I was solving Sum of All Subset XOR Totals on Leetcode. It was obviously a Backtracking problem so I solved it in n*(2^n) . But it surprisingly has a linear solution. Like this

class Solution {
public:
    int subsetXORSum(vector<int>& nums) {
        int sum=0;
        for(auto i:nums)sum|=i;
        return sum*(1<<(nums.size()-1));
    }
};

Why this works ? Does anyone have the proof??