Power Substring
题意翻译
给你一个长为 $n$ 的正整数序列。
对于每个 $a_{i}$,你需要找到一个正整数 $k_{i}$ ,使得 $a_{i}$(十进制)是 $2^{k_{i}}$(十进制)最后 $\min(100$,$2^{k_{i}})$ 位的数字的一个子串。
不需要最小化 $k_{i}$。
问题中的十进制不包含前导零。
$1\le n\le 2000$,$1\le a_i\le 10^{11}$,正整数 $k_{i}$ 必须满足 $1\le k_i\le 10^{50}$。
保证有解。
如果有多个答案,输出任意一个。
题目描述
You are given $ n $ positive integers $ a_{1},a_{2},...,a_{n} $ .
For every $ a_{i} $ you need to find a positive integer $ k_{i} $ such that the decimal notation of $ 2^{k_{i}} $ contains the decimal notation of $ a_{i} $ as a substring among its last $ min(100,length(2^{k_{i}})) $ digits. Here $ length(m) $ is the length of the decimal notation of $ m $ .
Note that you don't have to minimize $ k_{i} $ . The decimal notations in this problem do not contain leading zeros.
输入输出格式
输入格式
The first line contains a single integer $ n $ ( $ 1<=n<=2000 $ ) — the number of integers $ a_{i} $ .
Each of the next $ n $ lines contains a positive integer $ a_{i} $ ( $ 1<=a_{i}<10^{11} $ ).
输出格式
Print $ n $ lines. The $ i $ -th of them should contain a positive integer $ k_{i} $ such that the last $ min(100,length(2^{k_{i}})) $ digits of $ 2^{k_{i}} $ contain the decimal notation of $ a_{i} $ as a substring. Integers $ k_{i} $ must satisfy $ 1<=k_{i}<=10^{50} $ .
It can be shown that the answer always exists under the given constraints. If there are multiple answers, print any of them.
输入输出样例
输入样例 #1
2
8
2
输出样例 #1
3
1
输入样例 #2
2
3
4857
输出样例 #2
5
20