Perfect Pair

1000ms

262144K

Description:

Let us call a pair of integer numbers m-perfect, if at least one number in the pair is greater than or equal to m. Thus, the pairs (3, 3) and (0, 2) are 2-perfect while the pair (-1, 1) is not.

Two integers x, y are written on the blackboard. It is allowed to erase one of them and replace it with the sum of the numbers, (x + y).

What is the minimum number of such operations one has to perform in order to make the given pair of integers m-perfect?

Input:

Single line of the input contains three integers x, y and m ( - 10¹⁸ ≤ x, y, m ≤ 10¹⁸).

Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preffered to use the cin, cout streams or the %I64d specifier.

Output:

Print the minimum number of operations or "-1" (without quotes), if it is impossible to transform the given pair to the m-perfect one.

Sample Input:

1 2 5

Sample Output:

Sample Input:

-1 4 15

Sample Output:

Sample Input:

0 -1 5

Sample Output:

-1

Note:

In the first sample the following sequence of operations is suitable: (1, 2) $\text{[math]}$ (3, 2) $\text{[math]}$ (5, 2).

In the second sample: (-1, 4) $\text{[math]}$ (3, 4) $\text{[math]}$ (7, 4) $\text{[math]}$ (11, 4) $\text{[math]}$ (15, 4).

Finally, in the third sample x, y cannot be made positive, hence there is no proper sequence of operations.

Informação

Provedor Codeforces

Código CF317A