CF1770F Koxia and Sequence

Mari has three integers $ n $ , $ x $ , and $ y $ . Call an array $ a $ of $ n $ non-negative integers good if it satisfies the following conditions: - $ a_1+a_2+\ldots+a_n=x $ , and - $ a_1 \, | \, a_2 \, | \, \ldots \, | \, a_n=y $ , where $ | $ denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#OR). The score of a good array is the value of $ a_1 \oplus a_2 \oplus \ldots \oplus a_n $ , where $ \oplus $ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Koxia wants you to find the total bitwise XOR of the scores of all good arrays. If there are no good arrays, output $ 0 $ instead.

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In the first test case, there are $ 12 $ good arrays totally as follows. - $ [0,2,3] $ , $ [0,3,2] $ , $ [2,0,3] $ , $ [2,3,0] $ , $ [3,0,2] $ and $ [3,2,0] $ — the score is $ 0 \oplus 2 \oplus 3 = 1 $ ; - $ [1, 2, 2] $ , $ [2, 1, 2] $ and $ [2, 2, 1] $ — the score is $ 1 \oplus 2 \oplus 2 = 1 $ ; - $ [1, 1, 3] $ , $ [1, 3, 1] $ and $ [3, 1, 1] $ — the score is $ 1 \oplus 1 \oplus 3 = 3 $ . Therefore, the total bitwise xor of the scores is $ \underbrace{1 \oplus \ldots \oplus 1}_{9\text{ times}} \oplus 3 \oplus 3 \oplus 3 = 2 $ . In the second test case, there are no good sequences. The output should be $ 0 $ .