The Euclidean algorithm gives us
356 = (1 • 252) + 104
252 = (2 • 104) + 44
104 = (2 • 44) + 16
44 = (2 • 16) + 12
16 = (1 • 12) + 4
12 = (3 • 4) + 0
which means gcd(252, 356) = 4. Now we work backwards:
4 = 16 - 12
4 = 16 - (44 - (2 • 16)) = (3 • 16) - 44
4 = 3 • (104 - (2 • 44)) - 44 = (3 • 104) - (7 • 44)
4 = (3 • 104) - (7 • (252 - (2 • 104))) = (17 • 104) - (7 • 252)
4 = (17 • (356 - 252)) - (7 • 252) = (17 • 356) - (24 • 252)
