Timus 1209. 1, 10, 100, 1000...

Timus 1209. 1, 10, 100, 1000... 要求给出特定序列的指定位置的值。

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1209. 1, 10, 100, 1000...

Time Limit: 1.0 second
Memory Limit: 16 MB

Let's consider an infinite sequence of digits constructed of ascending powers of 10 written one after another. Here is the beginning of the sequence: 110100100010000… You are to find out what digit is located at the definite position of the sequence.

Input

There is the only positive integer number N in the first line, N < 65536. The i-th of N left lines contains the positive integer K_i — the number of position in the sequence. It's given that K_i < 2³¹.

Output

You are to output N digits 0 or 1 separated with a space. More precisely, the i-th digit of output is to be equal to the K_i-th digit of described above sequence.

Sample

input	output
4 3 14 7 6	0 0 1 0

Problem Author: Alexey Lakhtin
Problem Source: USU Open Collegiate Programming Contest October'2002 Junior Session

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这道题目是说，让我们考虑依次由10的非负整数次方连接在一起构成的无限序列：110100100010000…。你的任务是给出该序列指定位置的值。

通过仔细观察，可以看出，该序列中第 (x + 1) 个 1 位于第 N = 1 + (1 + 2 + ... x) = 1 + x(x + 1) / 2 个位置。解这个关于 x 的一元二次方程，得到它的非负根为：x = (√8N - 7 - 1) / 2。于是，当 x 是整数时，该序列中对应的第 N 个位置的值是 1，其余位置的值是 0。

下面就是相应的 C# 程序：

 1 using System;
 2 
 3 // http://acm.timus.ru/problem.aspx?space=1&num=1209
 4 class T1209
 5 {
 6   static void Main()
 7   {
 8     for (int i = int.Parse(Console.ReadLine()); i > 0; i--)
 9     {
       double x = (Math.Sqrt(8.0 * int.Parse(Console.ReadLine()) - 7) - 1) / 2;
       Console.Write(((x == (int)x) ? 1 : 0) + " ");
     }
   }
 }

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