The k-th Binary Decimal Number

A number is called a binary decimal number if its decimal representation consists only of the digits 0 and 1. For example, 101001 is a binary decimal number, but 102002 is not.

For a positive integer $n$, the set $A_n$ is defined as the set of binary decimal multiples of $n$ that have the smallest number of digits. If no binary decimal number is a multiple of $n$, then $A_n$ is the empty set.

Given a positive integer $n$ and a sequence of $m$ positive integers $\\{k_1, k_2, \\cdots, k_m\\}$, write a program that computes the $k_i$-th smallest element of $A_n$ for each value $k_i$ ($1 \le i \le m$) in the sequence.

The first line contains two positive integers $n$ and $m$, separated by a space. ($1 \le n \le 10^6$, $1 \le m \le 10^4$)

From the second line onward, the $(i+1)$-th line contains the value $k_i$. ($1 \le i \le m$, $1 \le k_i \le 10^{18}$)

For each $i$ from 1 to $m$, output one line. If $A_n$ has at least $k_i$ elements, print the $k_i$-th smallest element of $A_n$. Otherwise, print X.