FRIENDLY NUMBERS#7461

FRIENDLY NUMBERS

0.2 seconds
64 megabytes
Medium

Two distinct natural numbers are termed amicable if the first number is equal to the sum of the proper divisors of the second number, and the second number is equal to the sum of the proper divisors of the first number. Your task is to identify all pairs of amicable numbers where both numbers fall within the range from to (1 \le M \le N \le 1\,000\,000), with all numbers being integers.

Input

The input consists of a single line containing two integers, and , separated by a space.

Output

For each pair of amicable numbers, output a line containing the two numbers separated by a space, ensuring the first number is smaller than the second. The output should be sorted in ascending order based on the first number of each pair. If no amicable numbers are found within the specified range, output "**Absent**".

Examples

Example 1

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Example 2

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Example 3

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