Hey guys, I need help with this question. "Use Euclids algorithm to find integer solutions of the given equation and hence find solutions of the congruence equations that are also given."

Equation:127a + 583b = 1

Congruence equation:127x = 1 (mod 583)

After doing Euclids algorithm, I found a = 101 and b = -22. But knowing this information, how do I findxin: 127x= 1 (mod 583)

thank you!