Bessie has mastered the art of turning into a cannonball and bouncing along a number line of length N

$(1<=$N$<=105)$

with locations numbered $1,2,...,$N

from left to right. She starts at some integer location S

$(1<=$S$<=$N$)$

bouncing to the right with a starting power of $1$

$.$ If Bessie has power k

$,$ her next bounce will be at a distance k

forward from her current location.