#P1216E1. Numerical Sequence (easy version)
Numerical Sequence (easy version)
No submission language available for this problem.
Description
The only difference between the easy and the hard versions is the maximum value of $k$.
You are given an infinite sequence of form "112123123412345$\dots$" which consist of blocks of all consecutive positive integers written one after another. The first block consists of all numbers from $1$ to $1$, the second one — from $1$ to $2$, the third one — from $1$ to $3$, $\dots$, the $i$-th block consists of all numbers from $1$ to $i$.
So the first $56$ elements of the sequence are "11212312341234512345612345671234567812345678912345678910". Elements of the sequence are numbered from one. For example, the $1$-st element of the sequence is $1$, the $3$-rd element of the sequence is $2$, the $20$-th element of the sequence is $5$, the $38$-th element is $2$, the $56$-th element of the sequence is $0$.
Your task is to answer $q$ independent queries. In the $i$-th query you are given one integer $k_i$. Calculate the digit at the position $k_i$ of the sequence.
The first line of the input contains one integer $q$ ($1 \le q \le 500$) — the number of queries.
The $i$-th of the following $q$ lines contains one integer $k_i$ $(1 \le k_i \le 10^9)$ — the description of the corresponding query.
Print $q$ lines. In the $i$-th line print one digit $x_i$ $(0 \le x_i \le 9)$ — the answer to the query $i$, i.e. $x_i$ should be equal to the element at the position $k_i$ of the sequence.
Input
The first line of the input contains one integer $q$ ($1 \le q \le 500$) — the number of queries.
The $i$-th of the following $q$ lines contains one integer $k_i$ $(1 \le k_i \le 10^9)$ — the description of the corresponding query.
Output
Print $q$ lines. In the $i$-th line print one digit $x_i$ $(0 \le x_i \le 9)$ — the answer to the query $i$, i.e. $x_i$ should be equal to the element at the position $k_i$ of the sequence.
Samples
5
1
3
20
38
56
1
2
5
2
0
4
2132
506
999999999
1000000000
8
2
9
8
Note
Answers on queries from the first example are described in the problem statement.