There are seven cards in a hat, and on card $k$ there is a number $2^{k-1}$, where $k=1,2,...,7$. Solarin picks the cards at random from the hat, one card at a time, until the sum of the numbers on the cards in his hand exceeds $124$. What is the most probable sum he can get?

Let's think step by step and output the final answer within \boxed{}.
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