assertEquals(expected, BigIntegerMath.binomial(n, k));
      }
    }
  }

  public void testBinomialOutside() {
    for (int i = 0; i <= 50; i++) {
      int n = i;
      assertThrows(IllegalArgumentException.class, () -> BigIntegerMath.binomial(n, -1));
      assertThrows(IllegalArgumentException.class, () -> BigIntegerMath.binomial(n, n + 1));
    }
  }

  @J2ktIncompatible

  /**
   * Returns {@code n} choose {@code k}, also known as the binomial coefficient of {@code n} and
   * {@code k}, that is, {@code n! / (k! (n - k)!)}.
   *
   * <p><b>Warning:</b> the result can take as much as <i>O(k log n)</i> space.
   *
   * @throws IllegalArgumentException if {@code n < 0}, {@code k < 0}, or {@code k > n}
   */
  public static BigInteger binomial(int n, int k) {
    checkNonNegative("n", n);

  };

  /**
   * Returns {@code n} choose {@code k}, also known as the binomial coefficient of {@code n} and
   * {@code k}, or {@link Integer#MAX_VALUE} if the result does not fit in an {@code int}.
   *
   * @throws IllegalArgumentException if {@code n < 0}, {@code k < 0} or {@code k > n}
   */
  public static int binomial(int n, int k) {
    checkNonNegative("n", n);
    checkNonNegative("k", k);

            .size());

    // Almost force an overflow in the binomial coefficient calculation
    assertEquals(
        1391975640 /*C(34,14)*/,
        Collections2.orderedPermutations(concat(nCopies(20, 1), nCopies(14, 2))).size());
    // Do force an overflow in the binomial coefficient calculation
    assertEquals(
        Integer.MAX_VALUE,

          permutations = IntMath.saturatedMultiply(permutations, IntMath.binomial(n, r));
          r = 0;
          if (permutations == Integer.MAX_VALUE) {
            return Integer.MAX_VALUE;
          }
        }
        n++;
        r++;
      }
      return IntMath.saturatedMultiply(permutations, IntMath.binomial(n, r));
    }

    @Override
    public int size() {
      return size;

            .size());

    // Almost force an overflow in the binomial coefficient calculation
    assertEquals(
        1391975640 /*C(34,14)*/,
        Collections2.orderedPermutations(concat(nCopies(20, 1), nCopies(14, 2))).size());
    // Do force an overflow in the binomial coefficient calculation
    assertEquals(
        Integer.MAX_VALUE,

  };

  /**
   * Returns {@code n} choose {@code k}, also known as the binomial coefficient of {@code n} and
   * {@code k}, or {@link Long#MAX_VALUE} if the result does not fit in a {@code long}.
   *
   * @throws IllegalArgumentException if {@code n < 0}, {@code k < 0}, or {@code k > n}
   */
  public static long binomial(int n, int k) {
    checkNonNegative("n", n);
    checkNonNegative("k", k);

          permutations = IntMath.saturatedMultiply(permutations, IntMath.binomial(n, r));
          r = 0;
          if (permutations == Integer.MAX_VALUE) {
            return Integer.MAX_VALUE;
          }
        }
        n++;
        r++;
      }
      return IntMath.saturatedMultiply(permutations, IntMath.binomial(n, r));
    }

    @Override
    public int size() {
      return size;

                return size;
              }
            };
          }
        };
      }

      @Override
      public int size() {
        return IntMath.binomial(index.size(), size);
      }

      @Override
      public String toString() {
        return "Sets.combinations(" + index.keySet() + ", " + size + ")";
      }
    };
  }

                return size;
              }
            };
          }
        };
      }

      @Override
      public int size() {
        return IntMath.binomial(index.size(), size);
      }

      @Override
      public String toString() {
        return "Sets.combinations(" + index.keySet() + ", " + size + ")";
      }
    };
  }