Sanggeun's Idea

Sanggeun gave his son the following problem.

Two integers $n_1$ and $n_2$ satisfy $1 \le n_1 < n_2 \le 10^4$. Let $\mathbb{N}^*$ be the set of positive integers and define $p:\mathbb{N}^* \rightarrow \mathbb{N}^*$ by $p(n) = 2^n$ for every $n \in \mathbb{N}^*$. This function defines the set $S$.

$S(n_1,n_2)=\left\{ p(p(n))+1 \mid n_1 \le n \le n_2 \right\}$

The set of pairs built from the elements of $S$ is defined as well.

$T(n_1,n_2)=\left\{ (m_1,m_2) \mid m_1,m_2 \in S(n_1,n_2),\ m_1 < m_2 \right\}$

Now define the value

$R(n_1,n_2)=\sum_{(m_1,m_2) \in T(n_1,n_2)} \gcd(m_1,m_2)$

where $\gcd(m_1,m_2)$ is the greatest common divisor of $m_1$ and $m_2$.

Given $n_1$ and $n_2$, write a program that computes $R(n_1,n_2)$.

The first line contains two integers $n_1$ and $n_2$ separated by a space. ($1 \le n_1 < n_2 \le 10^4$)

Print the value of $R(n_1,n_2)$ on the first line.