ab`

,`ba`

, and`aj`

are similar, so our answer is .`gig`

and`aba`

are similar, so our answer is .`igg`

has no similar string, so our answer is .