Fail to modify the elements of a global vector in ParallelTable

Question

I want to modify a vector in a Table function, such as

vec = {0, 0, 0, 0};
Table[vec[[i]] = i, {i, 1, 4}];
vec
// output {1,2,3,4}

however, when I use ParallelTable function to speed up the progress, it fails to work.

vec = {0, 0, 0, 0};
ParallelTable[vec[[i]] = i, {i, 1, 4}];
vec
// output {0,0,0,0}

How can I fix it?