CF317A.Perfect Pair

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题目描述

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

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

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

输入格式

Single line of the input contains three integers xx , yy and mm ( 1018<=x-10^{18}<=x , yy , m<=1018m<=10^{18} ).

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.

输出格式

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

输入输出样例

  • 输入#1

    1 2 5
    

    输出#1

    2
    
  • 输入#2

    -1 4 15
    

    输出#2

    4
    
  • 输入#3

    0 -1 5
    

    输出#3

    -1
    

说明/提示

In the first sample the following sequence of operations is suitable: (1, 2) (3, 2) (5, 2).

In the second sample: (-1, 4) (3, 4) (7, 4) (11, 4) (15, 4).

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

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