openmp tasks in nested loops - c++

Question

I am trying to write the following piece of code.
#pragma omp parallel
{
int .... some variables
for (int x:map){
int ...
#pragma omp single
{
#pragma omp task firstprivate(x,..) depend(out:a)
{
assigning the variables some values
}
for (int loop over j)
{
#pragma omp task firstprivate(j) depend (in:a) depend (out:b)
{
}
third loop over k
#pragma omp task depend(in:a,b)
{
}
}
}
}
Is this valid? The threads are getting formed but they are not getting into either (the loop over j i.e. the second loop) or the 3rd loop (I checked by print statements).
Please suggest how to correct this.
I tried printing inside the 2 loops and saw that nothing is getting printed which implies the threads don't enter into the loops at all. I was expecting that the work would be distributed among the threads but unfortunately I am unable to achieve this.
Minimum reproducible example:
(as asked in the comments I am making an example)
int a,b;
#pragma omp parallel
{
#pragma omp single
{for (int &x:map)
{
#pragma omp task
for(int i=0;i<x.second;++i)
{
vector<int> val = m2[i];
for (int j=0;j<val.size();++j)
{
#pragma omp critical
update a global map m3.
}
}
}
}