AnEasyProblem | Topcoder Archive

Problem Statement

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For positive integers h and r (1 &lt= r &lt= h) we define sequence F_h,r as {1, 2, 3, ..., h-1, h, h-1, h-2, ..., r+1, r}. Let S(F_h,r) be the the sum of all numbers in F_h,r and N(F_h,r) - the length of F_h,r.

For example, F_3,2 is {1, 2, 3, 2}, S(F_3,2) = 1 + 2 + 3 + 2 = 8, and N(F_3,2) = 4. F_5,5 is {1, 2, 3, 4, 5}, S(F_5,5) = 15, and N(F_5,5) = 5.

You are given a long sum. Return minimal possible N(F_i,j) such that S(F_i,j) = sum. If there is no such sequence F_i,j, return -1 instead.

Definition

Class:: AnEasyProblem
Method:: solve
Parameters:: long
Returns:: int
Method signature:: int solve(long sum)
(be sure your method is public)

Constraints

sum will be between 1 and 1,000,000,000,000(10^12).

Examples

```
6
```
```
Returns: 3
```
When h = r = 3, S(Fh,r) = 6 and N(Fh,r) = 3. There is no other h,r satisfing S(Fh,r) = 6. So you should return 3.
```
7
```
```
Returns: -1
```
```
100
```
```
Returns: 15
```
```
1000000000000
```
```
Returns: 1428571
```

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