--description--

A positive integer is a Kaprekar number if:

<ul> <li>It is 1, or,</li> <li>The decimal representation of its square may be split once into two parts consisting of positive integers which sum to the original number. </li> </ul>

Note that a split resulting in a part consisting purely of 0s is not valid, as 0 is not considered positive.

Example Kaprekar numbers:

<ul> <li><code>2223</code> is a Kaprekar number, as <code>2223 * 2223 = 4941729</code>, <code>4941729</code> may be split to <code>494</code> and <code>1729</code>, and <code>494 + 1729 = 2223</code></li> <li>The series of Kaprekar numbers is known as A006886, and begins as <code>1, 9, 45, 55, ...</code></li> </ul>

--instructions--

Write a function that takes a number $n$, a base $bs$, and returns true if the number is a Kaprekar number for the given base. Otherwise, the function returns false.

--hints--

isKaprekar should be a function.

assert(typeof isKaprekar == 'function');

isKaprekar(1, 10) should return a boolean.

assert(typeof isKaprekar(1, 10) == 'boolean');

isKaprekar(1, 10) should return true.

assert.equal(isKaprekar(1, 10), true);

isKaprekar(9, 10) should return true.

assert.equal(isKaprekar(9, 10), true);

isKaprekar(2223, 10) should return true.

assert.equal(isKaprekar(2223, 10), true);

isKaprekar(22823, 10) should return false.

assert.equal(isKaprekar(22823, 10), false);

isKaprekar(9, 17) should return false.

assert.equal(isKaprekar(9, 17), false);

isKaprekar(225, 17) should return true.

assert.equal(isKaprekar(225, 17), true);

isKaprekar(999, 17) should return false.

assert.equal(isKaprekar(999, 17), false);

--seed--

--seed-contents--

function isKaprekar(n, bs) {

}

--solutions--

function isKaprekar(n, bs) {
  if (n < 1) return false;
  if (n == 1) return true;
  for (var a = n * n, b = 0, s = 1; a; s *= bs) {
    b += (a % bs) * s;
    a = Math.floor(a / bs);
    if (b && a + b == n) return true;
  }
  return false;
}