Coefficients \( :)\)

If the value of
\( \displaystyle ^{404}C_{4} -^{4}C_{1} ^{303}C_{4} + ^{4}C_{2} ^{202}C_{4} - ^{4}C_{3} ^{101}C_{4} \) can be represented as \(101 ^{\alpha}\) . The value of \(\alpha\) is

This problem is a part of the set Advanced is basic.
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