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문제

어느날, 상근이는 길을 걷던 중에 신기한 물체를 발견했다. 외계의 것으로 추정되는 이 물체의 왼편에는 빈 박스가 N개 있었다. 기계의 사용방법을 알아내기 위해서 하루종일 기계를 더듬거렸고, 마침내 상근이는 이 기계를 어떻게 사용하는지를 알게되었다.

기계는 정수 4개 L, R, A, B를 입력으로 받는다. 크고 빨갛게 빛나는 실행버튼을 누르면 기계는 다음과 같은 움직인다.

먼저, L번 박스에 들어 있는 돌의 개수를 A mod B개로 만든다. 그 다음 L+1번 박스에 들어 있는 돌을 (2*A) mod B개로 만든다. 마찬가지로, L+2번 박스에 들어 있는 돌을 (3*A ) mod B개로 만든다. 즉, L번과 R번 사이의 X번 박스에 들어 있는 돌의 개수를 ((X-L+1)*A) mod B개로 만드는 것이다. R번 박스까지 돌을 채우고나면, 기계는 다음 명령을 기다린다.

기계에 여러 가지 명령을 내리던 중에, 상근이는 어떤 박스의 구간에 들어있는 돌의 개수가 궁금해졌다.

상근이가 기계에 입력한 명령이 주어졌을 때, 이 기계를 시뮬레이팅 하면서, 상근이의 궁금증도 해결해주는 프로그램을 작성하시오.

입력

첫째 줄에 박스의 수 N과 쿼리의 수 Q가 주어진다. (1 ≤ N ≤ 1,000,000,000, 1 ≤ Q ≤ 50,000)

다음 Q개 줄에는 시뮬레이션에 관한 정보가 주어진다.

만약, 정보가 1로 시작한다면, 형식은 "1 L R A B" (1 ≤ L ≤ R ≤ N, 1 ≤ A, B ≤ 1,000,000)가 된다. 이 뜻은 상근이가 기계에 L, R, A, B를 입력했다는 뜻이다.

정보가 2로 시작한다면, 형식은 "2 L R"이 된다. (1 ≤ L ≤ R ≤ N) 이 뜻은 상근이가 L과 R번 박스 사이에 들어있는 돌의 개수를 궁금했다는 뜻이고, 개수를 구한뒤, 출력해야 한다. L과 R도 범위에 포함된다.

출력

2로 시작하는 명령이 들어올 때 마다, 그 구간에 들어있는 돌의 개수를 출력한다.

예제 입력 1

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

예제 출력 1

0
3
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(1 &le; N &le; 1,000,000,000, 1 &le; Q &le; 50,000)<\/p>\r\n\r\n\r\n\r\n<p>\ub2e4\uc74c Q\uac1c \uc904\uc5d0\ub294 \uc2dc\ubbac\ub808\uc774\uc158\uc5d0 \uad00\ud55c \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n\r\n\r\n<p>\ub9cc\uc57d, \uc815\ubcf4\uac00 1\ub85c \uc2dc\uc791\ud55c\ub2e4\uba74, \ud615\uc2dd\uc740 &quot;1 L R A B&quot; (1 &le; L &le; R &le; N, 1 &le; A, B &le; 1,000,000)\uac00 \ub41c\ub2e4. \uc774 \ub73b\uc740 \uc0c1\uadfc\uc774\uac00 \uae30\uacc4\uc5d0 L, R, A, B\ub97c \uc785\ub825\ud588\ub2e4\ub294 \ub73b\uc774\ub2e4.<\/p>\r\n\r\n\r\n\r\n<p>\uc815\ubcf4\uac00 2\ub85c \uc2dc\uc791\ud55c\ub2e4\uba74, \ud615\uc2dd\uc740 &quot;2 L R&quot;\uc774 \ub41c\ub2e4. (1 &le; L &le; R &le; N) \uc774 \ub73b\uc740 \uc0c1\uadfc\uc774\uac00 L\uacfc R\ubc88 \ubc15\uc2a4 \uc0ac\uc774\uc5d0 \ub4e4\uc5b4\uc788\ub294 \ub3cc\uc758 \uac1c\uc218\ub97c \uad81\uae08\ud588\ub2e4\ub294 \ub73b\uc774\uace0, \uac1c\uc218\ub97c \uad6c\ud55c\ub4a4, \ucd9c\ub825\ud574\uc57c \ud55c\ub2e4. L\uacfc R\ub3c4 \ubc94\uc704\uc5d0 \ud3ec\ud568\ub41c\ub2e4.<\/p>\r\n","output":"<p>2\ub85c \uc2dc\uc791\ud558\ub294 \uba85\ub839\uc774 \ub4e4\uc5b4\uc62c \ub54c \ub9c8\ub2e4, \uadf8 \uad6c\uac04\uc5d0 \ub4e4\uc5b4\uc788\ub294 \ub3cc\uc758 \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2925","problem_lang":"1","title":"ALADIN","description":"<p>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 &quot;NEDIRAJ&quot; causes the machine to go crazy and follow the next routine:<\/p>\r\n\r\n<ul>\r\n\t<li>Set the number of stones in the box labeled L to A modulo B.<\/li>\r\n\t<li>It procedes to fly to the box labeled L+1, and set the number of stones there to (2\u2219A) mod B.<\/li>\r\n\t<li>It procedes to fly to the box labeled L+2, and set the number of stones there to (3\u2219A) mod B.<\/li>\r\n\t<li>Generaly, it visits each box labeled between L and R, and set the number of stones there to ( (X - L + 1)\u2219A) mod B. where X is the box label.<\/li>\r\n\t<li>After it visits the box labeled R. It settles down for further instructions.<\/li>\r\n<\/ul>\r\n\r\n<p>During the game Aladin wonders what is the total number of stones in some range of boxes.<\/p>\r\n\r\n<p>Write a program that simulates the device and answers Aladins questions.<\/p>\r\n","input":"<p>The first line contains two integers N i Q (1 &le; N &le; 1 000 000 000) (1 &le; Q &le; 50 000), number of boxes and number of queries.<\/p>\r\n\r\n<p>The next Q lines contain information about the simulation.<\/p>\r\n\r\n<p>If the line starts with 1, than it follows the format &quot;1 L R A B&quot; (1 &le; L &le; R &le; N) (1 &le; A, B &le; 1000000), meaning that Aladin keyed in numbers L, R, A and B in the device and allowed the device to do its job.<\/p>\r\n\r\n<p>If the line starts with 2, than it follows the format &quot;2 L R&quot; (1 &le; L &le; R &le; N). Meaning that Aladin wonders how many stones in total are ther stones are in boxes labeled L to R (inclusive).<\/p>\r\n","output":"<p>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.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]