13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T745,

An array $$$a$$$ is called a subsequence of an array $$$b$$$ if some elements can be removed from array $$$b$$$ (possibly all, possibly none) to obtain the array $$$a$$$.

You are given an array $$$a = [a_1, a_2, \dots, a_n]$$$. We call an array $$$b = [b_1, b_2, \dots, b_m]$$$ beautiful if:

$$$a$$$ is a subsequence of $$$b$$$;
for each $$$i$$$ from $$$1$$$ to $$$m-1$$$, the elements $$$b_i$$$ and $$$b_{i+1}$$$ differ by exactly $$$1$$$ (that is, $$$|b_i - b_{i+1}| = 1$$$);
among all arrays that satisfy these two requirements, the length of $$$b$$$ is minimum.

You have to process $$$q$$$ queries. In the $$$i$$$-th query, a single integer $$$x_i$$$ is given. Your task is as follows:

if $$$x_i$$$ is greater than the minimum possible number of elements in a beautiful array, print $$$-1$$$;
otherwise, if the same number occupies position $$$x_i$$$ in all beautiful arrays, print that number;
otherwise, print $$$0$$$.

Supersequence

Examples