Description

The Tower of Hanoi is a mathematical game puzzle. It consists of three rods, which are A, B and C. The puzzle starts with n disks in ascending order of size on rod A, the smallest at the top.

The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules:

1.   Only one disk can be moved at a time.

2.   Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack i.e. a disk can only be moved if it is the uppermost disk on a stack.

3.   No disk may be placed on top of a smaller disk.

Write a program to simulate the optimal moves of the disks. Print the number of disk which is moved in each step.

For example, if n = 3, the moves of each steps are:

move disk 1 from rod A to rod C
move disk 2 from rod A to rod B
move disk 1 from rod C to rod B
move disk 3 from rod A to rod C
move disk 1 from rod B to rod A
move disk 2 from rod B to rod C
move disk 1 from rod A to rod C

HINT : You can modify this sample code and implement the function 'hanoi'

#include <stdio.h>
void hanoi(int n, char A, char B, char C);

int main(){
    int n;
    scanf("%d", &n);
    hanoi(n, 'A', 'B', 'C');
    return 0;
}

Input

An integer n (0<n<20), which means the number of disk.

Output

Print out the information of each step, and there is a '\n' at the end of each line.

Sample Input  Download

Sample Output  Download

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Description

In mathematics, the Fibonacci numbers can be defined by the recurrence relation:

For example, if n = 3, the corresponding result will be 3.

 

Here, we want to find the reverse Fibonacci numbers defined by a similar but different recurrence relation:

For example, if G0 = 1, G1=-1, the reverse Fibonacci sequence will be like: 1,-1,2,-3,5,-8, ....

 

In this problem, given G0, G1, and n, please calculate Gn.

Input

There will be three integers(G0, G1, and n) separated by white space.

Note: ( -100000 <=G0, G1<= 100000) and (0 <= n <= 30)

Output

The nth number, Gn,  in the reverse Fibonacci number.

Note that you need to print "\n" at the end.

Sample Input  Download

Sample Output  Download

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Description

Calculate the greatest common divisor of two integers.

In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted .

For example, the GCD of 8 and 12 is 4, that is, 

Input

Two integers x, y

1 < x, y< 10000

Output

Output the greatest common divisor.

Don't forget to include '\n'

Sample Input  Download

Sample Output  Download

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