Big thanks to @dfhwze for the approval.

This kata is inspired by @Voile's One Line Task: Hard Fibonacci Numbers.

Task

Write a function that takes two non-negative integers n and k, and computes the mathematical combination $\left(\genfrac{}{}{0px}{}{n}{k}\right)\backslash binom\{n\}\{k\}$.

---

Examples

• $\left(\genfrac{}{}{0px}{}{1}{0}\right)=1,\left(\genfrac{}{}{0px}{}{1}{1}\right)=1,\left(\genfrac{}{}{0px}{}{1}{2}\right)=0\backslash binom\{1\}\{0\}\; =\; 1,\backslash \; \backslash binom\{1\}\{1\}\; =\; 1,\backslash \; \backslash binom\{1\}\{2\}\; =\; 0$

• $\left(\genfrac{}{}{0px}{}{6}{3}\right)=20,\left(\genfrac{}{}{0px}{}{6}{4}\right)=15,\left(\genfrac{}{}{0px}{}{6}{9}\right)=0\backslash binom\{6\}\{3\}\; =\; 20,\backslash \; \backslash binom\{6\}\{4\}\; =\; 15,\backslash \; \backslash binom\{6\}\{9\}\; =\; 0$

---

Note

• $\mathrm{\forall }n\in \mathbb{N}\cup \{0\}⟹\left(\genfrac{}{}{0px}{}{n}{0}\right)=\left(\genfrac{}{}{0px}{}{n}{n}\right)=1\backslash forall\backslash \; n\; \backslash in\; \backslash mathbb\{N\}\; \backslash cup\; \backslash \{\; 0\; \backslash \}\; \backslash implies\; \backslash binom\{n\}\{0\}\; =\; \backslash binom\{n\}\{n\}\; =\; 1$.

• $\mathrm{\forall }n,k\in \mathbb{N}\cup \{0\}\wedge k>n⟹\left(\genfrac{}{}{0px}{}{n}{k}\right)=0\backslash forall\backslash \; n,k\; \backslash in\; \backslash mathbb\{N\}\; \backslash cup\; \backslash \{\; 0\; \backslash \}\; \backslash land\; k\; \backslash gt\; n\; \backslash implies\; \backslash binom\{n\}\{k\}\; =\; 0$.

• Lines of your code must not exceed 1.

• Length of your code must not exceed 44. (Record: @monadius's 41 characters)

• Disabled modules are numpy, scipy, sklearn, gmpy2, math and sys.

• Disabled built-in functions are open, exec, eval, globals, locals and exit.

• Credits to @Blind4Basics's module forbidder.

---

Tests

• For all tests, $n,k\in \mathbb{N}\cup \{0\}\wedge k<\max (n+2,2n)n,k\; \backslash in\; \backslash mathbb\{N\}\; \backslash cup\; \backslash \{\; 0\; \backslash \}\; \backslash land\; k\; \backslash lt\; \backslash max\; (n+2,\; 2n)$.

• 108 fixed tests, including 6 example tests, 93 mini tests and 9 big tests.

• 300 small random tests, $n\in [100,200)n\; \backslash in\; [100,\; 200)$.

• 20 big random tests, $n\in [1100,1200)n\; \backslash in\; [1100,\; 1200)$.

• One Last Test, $n\in [4990,5000)\wedge k\in [\lfloor \frac{49n}{100}\rfloor ,\lfloor \frac{51n}{100}\rfloor )n\; \backslash in\; [4990,\; 5000)\; \backslash land\; k\; \backslash in\; \backslash left[\backslash lfloor\; \backslash frac\{49n\}\{100\}\; \backslash rfloor,\; \backslash lfloor\; \backslash frac\{51n\}\{100\}\; \backslash rfloor\; \backslash right)$.

---

I hope you enjoy the tests. I had fun writing them. ;)