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35 lines
1.9 KiB
HTML
35 lines
1.9 KiB
HTML
<!DOCTYPE html>
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<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
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<h1>1019. General Palindromic Number (20)</h1>
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<div id="problemContent">
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<p>A number that will be the same when it is written forwards or backwards is known as a Palindromic Number. For example, 1234321 is a palindromic number. All single digit numbers are palindromic numbers.
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</p>
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<p>Although palindromic numbers are most often considered in the decimal system, the concept of palindromicity can be applied to the natural numbers in any numeral system. Consider a number N > 0 in base b >= 2, where it is written in standard notation with k+1 digits a<sub>i</sub> as the sum of (a<sub>i</sub>b<sup>i</sup>) for i from 0 to k. Here, as usual, 0 <= a<sub>i</sub> < b for all i and a<sub>k</sub> is non-zero. Then N is palindromic if and only if a<sub>i</sub> = a<sub>k-i</sub> for all i. Zero is written 0 in any base and is also palindromic by definition.
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</p>
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<p>Given any non-negative decimal integer N and a base b, you are supposed to tell if N is a palindromic number in base b.
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</p>
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<p><b>
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Input Specification:
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</b></p>
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<p>Each input file contains one test case. Each case consists of two non-negative numbers N and b, where 0 <= N <= 10<sup>9</sup> is the decimal number and 2 <= b <= 10<sup>9</sup> is the base. The numbers are separated by a space.
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</p>
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<p><b>
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Output Specification:
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</b></p>
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<p>For each test case, first print in one line "Yes" if N is a palindromic number in base b, or "No" if not. Then in the next line, print N as the number in base b in the form "a<sub>k</sub> a<sub>k-1</sub> ... a<sub>0</sub>". Notice that there must be no extra space at the end of output.
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</p>
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<b>Sample Input 1:</b><pre>
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27 2
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</pre>
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<b>Sample Output 1:</b><pre>
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Yes
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1 1 0 1 1
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</pre>
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<b>Sample Input 2:</b><pre>
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121 5
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</pre>
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<b>Sample Output 2:</b><pre>
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No
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4 4 1
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</pre>
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</div> |