Producto de números grandes

#include <iostream>
#include <algorithm>
#include <string>
using namespace std;

string suma (string a, string b)
{
    int may = max( a.size(), b.size() );

    reverse( a.begin(), a.end() );
    reverse( b.begin(), b.end() );

    for(int i=a.size(); i<may; i++)
        a.push_back('0');
    for(int i=b.size(); i<may; i++)
        b.push_back('0');

    bool ac = false;
    string c;

    for(int i=0; i<a.size(); i++)
    {
        int A = a[i]-'0';
        int B = b[i]-'0';

        int C = A+B+ac;
        ac = C/10;
        c.push_back( (C)%10 +'0' );
    }
    if(ac)
        c.push_back('1');

    reverse(c.begin(), c.end());

    return c;
}

string prod (string &a, string &b)
{
    string p, c;
    int ac;

    reverse( a.begin(), a.end() );
    reverse( b.begin(), b.end() );

    for(int i=0; i<a.size(); i++)
    {
        int A = a[i]-'0';
        ac = false;
        c.clear();

        for(int j=0; j<b.size(); j++)
        {
            int B = b[j]-'0';

            int C = (A*B)+ac;
            ac = C/10;
            c.push_back( (C)%10 +'0' );
        }
        if(ac)
            c.push_back(ac+'0');

        reverse( c.begin(), c.end() );
        for(int R=0; R<i; R++)
            c.push_back('0');

        p = suma(p,c);
    }

    return p;
}

int main()
{
    string a, b;

    cin>>a;
    cin>>b;
    cout<<prod(a,b);

    return 0;
}