public static long fallingPower(int n, int k) (please use Java to solve) Python has the integer exponentation operator ** conveniently built in the language, whereas Java unfortunately does not offer...

public static long fallingPower(int n, int k)

(please use Java to solve)

Python has the integer exponentation operator ** conveniently built in the language, whereas Java unfortunately does not offer that operator that would be mostly useless anyway in a language with fixed size integers that silently hide the overflows easily produced by integer exponentiation. (In both languages, thecaretcharacter ^ denotes thebitwise exclusive oroperation that has bupkis to do with integer exponentiation.)

In the related operation offalling power
that is useful in many combinatorial formulas and denoted syntactically by underlining the exponent, each term that gets multiplied into the product is always one less than the previous term. For example, the falling power 8³
is computed as 8 * 7 * 6 = 336. Similarly, the falling power 10⁵
equals 10 * 9 * 8 * 7 * 6 = 30240. Nothing essential changes even if the base n is negative; the falling power (-4)⁵
is computed as -4 * -5 * -6 * -7 * -8 = -6720.

This method should compute and return the falling power n^k
where the base n can be any integer, and the exponent k can be anynonnegative
integer. (Analogous to ordinary powers, n⁰
= 1 for any integer n.) The JUnit fuzz tests are designed so that your method does not have to worry about potential integer overflow... provided that you perform your arithmetic calculations with the long kind of 64-bit integers! If you use the bare 32-bit int type, a silent integeroverflow
will make your method occasionally return incorrect results and fail the JUnit tests, even if that method totes worked correctly when you tried it with your own small values of n.