In ACM labs, there are only few members who have girlfriends. And these people can make FFF Party angry easily. One day, FFF Party prepared a function FF and a set SS.
\displaystyle F(x)=\left\{ \begin{aligned} 1,&& n = 1,2 \\ F(n - 1) + F(n - 2), && n\ge3 \end{aligned} \right.F(x)={1,F(n−1)+F(n−2),n=1,2n≥3
There are several unequal positive integers f_ifi in the set SS.
They calculated the value of W = \sum_{f \in S} F(F(f))W=∑f∈SF(F(f)) , and tried to cause WWdamage to those who have girlfriends. Suppose you are not a single dog and have been attacked. Now, give you the value of WW and please write a program to calculate these f_ifi in set SS.
Input
The first line consists of a single integer TTdenoting the number of test cases.
TT lines follow, with an integer in each, denoting the result of WW.
Output
For each test case, print a sequence of space-separated integers f_ifi satisfying the equation.
If there are more than one answers, please print the lexicographically smallest one.
If there’s no such sequence, print -1−1 instead.
Constraints
1 \le T \le 101≤T≤10
1 \le W \le 10^{100,000}1≤W≤10100,000
样例输入复制
2 1 3
样例输出复制
1 1 2 3
队友说是暴力？。
import java.math.BigInteger;
import java.util.Scanner;
//import java.io.FileOutputStream;
//import java.io.PrintStream;
//import java.io.FileNotFoundException;
public class Main {
public static void main(String[] args) {// throws FileNotFoundException {
// TODO 自动生成的方法存根
// PrintStream ps = new PrintStream("D:\\Albert\\out.txt");
// System.setOut(ps);
BigInteger ONE = BigInteger.ONE;
BigInteger ZER = BigInteger.ZERO;
BigInteger TWO = BigInteger.valueOf(2);
BigInteger THR = BigInteger.valueOf(3);
BigInteger FOR = BigInteger.valueOf(4);
BigInteger FIV = BigInteger.valueOf(5);
BigInteger SIX = BigInteger.valueOf(6);
BigInteger SEV = BigInteger.valueOf(7);
BigInteger EIG = BigInteger.valueOf(8);
BigInteger NIN = BigInteger.valueOf(9);
BigInteger TEN = BigInteger.valueOf(10);
BigInteger res[] = new BigInteger[30];
Scanner sc = new Scanner(System.in);
for(int i = 1; i <= 29; ++i)
{
BigInteger n = BigInteger.valueOf(i);
n = n.subtract(BigInteger.ONE);//
BigInteger a[][] = { { ONE, ONE }, { ONE, ZER } };
BigInteger b[][] = { { ONE, ZER }, { ZER, ONE } };// 单位矩阵
while (n.compareTo(ZER) != 0) {
if ((n.and(ONE)).compareTo(ONE) == 0) {
b = q(a, b);
}
a = q(a, a);
n = n .divide(TWO);
}
n = b[0][0];
n = n.subtract(ONE);
// System.out.print(i);
// System.out.print(' ');
//
// System.out.print(n);
// System.out.print(' ');
a[0][0] = b[0][0] = ONE;
a[0][1] = ONE;
a[1][0] = b[1][1] = ONE;
a[1][1] = b[0][1] = b[1][0] = ZER;
while (n.compareTo(ZER) != 0) {
if ((n.and(ONE)).compareTo(ONE) == 0) {
b = q(a, b);
}
a = q(a, a);
n = n .divide(TWO);
}
res[i]= b[0][0];
// System.out.println(res[i]);
}
// for(int i = 1; i <= 10; ++i)
// System.out.println(res[i]);
int t = sc.nextInt(), idx;
int ans[] = new int[30];
BigInteger tar;
while((t--) > 0)
{
idx = 0;
tar = sc.nextBigInteger();
// System.out.println(tar);
for(int i = 29; i >= 1; --i)
{
if(tar.compareTo(TEN) < 0)
{
if(tar.compareTo(NIN) == 0)
{
ans[idx++] = 5;
ans[idx++] = 4;
ans[idx++] = 2;
ans[idx++] = 1;
}
else if(tar.compareTo(EIG) == 0)
{
ans[idx++] = 5;
ans[idx++] = 3;
ans[idx++] = 2;
ans[idx++] = 1;
}
else if(tar.compareTo(SEV) == 0)
{
ans[idx++] = 5;
ans[idx++] = 2;
ans[idx++] = 1;
}
else if(tar.compareTo(SIX) == 0)
{
ans[idx++] = 5;
ans[idx++] = 1;
}
else if(tar.compareTo(FIV) == 0)
{
ans[idx++] = 4;
ans[idx++] = 3;
ans[idx++] = 2;
ans[idx++] = 1;
}
else if(tar.compareTo(FOR) == 0)
{
ans[idx++] = 4;
ans[idx++] = 2;
ans[idx++] = 1;
}
else if(tar.compareTo(FOR) == 0)
{
ans[idx++] = 3;
ans[idx++] = 2;
ans[idx++] = 1;
}
else if(tar.compareTo(THR) == 0)
{
ans[idx++] = 3;
ans[idx++] = 2;
ans[idx++] = 1;
}
else if(tar.compareTo(TWO) == 0)
{
ans[idx++] = 2;
ans[idx++] = 1;
}
else if(tar.compareTo(ONE) == 0)
{
ans[idx++] = 1;
}
tar = ZER;
}
if(tar.compareTo(res[i]) >= 0)
{
tar = tar.subtract(res[i]);
ans[idx++] = i;
}
}
if(tar.compareTo(ZER) == 0)
{
for(int i = idx - 1; i > 0; --i)
{
System.out.print(ans[i]);
System.out.print(' ');
}
System.out.println(ans[0]);
}
else
System.out.println(-1);
}
}
static BigInteger[][] q(BigInteger a[][], BigInteger b[][]) {//
BigInteger value1 = (a[0][0].multiply(b[0][0])).add((a[0][1].multiply(b[1][0])));// 左上
BigInteger value2 = (a[0][0].multiply(b[0][1])).add((a[0][1].multiply(b[1][1])));// 左上
BigInteger value3 = (a[1][0].multiply(b[0][0])).add((a[1][1].multiply(b[1][0])));// 左上
BigInteger value4 = (a[1][0].multiply(b[0][1])).add((a[1][1].multiply(b[1][1])));// 左上
BigInteger c[][] = new BigInteger[2][2];
c[0][0] = value1;
c[0][1] = value2;
c[1][0] = value3;
c[1][1] = value4;
return c;
}
}