The survivor in the circle

$N$ people stand in a circle labelled $1$ through $N$; let $X$ be the largest power of $2$ that is $\le N$. Starting at person $1$, each living person kills the next living person clockwise and passes the sword on, until one survives. The survivor's label can be written as $a\,N + b\,X + c$ for integers $a, b, c$. Find $a + 2b + 3c$.