Inheritance and default constructor

I have a class A that I what to be instantiated only via A(int arg1) constructor and I have class B that derived from class A that I want to be instantiated only via B(int arg1, int arg2) constructor.

Here is example:

class A
{
public:
    int i;
    A(int arg1)
    {
        i= arg1;
    }
};

class B : public A
{
    int j;

    B(int arg1, int arg2)
    {
        i= arg1;
        j= arg2;
    }
};

that produce error:

inheritance_default_constructor.cpp: In constructor ‘B::B(int, int)’:
inheritance_default_constructor.cpp:16:6: error: no matching function for call to ‘A::A()’
      {
      ^
inheritance_default_constructor.cpp:16:6: note: candidates are:
inheritance_default_constructor.cpp:5:6: note: A::A(int)
      A(int arg1)

I can fix it like this:

class A
{
public:
    int i;
    A(int arg1)
    {
        i= arg1;
    }
};

class B : public A
{
    int j;

    B(int arg1, int arg2) : A(arg1)
    {
        j= arg2;
    }
};

But what if I need the body of B(int arg1, int arg2) constructor to be not in .h file, but in .cpp file, is it possible?

UPDATE:

I was doing it wrong:

//inheritance_default_constructor.h
class A
{
public:
   int i;
   A(int arg1)
   {
        i= arg1;
   }
};

class B : public A
{
    int j;

    B(int arg1, int arg2) : A(arg1);
};


//inheritance_default_constructor.cpp
#include "inheritance_default_constructor.h"

B::B(int arg1, int arg2) : A(arg1)
{
    j= arg2;
}

int main()
{
    return 0;
}

In file included from inheritance_default_constructor.cpp:1:0:
inheritance_default_constructor.h: In constructor ‘B::B(int, int)’:
inheritance_default_constructor.h:15:32: error: expected ‘{’ at end of input
  B(int arg1, int arg2) : A(arg1);
                                ^
inheritance_default_constructor.cpp: At global scope:
inheritance_default_constructor.cpp:3:1: error: redefinition of ‘B::B(int, int)’
 B::B(int arg1, int arg2) : A(arg1)
 ^
In file included from inheritance_default_constructor.cpp:1:0:
inheritance_default_constructor.h:15:2: error: ‘B::B(int, int)’ previously defined here
  B(int arg1, int arg2) : A(arg1);