I have been given the following problems

(a) Use the $GCD$ algorithm to compute the greatest common divisor of $546$ and $416$. 

(b) Use your working for the previous part to express $\frac{416}{-546}$ as a rational ${m \over n}$ where $n\geq 1$ and $\gcd(m,n)=1$.

I am able to do part (a) and was left with the following working

$\gcd(416,546)$

$\rightarrow 546 = 1 \* 416 + 130$

$\gcd(130,416)$

$\rightarrow 416 = 130 \* 3 + 26$

$\gcd(26,130)$

$\rightarrow 130 = 5 \* 26 + 0$

$\gcd(0, 26)$

therefore $\gcd(416,546)=26$

Then with part (a), I found that because

$416 = 16 \* 26$ and $546 = 21 \* 26$

That ${16 \over -21}$ is the answer, this is wrong, and I'm struggling to see what I need to do to begin on this problem