- Prepare
- Data Structures
- Advanced
- Palindromic Subsets

# Palindromic Subsets

# Palindromic Subsets

- Prepare
- Data Structures
- Advanced
- Palindromic Subsets

Consider a lowercase English alphabetic letter character denoted by . A *shift* operation on some turns it into the next letter in the alphabet. For example, and , , .

Given a zero-indexed string, , of lowercase letters, perform queries on where each query takes one of the following two forms:

`1 i j t`

: All letters in the inclusive range from to are shifted times.`2 i j`

: Consider all indices in the inclusive range from to . Find the number of non-empty subsets of characters, where , such that characters*can be rearranged*to form a palindrome. Then print this number modulo on a new line. Two palindromic subsets are considered to be different if their component characters came from different indices in the original string.

**Note**
Two palindromic subsets are considered to be different if their component characters came from different indices in the original string.

**Input Format**

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

The second line contains a string of lowercase English alphabetic letters (i.e., `a`

through `z`

) denoting .

Each of the subsequent lines describes a query in one of the two formats defined above.

**Constraints**

- for each query.
- for each query of type .

**Subtasks**

For of the maximum score:

For another of the maximum score:

- All queries will be of type .

**Output Format**

For each query of type (i.e., `2 i j`

), print the number of non-empty subsets of characters satisfying the conditions given above, modulo , on a new line.

**Sample Input 0**

```
3 5
aba
2 0 2
2 0 0
2 1 2
1 0 1 1
2 0 2
```

**Sample Output 0**

```
5
1
2
3
```

**Explanation 0**

We perform the following queries:

`2 0 2`

: and we want to find the palindromic subsets of substring . There are five such subsets that form palindromic strings (, , , , and ), so we print the result of on a new line`2 0 0`

: and we want to find the palindromic subsets of substring . Because this substring only has one letter, we only have one subset forming a palindromic string (). We then print the result of on a new line.`2 1 2`

: and we want to find the palindromic subsets of substring . There are two such subsets that form palindromic strings ( and ), so we print the result of on a new line.`1 0 1 1`

: and we need to perform shift operations on each character from index to index . After performing these shifts, .`2 0 2`

: and we want to find the palindromic subsets of substring . There are three valid subsets that form palindromic strings (, , and ), so we print the result of on a new line.