COCI 2009/2010, Contest #1

Task ALADIN

Aladin was walking down the path one day when he found the strangest thing. N empty boxes right next to a weird alien machine. After a bit of fumbling around he got the machine to do something. The machine now accepts 4 integers L, R, A and B. After that hitting the big red glowing button labeled "NE DIRAJ" causes the machine to go crazy and follow the next routine:

• Set the number of stones in the box labeled L to A modulo B.
• It procedes to fly to the box labeled L+1, and set the number of stones there to (2•A) mod B.
• It procedes to fly to the box labeled L+2, and set the number of stones there to (3•A) mod B.
• Generally, it visits each box labeled between L and R, and set the number of stones there to ((X - L + 1)•A) mod B. where X is the box label.
• After it visits the box labeled R. It settles down for further instructions.

During the game Aladin wonders what is the total number of stones in some range of boxes.

Write a program that simulates the device and answers Aladin's questions

Input

The first line contains two integers N (1 ≤ N ≤ 1 000 000 000) and Q (1 ≤ Q ≤ 50 000), number of boxes and number of queries.

The next Q lines contain information about the simulation.

If the line starts with 1, than it follows the format "1 L R A B" (1 ≤ L ≤ R ≤ N) (1 ≤ A, B ≤ 1 000 000), meaning that Aladin keyed in numbers L, R, A and B in the device and allowed the device to do its job.

If the line starts with 2, than it follows the format "2 L R" (1 ≤ L ≤ R ≤ N). Meaning that Aladin wonders how many stones in total are ther stones are in boxes labeled L to R (inclusive).

Output

For each query beginning with 2 output the answer to that particular query. Queries should be processed in the order they are given in the input.

Scoring

Test cases worth 30% of total points have N and Q ≤ 1000.

Test cases worth 70% of total points have Q ≤ 1000.

Sample Tests

6 3
2 1 6
1 1 5 1 2
2 1 6

0
3

4 5
1 1 4 3 4
2 1 1
2 2 2
2 3 3
2 4 4

3
2
1
0

4 4
1 1 4 7 9
2 1 4
1 1 4 1 1
2 1 4

16
0

First sample description:

The boxes start containing {0, 0, 0, 0, 0, 0}, 0 stones in total.

After that the device sets the stones to {1 mod 2, 2 mod 2, 3 mod 2, 4 mod 2, 5 mod 2, 0} = {1,0,1,0,1,0}, or 3 stones in total.

All Submissions
Best Solutions

Point Value: 25 (partial)
Time Limit: 8.00s
Memory Limit: 64M
Added: Aug 13, 2013

Languages Allowed:
C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

Comments (Search)

Try to use segment tree, but the L and R are so large... 

you need to use coordinate compression
there are going to be a maximum of 2Q points that actually matter