Multiplying big numbers in C++ - code with mistakes? How to improve it?

Here's the code for the function multiplying big numbers, which prints the result on screen:

void multiplying(string a, string b)
{
    if(a=="0"||b=="0")
        cout<<0;
  else 
  {
    vector<int> C;
    for(int i=0; i<a.size()+b.size(); i++)
        C.push_back(0);

    bool minus=false;

    if((a[0]=='-'&&b[0]!='-')||(b[0]=='-'&&a[0]!='-'))
        minus=true;

    if(a[0]='-')
        a.erase(a.begin());

    if(b[0]='-')
        b.erase(b.begin());    

    if(a.size()<b.size())
        swap(a,b);

    for(int i=b.size()-1; i>=0; i--)
    {
        for(int j=a.size()-1; j>=0; j--)
        {
            C[i+j+1]+=((a[j]-'0')*(b[i]-'0'));
            int k=i+j+1;
            while(C[k]>9&&k>0)
            {
               C[k-1]+=C[k]/10;
               C[k]=C[k]%10;
               k--; 
            }

        }



    }

    while(C[0]==0)
        C.erase(C.begin());

    if(minus)
        cout<<"-";

    for(int i=0; i<C.size(); i++)
        cout<<C[i];

    cout<<endl;
   }     



}

However, it is never correct and I need to improve this. I can't see where is my mistake though - spent quite a long time on this code.

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