Double it（水题模拟+逆向思维）

Alex has two magic machines A and B. Machine A will give you 2x + 1 coins if you insert x coins in it, machine B will give you 2x + 2. Alex has no coins and wants to get exactly n coins in order to buy a new unicorn, but he can't figure out how to do it. Your task is to find a way to use the machines to get exactly n coins.

 

Input

The input consists of a single line containing n(1 ≤ n ≤ 10⁹).

Output

For each one output a string of A's and B's giving the order in which the machines are used.

 

Examples

Input

7

Output

AAA

Input

10

Output

ABB

这道题写了好长时间才过，最后我只能说读题很重要！

 

 

题意：

利用A，B两台机器可以获得硬币，规则如下：

ya = 2 * x + 1;

yb = 2 * x + 2; 

x为投进机器的硬币数

刚开始没硬币，想获得恰好n枚硬币，问投硬币的顺序如何

没钱也能钱生钱，你说这气不气人

 

 

思路：

可以以n为起点往后推，若当前硬币数为偶数，则一定是从B来的，否则则是A

 

#include <stdio.h>
#include <string.h>

char re[1000000];

int main()
{
    long long n, cur, i;
    scanf("%lld", &n);
    cur = 0;
    
    while(n!=0)
    {
        if(n%2==0)
        {
            re[cur++] = 'B';
            n = (n-2)/2;
        }
        else
        {
            re[cur++] = 'A';
            n = (n-1)/2;
        }
    }

    for(i=cur-1;i>=0;i--)
    {
        printf("%c", re[i]);
    }
    printf("\n");

    return 0;
}