Decode XORed Array

There is a hidden integer array arr that consists of n non-negative integers.

It was encoded into another integer array encoded of length n - 1, such that encoded[i] = arr[i] XOR arr[i + 1]. For example, if arr = [1,0,2,1], then encoded = [1,2,3].

You are given the encoded array. You are also given an integer first, that is the first element of arr, i.e. arr[0] == first.

Return the original array arr. It can be proved that the answer exists and is unique.

Examples

Example 1:

Input: encoded = [1,2,3], first = 1

Output: [1,0,2,1]

Explanation: If arr = [1,0,2,1], then first = 1 and encoded = [1 XOR 0, 0 XOR 2, 2 XOR 1] = [1,2,3].

Example 2:

Input: encoded = [6,2,7,3], first = 4

Output: [4,2,0,7,4]

Constraints

• 2 <= n <= 10^4
• encoded.length == n - 1
• 0 <= encoded[i] <= 10^5
• 0 <= first <= 10^5