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Given `val` such that `flag * 2^{10000} mod 10^{175} == val`.
From definition of modulus, we get
`flag * 2^{10000} - k * 10^{175} == val`.
Divide by `2^{175}`,
`flag * 2^{10000-175} - k * 5^{175} == val / 2^{175}`
Then we get modulo `5^{175}`,
`flag * 2^{10000-175} == val / 2^{175} (mod 5^{175})`
and multiply the inverse.
`flag == (val / 2^{175}) * inv(2^{10000-175}) (mod 5^{175})`
