Let $k$ be the smallest positive integer such that the binomial coefficient $\binom{10^9}{k}$ is less than the binomial coefficient $\binom{10^9 + 1}{k - 1}$.  Let $a$ be the first (from the left) digit of $k$ and let $b$ be the second (from the left) digit of $k$.  What is the value of $10a + b$?
<|im_start|>system
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<|im_start|>user
Let $k$ be the smallest positive integer such that the binomial coefficient $\binom{10^9}{k}$ is less than the binomial coefficient $\binom{10^9 + 1}{k - 1}$.  Let $a$ be the first (from the left) digit of $k$ and let $b$ be the second (from the left) digit of $k$.  What is the value of $10a + b$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
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Let $k$ be the smallest positive integer such that the binomial coefficient $\binom{10^9}{k}$ is less than the binomial coefficient $\binom{10^9 + 1}{k - 1}$.  Let $a$ be the first (from the left) digit of $k$ and let $b$ be the second (from the left) digit of $k$.  What is the value of $10a + b$?
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