P1633 Binary

There are three integers $A, B, C$, where $N_{(2)}$ denotes the binary representation of $N$ (without leading 0s). Let $L$ be the maximum length among $A_{(2)}, B_{(2)}, C_{(2)}$. You need to construct three positive integers $X, Y, Z$ that satisfy the following conditions: 1. The lengths of $X_{(2)}, Y_{(2)}, Z_{(2)}$ do not exceed $L$. 2. The number of 1s in $A_{(2)}$ equals that in $X_{(2)}$. 3. The number of 1s in $B_{(2)}$ equals that in $Y_{(2)}$. 4. The number of 1s in $C_{(2)}$ equals that in $Z_{(2)}$. 5. $X + Y = Z$.

The first line contains a positive integer $T$, indicating there are $T$ test cases. The next $T$ lines each contain three positive integers $A, B, C$.

Output $T$ lines, one answer per line. Output the minimal $Z$. If there is no valid $Z$, output $-1$.

### Constraints and Notes - For 30% of the testdata, $1 \le A, B, C \le 100$. - For 100% of the testdata, $1 \le T \le 10$, $1 \le A, B, C \le 2^{30}$. Translated by ChatGPT 5