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Consider all the words which can be formed by selecting letters, in any order, from the phrase:

$$\mathbf{\text{thereisasyetinsufficientdataforameaningfulanswer}}$$

Suppose those with 15 letters or less are listed in alphabetical order and numbered sequentially starting at 1.

The list would include:

$$\begin{align} & 1: \text{a} \\ & 2: \text{aa} \\ & 3: \text{aaa} \\ & 4: \text{aaaa} \\ & 5: \text{aaaaa} \\ & 6: \text{aaaaaa} \\ & 7: \text{aaaaaac} \\ & 8: \text{aaaaaacd} \\ & 9: \text{aaaaaacde} \\ & 10: \text{aaaaaacdee} \\ & 11: \text{aaaaaacdeee} \\ & 12: \text{aaaaaacdeeee} \\ & 13: \text{aaaaaacdeeeee} \\ & 14: \text{aaaaaacdeeeeee} \\ & 15: \text{aaaaaacdeeeeeef} \\ & 16: \text{aaaaaacdeeeeeeg} \\ & 17: \text{aaaaaacdeeeeeeh} \\ & \ldots \\ & 28: \text{aaaaaacdeeeeeey} \\ & 29: \text{aaaaaacdeeeeef} \\ & 30: \text{aaaaaacdeeeeefe} \\ & \ldots \\ & 115246685191495242: \text{euleoywuttttsss} \\ & 115246685191495243: \text{euler} \\ & 115246685191495244: \text{eulera} \\ & ... \\ & 525069350231428029: \text{ywuuttttssssrrr} \\ \end{align}$$

Define $P(w)$ as the position of the word $w$.

Define $W(p)$ as the word in position $p$.

We can see that $P(w)$ and $W(p)$ are inverses: $P(W(p)) = p$ and $W(P(w)) = w$.

Examples:

$$\begin{align} & W(10) = \text{ aaaaaacdee} \\ & P(\text{aaaaaacdee}) = 10 \\ & W(115246685191495243) = \text{ euler} \\ & P(\text{euler}) = 115246685191495243 \\ \end{align}$$

Find $$W(P(\text{legionary}) + P(\text{calorimeters}) - P(\text{annihilate}) + P(\text{orchestrated}) - P(\text{fluttering})).$$

Give your answer using lowercase characters (no punctuation or space).

--hints--

euler480() should return a string.

assert.isString(euler480());

euler480() should return the string turnthestarson.

assert.strictEqual(euler480(), 'turnthestarson');

--seed--

--seed-contents--

function euler480() {

  return true;
}

euler480();

--solutions--

// solution required