Percentage division

Algebra Level 3

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

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