Number Theory and Applications: Recitation

Cheongeung, who became a teaching assistant for Number Theory and Applications, was too busy to prepare a recitation problem. Knowing that the students learned the Euler's totient function ($\varphi$) in this week's class, he was about to fall back on handing out many problems that ask for $\varphi(n)$ given some $n$.

\begin{equation*} \varphi(n)=\left|\left{k\in\mathbb{N}:::k\leq n,:\gcd(k,n)=1\right}\right| \end{equation*}

However, he realized that for this problem the formula is too well known once you factorize, so it would not fill up the whole recitation hour. So he prepared a problem that asks for the Jordan's totient function, a generalization of the Euler's totient function.

\begin{equation*} \varphi(n,v)=\left|\left{(k_1,k_2,\cdots,k_v)\in\mathbb{N}^v:::\forall i,:k_i\leq n,:\gcd(k_1,k_2,\cdots,k_v,n)=1\right}\right| \end{equation*}

But he fell into worry that this problem would also be solved too easily. While thinking of a harder problem, he recalled a famous anecdote about Gauss.

"When Gauss was young, his teacher Büttner told him to find the sum of the numbers from $1$ to $100$, and Gauss was the fastest to give the answer $5050$."

Inspired by this, he made the problem ask for $\sum\limits_{i=1}^n\sum\limits_{u=1}^{v}\varphi(i,u)$. Now solving this problem is up to you. Given $n$ and $v$, write a program that finds $\sum\limits_{i=1}^n\sum\limits_{u=1}^{v}\varphi(i,u)$.

The input is given on a single line, containing two positive integers $n$ and $v$. The input satisfies $1\leq n\leq 10^9$ and $1\leq v\leq 10^2$.

Print $\sum\limits_{i=1}^n\sum\limits_{u=1}^{v}\varphi(i,u)$. The answer can become very large, so print it modulo $10^9+7$.