Percentage division

Algebra Level 3

1%÷2%÷3%÷÷98%÷99%\large {1\%} \div{2\%} \div {3\%} \div \dots \div{98\%} \div {99\%}

If the expression above is equal to 100ab!\dfrac{100^{a}}{b!}, where aa and bb are integers, find the minimum value of a+ba+b.

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