模板专用化的实例化不正确

在下面的代码中，我尝试将类A专用化为模板参数T具有值B<m>的基本情况。

#include <array>
#include <iostream>
template <std::size_t m>
struct B
{
  std::array<double,m> arr;
};

template <std::size_t n, typename T>
struct A
{
  std::array<T,n> arr;
  const static int inner_dim = T::inner_dim;
};
template <std::size_t n >
template <std::size_t m>
struct A<n,B<m>>
{
  std::array<B<m>,n> arr;
  const static int inner_dim = m;
};

int main(int argc, char *argv[])
{
  A<5,A<4,B<3>>> a;
  std::cout << a.inner_dim << std::endl;
  A<5,B<4>> b;
  std::cout << b.inner_dim << std::endl;
  return 0;
}

但是，在main的实例化中，当我使用g ++ 5.4编译时，我收到以下错误：

$ g++ -Wall --std=c++11 specialization.cc 
specialization.cc: In instantiation of ‘const int A<4ul, B<3ul> >::inner_dim’:
specialization.cc:15:20:   required from ‘const int A<5ul, A<4ul, B<3ul> > >::inner_dim’
specialization.cc:30:18:   required from here
specialization.cc:15:20: error: ‘inner_dim’ is not a member of ‘B<3ul>’
   const static int inner_dim = T::inner_dim;
                    ^
specialization.cc: In instantiation of ‘const int A<5ul, B<4ul> >::inner_dim’:
specialization.cc:33:18:   required from here
specialization.cc:15:20: error: ‘inner_dim’ is not a member of ‘B<4ul>’

似乎只使用一般定义，而不是专业化。如何确保实例化正确的专业化？