Processing a large vector crashes the program with bad_alloc

I have a large vector<string> (about 1 million in size) that I need to process:

stringstream numStr;
cout << "before loop" << endl;
for(unsigned int i = 0; i < numList.size(); i++) {
    cout << i << ": " << ((NORM_MAX - NORM_MIN) * (atoi(numList[i].c_str()) - min)) / (max - min) + NORM_MIN << endl;
    int number = ((NORM_MAX - NORM_MIN) * (atoi(numList[i].c_str()) - min)) / (max - min) + NORM_MIN;
    numStr << number;
    numList[i] = numStr.str();
}

However, the program crashes upon reaching 36691 ~ 36693

(snip)  
36689: 288  
36690: 264  
36691: 245  

This application has requested the Runtime to terminate it in an unusual way.
Please contact the application's support team for more information.
terminate called after throwing an instance of 'std::bad_alloc'
  what():  std::bad_alloc

What can I do to find out the cause of this problem?