multiply two large number

string multiplyStrings(string s1, string s2) {
   int i,j,m,n,x=1;
   if(s1[0]=='-'){x*=(-1); s1.erase(s1.begin());}
   if(s2[0]=='-'){x*=(-1); s2.erase(s2.begin());}
   if(s1.length()==0||s2.length()==0)return "0";
   m=s1.length();
   n=s2.length();
   vector<int>a(m+n,0);
   int k1=0;
   for(i=m-1;i>=0;i--)
   {
       int c=0,k2=0;
       for(j=n-1;j>=0;j--)
       {
           int num=(s1[i]-'0')*(s2[j]-'0');
           int sum=num+c+a[k1+k2];
           c=sum/10;
           a[k1+k2]=sum%10;
           k2++;
       }
       a[k1+k2]+=c;
       k1++;
   }
   i=a.size()-1;
   while(i>=0&&a[i]==0)i--;
   if(i==-1)return "0";
   string s="";
   while(i>=0)
   {
       s+=to_string(a[i]);
       i--;
   }
   if(x==-1)s.insert(s.begin(),'-');
   return s;
}