id	title	challengeType	forumTopicId	dashedName
5900f4ea1000cf542c50fffc	Problem 381: (prime-k) factorial	5	302045	problem-381-prime-k-factorial

--description--

For a prime p let S(p) = (∑(p-k)!) mod(p) for 1 ≤ k ≤ 5.

For example, if p=7, (7-1)! + (7-2)! + (7-3)! + (7-4)! + (7-5)! = 6! + 5! + 4! + 3! + 2! = 720+120+24+6+2 = 872. As 872 mod(7) = 4, S(7) = 4.

It can be verified that ∑S(p) = 480 for 5 ≤ p < 100.

Find ∑S(p) for 5 ≤ p < 108.

--hints--

euler381() should return 139602943319822.

assert.strictEqual(euler381(), 139602943319822);

function euler381() {

  return true;
}

euler381();

// solution required