## The Last Question

### Problem 480

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

**thereisasyetinsufficientdataforameaningfulanswer**

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

The list would include:

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

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:

`W`(10) = aaaaaacdee`P`(aaaaaacdee) = 10`W`(115246685191495243) = euler`P`(euler) = 115246685191495243

Find `W`(`P`(legionary) + `P`(calorimeters) - `P`(annihilate) + `P`(orchestrated) - `P`(fluttering)).

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