406572: GYM102443 C Fermat's Last Theorem

As you probably know, for all positive integers $$$a$$$, $$$b$$$, $$$c$$$ and $$$n$$$ with $$$n \ge 3$$$ the following inequality holds: $$$a^n + b^n \neq c^n$$$. But all existing proofs of this fact are hard to verify, so a group of software engineers has decided to write their own proof that will be, in their opinion, easier to verify.

This group has written a program that iterates over all quadruples of positive integers $$$(a, b, c, n)$$$ such that $$$n \ge 3$$$, in increasing order of the maximums of its elements, and in case of equality of maximums — in the lexicographical order.

Thus first the quadruple $$$(1, 1, 1, 3)$$$ will be considered, then the quadruple $$$(1, 1, 2, 3)$$$, and so on. And, for example, the quadruple $$$(3, 3, 3, 3)$$$ will be followed by the quadruple $$$(1, 1, 1, 4)$$$.

For each quadruple the program compares the values $$$a^n + b^n$$$ and $$$c^n$$$, and prints the corresponding inequality: $$$a^n + b^n > c^n$$$ or $$$a^n + b^n < c^n$$$.

Now the software engineers want to verify their proof. They ask you to repeat their calculations and output the inequalities printed by their program, from the $$$l$$$-th to the $$$r$$$-th one, inclusive.

The first line contains two integers $$$l$$$ and $$$r$$$ ($$$1 \le l \le r \le {10}^{12}$$$; $$$r - l \le {10}^4$$$).

Output the part of the printed proof, from the $$$l$$$-th inequality to the $$$r$$$-th one, each on a separate line. To denote exponentiation, use a caret ('^', the ASCII character with code 94). Don't output any spaces.

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1^3+1^3>1^3
1^3+1^3<2^3
1^3+1^3<3^3
1^3+2^3>1^3