equation: 111s + 153t = GCD(s,t)

Question Find s and t

I know how to do the problem first go through find the gcd of 111 and 153:

151 = 111 + 42

111 = 42*2 + 27

42 = 27 + 15

15 = 12 + 3

12 = 3*4 + 0

then I have to go back through and solve

42 = 153 - 111

27 = 111 - 42*2

.... etc

But everytime I try and solve it I get an answer that doesn't work, can anyone help me?