Yet another key extraction challenge (C++)

[Syoma]

The ciphertext here is 0x3141592653589793 ^ 0x1221777f1c3e4341.
Forward step is k[i][j] = k[i][0] = k[i-1][j] ^ k[i-1][0], where j = gamma[i]. Simplify and you will see the bit 0 on the current step is result of comparison of bits on the previous step.
Reverse step was explained by @ArC: build the bitlogic operation table and use it to restore source bits. You need to know 2 steps to restore the bit value.