Distribution problem # $1$

At an international event, there are $100$ countries participating, each with its own flag. There are $10$ distinct flagpoles at the stadium, labelled # $1$ ,# $2$ ,...,# $10$ in a row. All the $100$ flags are to be hoisted on these $10$ flagpoles, such that for each $i$ from $1$ to $10$ , the flagpole # $i$ has at least $i$ flags? (Note that the vertical order of the flagpoles on each flag is important) .If the number of ways to do this is

$C! \cdot$ ${A}\choose{B}$ where $B$ < $20$

Find the value of
$A +\ B +C$