const binomialCoefficient = (n: number, k: number) => {
  if (k < 0 || k > n) return 0;
  if (k === 0 || k === n) return 1;
  if (k === 1 || k === n - 1) return n;
  if (n - k < k) k = n - k;
  let res: number = n;
  for (let j: number = 2; j <= k; j++) res *= (n - j + 1) / j;
  return Math.round(res);
};