Das Blinkenlights

Photo by
Afrank99

There are two lights that blink at regular intervals. When
each one blinks, it turns on and then immediately back off;
they donâ€™t toggle. They are both off at time $t = 0$. The first one blinks at
$t=p, 2p, 3p, \ldots $
seconds; the second one blinks at $t=q, 2q, 3q, \ldots $ seconds. Once
they start, they both keep blinking forever. It is
*very* exciting to see them blink at the same time (on
the same second). But your patience is going to run out
eventually, in $s$
seconds. Will they blink at same time between $t=1$ and $t=s$ (inclusive)? Write a program
that can answer this question, quick, before they start
blinking again!

Input consists of one line containing three space-separated integers $p$, $q$, and $s$. The bounds are $1 \le p, q \le 100$ and $1 \le s \le 10\, 000$. The first light blinks every $p$ seconds, the second every $q$ seconds. The value of $s$ represents the maximum number of seconds to consider when determining if the two lights blink at the same time.

Output `yes` if the two lights blink on
the same second between time $1$ and time $s$, or `no`
otherwise.

Sample Input 1 | Sample Output 1 |
---|---|

2 5 20 |
yes |

Sample Input 2 | Sample Output 2 |
---|---|

4 3 11 |
no |