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Home » Problems (hard) » Adding Least Common Multiples

Adding Least Common Multiples

Problem code: LCM

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All submissions for this problem are available.

Given A and B, compute the sum of lcm(a, b) over all pairs of positive integers a and b such that:

(1) a<=A and b<=B.
(2) There is no integer n>1 such that n2 divides both a and b.

Give your answer modulo 230.

Input

The first line contains the number of test cases, t (about 200). Each of the next t lines contains two space-separated integers A and B (1<=A, B<=4000000).

Output

Print the answer to each test case on a separate line.

Example

Input:

4
2 4
3 3
6 5
8 3

Output:

24
28
233
178


Date:2010-05-06
Time limit:2s
Source limit:50000B
Languages:All except: TCL


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HELP

Program should read from standard input and write to standard output.

After you submit a solution you can see your results by clicking on the [My Submissions] tab on the problem page. Below are the possible results:

  • Accepted Your program ran successfully and gave a correct answer. If there is a score for the problem, this will be displayed in parenthesis next to the checkmark.
  • Time Limit Exceeded Your program was compiled successfully, but it didn't stop before time limit. Try optimizing your approach.
  • Wrong Answer Your program compiled and ran succesfully but the output did not match the expected output.
  • Runtime Error Your code compiled and ran but encountered an error. The most common reasons are using too much memory or dividing by zero. For the specific error codes see the help section.
  • Compilation Error Your code was unable to compile. When you see this icon, click on it for more information.

If you are still having problems, see a sample solution here.

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