Undo the Neighbor XOR

Easy

There was an array arr of n non-negative integers, but only two things about it were kept: - an array links of length n - 1, where links[i] = arr[i] XOR arr[i + 1]; - the first element, start = arr[0]. Rebuild and return the original array arr. It can be shown that it is determined uniquely.

Example 1

links=[5, 5, 0], start=3 → [3, 6, 3, 3]

3 XOR 5 = 6, 6 XOR 5 = 3, 3 XOR 0 = 3. Check: 3^6 = 5, 6^3 = 5, 3^3 = 0.

Example 2

links=[8], start=0 → [0, 8]

With 0 as the first element, the second is 0 XOR 8 = 8.

Constraints

2 ≤ n ≤ 10⁴, len(links) = n - 1
0 ≤ links[i] ≤ 10⁵
0 ≤ start ≤ 10⁵

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Topics

Bit Manipulation Array

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Input

links=[5, 5, 0], start=3

Expected

[3, 6, 3, 3]

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