**not**endorsed by Fax McClad!

The MacFax Donut Cafe is expanding its restaurants into Canada. To kickstart their operations, they decided to open up a restaurant on every intersection along Yonge Street. Yonge Street is one of the longest streets in the world, and is composed of intersections, beginning at Toronto's lakeshore with index and ending near Lake Simcoe with index . To simplify, each restaurant will be numbered the same as the intersection they are on. The company wants to celebrate their openings with a series of promotions, which they will announce on live television, each promotion consists of one of two events:

- Add free donut coupons to the stores in that order.
- Ask the audience to count the total number of coupons that have been placed in the stores modulo .

Since none of the other eager customers realize that they can use a computer program to find the answer, you try to code your program quickly before the game starts so you can win all the prizes.

#### Constraints

For all subtasks:

#### Subtasks

Subtask | Constraint | Points |
---|---|---|

1 | 10 | |

2 | 15 | |

3 | 20 | |

4 | No additional constraints | 55 |

#### Input Specifications

The first line will contain and .

lines of input follow in one of the following formats:

`U l r k`

Add free donut coupons to the stores as described above.`Q l r`

Find the total number of free donut coupons added to the stores modulo .

#### Output Specifications

For each `Q`

type query, print the answer modulo on a new line.

#### Sample Input 1

```
6 6
U 4 6 0
Q 4 5
U 1 4 1
Q 1 4
U 1 4 2
Q 4 4
```

#### Sample Output 1

```
2
11
21
```

#### Sample Explanation 1

The various stages of updates

#### Sample Input 2

```
10 11
U 1 10 5
Q 1 1
Q 2 2
Q 3 3
Q 4 4
Q 5 5
Q 6 6
Q 7 7
Q 8 8
Q 9 9
Q 10 10
```

#### Sample Output 2

```
1
32
243
1024
3125
7776
16807
32768
59049
100000
```

## Comments

How can I view others code/submissions?

By solving the problem.