Primorial vs LCM

You are given an integer $N$. Let $\mathrm{LCM}(1, 2, \ldots, N)$ be the least common multiple of every integer from $1$ to $N$, and let $P(N)$ be the product of every prime that is at most $N$.

$\mathrm{LCM}(1, 2, \ldots, N)$ is always divisible by $P(N)$. Print that quotient modulo $1000000007$.

For example, with $N = 5$ we have $\mathrm{LCM}(1, 2, 3, 4, 5) = 60$ and $P(5) = 2 \times 3 \times 5 = 30$, so the quotient is $60 / 30 = 2$.

The first line contains the number of test cases $T$. ($1 \le T \le 50\,000$)

Each of the next $T$ lines contains one integer $N$. ($2 \le N \le 10^{14}$)

For each test case print one line in the format Case x: S, where $x$ is the test case number starting from $1$ and $S$ is the quotient modulo $1000000007$.