P5106 dkw's LCM.

In particular, the LCM of a single number is the number itself. Kind dkw decides to tell you the statement directly: $$\prod_{i_1=1}^n\prod_{i_2=1}^n …\prod_{i_k=1}^n \varphi\big(lcm(i_1,i_2,…,i_k)\big)$$ Please compute the expression above, and output the answer modulo $10^9+7$. Here, $lcm(i_1,i_2,...,i_k)$ denotes the least common multiple of these $k$ numbers. Here, $\varphi$ denotes Euler's totient function. Here, $\prod$ denotes the product symbol, which is the multiplicative version of $\sum$.

Two positive integers, $n,k$.

One non-negative integer, representing the value of the expression modulo $10^9+7$.

For 50% of the testdata, $1\le n,k\le 8$. For 100% of the testdata, $1\le n,k\le 10^6$. Translated by ChatGPT 5