Totient Count in a Large Range

Consider the range \([1,2023^{2023}]\). You are to compute the number of integers in this range that are coprime with 2023. Since 2023 is composite, note that 2023 = 7 \(\times\) 17². Using Euler's Totient function, we have:

[ \varphi(2023^{2023}) = 2023^{2023} \Bigl(1-\frac{1}{7}\Bigr)\Bigl(1-\frac{1}{17}\Bigr) = \frac{96\cdot2023^{2023}}{119}. ]

Because the answer can be very large, output it modulo \(10^9+7\).

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This problem does not require any input.

outputFormat

Output a single integer – the number of integers in the range \([1,2023^{2023}]\) that are coprime with 2023, modulo \(10^9+7\).

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No input

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