Weighted Binomial Coefficient Sum

If the value of \[\dbinom{36}{1}+4\dbinom{36}{4}+7\dbinom{36}{7}+\cdots+34\dbinom{36}{34}\] can be expressed as \(a\times b^{c}+12,\) where \(a\) and \(b\) are prime numbers, then find the value of \(a+b+c+12.\)

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