A11516 | Power Substring

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.

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 $a_{i}$ ( $1<=a_{i}<10^{11}$ ).

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.