Unusual Permutation

Consider a permutation $A$ containing each integer from $1$ to $N$ exactly once. Count the permutations satisfying

Print the answer modulo $1\,000\,000\,007$.

The input is given in the following format:

$T$ case$_1$ case$_2$ $\vdots$ case$_T$

Each test case is given in the following format:

$N\ l\ r\ k$

For each test case, print the number of valid permutations modulo $1\,000\,000\,007$ on one line.

• $1 \leq T \leq 100$.
• $1 \leq l \leq r \leq N \leq 200\,000$.
• $1 \leq k \leq N$.
• The sum of $N$ over all test cases does not exceed $200\,000$.