ACM: Gym 101047B Renzo and the palindromic decoration

 Gym 101047B  Renzo and the palindromic decoration

Time Limit:2000MS     Memory Limit:65536KB     64bit IO Format:%I64d & %I64u

Practice

Description

standard input/output

At the ruins of Wat Phra Si Sanphet (วดพระศรสรรเพชญ), one can find famous inscriptions that have only recently been decoded. Several numbers written using Thai numerals decorate these ruins.

A couple of years ago, the famous Peruvian researcher Renzo "el intrépido" Morales found out that most numbers found at the ruins are palindromic, that is, they represent the same number when read backwards. For instance, 171 is palindromic, whereas 17 is not.

Intrigued by the existence of non palidromic numbers as decorations in the ruins, Renzo found out that, while these numbers are not palindromic when represented in base 10 (which is the base used in the Thai numeral system), they are palindromic when represented in another base. For b > 0, the base-b representation of a number N is the sequence a_ma_m - 1... a₁a₀ so that 0 ≤ a_i ≤ b - 1 for each 0 ≤ i ≤ m, a_m ≠ 0, and

a_mb^m + a_m - 1b^m - 1 + ... + a₁b + a₀ = N.For the previous example, the base-2 representation of 17 is 10001, which is palindromic.

To validate his discovery, Renzo wants you to write a program that takes a number represented in base 10 and checks in which bases from 2 to 16 such number has a palindromic representation.

Input

The first line has a single integer T, the number of test cases.

Each test case has a single line with an integer N written in base 10.

Output

For each test case, print in a single line a space-separated list of integers, from 2 to 16 and in increasing order, of the bases for which the representation of N is palindromic. If N does not have a palindromic representation for any of the bases from 2 to 16, print -1.

Limits

• 0 ≤ T ≤ 10³
• 0 ≤ N < 2³¹

Sample Input

Input

2
17
2570

Output

2 4 16
4 16

/*/
题意：
给你一个数，将这个数换成2~16进制的任何数，如果换成其他进制的数之后能够形成一个回文数【不懂去百度】就输出这个进制。

如果一个都不能形成回文数，输出 -1 。

模拟短除法，暴力解题。

AC代码：
/*/

#include"algorithm"
#include"iostream"
#include"cstring"
#include"cstdio"
#include"string"
#include"vector"
#include"queue"
#include"cmath"
using namespace std;
#define FK(x) cout<<"["<<x<<"]"<<endl
#define memset(x,y) memset(x,y,sizeof(x))
#define memcpy(x,y) memcpy(x,y,sizeof(x))
#define bigfor(x) for(int qq=1;qq<=x;qq++)
#define FIN freopen("input.txt","r",stdin)
#define FOUT freopen("output.txt","w+",stdout)

int ans[20];

bool ok(int n,int i) {
	memset(ans,0);
	int erear=0;
	while(n) {
		ans[erear++]=n%i;
		n/=i;
	}
	for(int j=0; j<erear/2; j++) {
		if(ans[j]!=ans[erear-1-j])return 0;
	}
	return 1;
}

int main() {
	int T;
	scanf("%d",&T);
	bigfor(T) {
		int n;
		scanf("%d",&n);
		int first=1;
		int sign=1;
		for(int i=2; i<17; i++) {
			if(ok(n,i)) {
				if(first) first=0;
				else printf(" ");
				printf("%d",i);
				sign=0;
			}
		}
		if(sign)puts("-1");
		else puts("");
	}
	return 0;
}