401636: GYM100503 D Sequence analysis

D. Sequence analysistime limit per test10 secondsmemory limit per test64 megabytesinputinput.txtoutputoutput.txt

You are given a sequence of signed 64-bit integers defined as follows:

• x₀ = 1,
• ,

where mod is a remainder operator. All arithmetic operations are evaluated without overflow checking. Use standard "remainder" operator for programming languages (it differs from the mathematical version; for example in programming, while in mathematics). Use "long long" type in C++, "long" in Java and "int64" in Delphi to store x_i and all other values.

Let's call a sequence element x_p repeatable if it occurs later in the sequence — meaning that there exists such q, q > p, that x_q = x_p. The first repeatable element M of the sequence is such an element x_m that x_m is repeatable, and none of the x_p where p < m are repeatable.

Given A, B and C, your task is to find the index of the second occurrence of the first repeatable element M in the sequence if the index is less or equal to 2·10⁷. Per definition, the first element of the sequence has index 0.

Input

The only line of input contains three signed 64-bit integers: A, B and C (B > 0, C > 0).

Output

Print a single integer  — the index of the second occurence of the first repeatable member if it is less or equal to 2·10⁷. Print  - 1 if the index is more than 2·10⁷.

ExamplesInput

2 2 9

Output

4

Input

2305843009213693951 1 9223372036854775807

Output

5

Input

-2 1 5

Output

4

Note

In the first sample test the sequence starts with the following numbers: 1, 3, 7, 6, 3, 7. The first repeatable element is 3. The second occurence of 3 has index 4.

In the second sample test the sequence starts with the following numbers: 1, 2305843009213693951, -4611686018427387903, 6917529027641081855, 0, 0, 0. The first repeatable element is 0. The second occurence of 0 has index 5.

In the third sample test the sequence starts with the following numbers: 1, -2, 4, -3, 1, -2, 4. The first repeatable element is 1. The second occurence of 1 has index 4.