There are two kangaroos on an x-axis ready to jump in the positive direction (i.e, toward positive infinity). The first kangaroo starts at location $x_1$ and moves at a rate of $v_1$ meters per jump. The second kangaroo starts at location $x_2$ and moves at a rate of $v_2$ meters per jump. Given the starting locations and movement rates for each kangaroo, can you determine if they'll ever land at the same location at the same time?
A single line of four space-separated integers denoting the respective values of $x_1$, $v_1$, $x_2$, and $v_2$.
- $0 \le x_1 < x_2$
- $1 \le v_1$
- $1 \le v_2$
Print YES if they can land on the same location at the same time; otherwise, print NO.
Note: The two kangaroos must land at the same location after making the same number of jumps.
Sample Input 0
0 3 4 2
Sample Output 0
The two kangaroos jump through the following sequence of locations:
- 0 3 6 9 12
- 4 6 8 10 12
Thus, the kangaroos meet after 4 jumps and we print YES.
Sample Input 1
0 2 5 3
Sample Output 1
The second kangaroo has a starting location that is ahead (further to the right) of the first kangaroo's starting location (i.e., $x_2 > x_1$). Because the second kangaroo moves at a faster rate (meaning $v_2 > v_1$) and is already ahead of the first kangaroo, the first kangaroo will never be able to catch up. Thus, we print NO.
Note: I searched for the answer and got this puzzle here but without answer :( so had to ask.