## Algorithm

A single positive integer i is given. Write a program to find the digit located in the position i in the sequence of number groups S1S2 . . . Sk. Each group Sk consists of a sequence of positive integer numbers ranging from 1 to k, written one after another. For example, the first 80 digits of the sequence are as follows: 11212312341234512345612345671234567812345678912345678910123456789101112345678910 Input The first line of the input file contains a single integer t (1 ≤ t ≤ 25), the number of test cases, followed by one line for each test case. The line for a test case contains the single integer i (1 ≤ i ≤ 2147483647) Output There should be one output line per test case containing the digit located in the position i.

Sample Input 2 8 3

Sample Output 2 2

## Code Examples

### #1 Code Example with C Programming

```Code - C Programming```

``````#include <bits/stdc++.h>
using namespace std;

int main()
{
string sequence = ""; // store single sequence
int totalLength=0; // length from 1 to n
vector < long long> lens(1,0); // cumulative length of concat seq
for(int i=1;i < 35000;i++){
int length = (int)log10(i)+1;
totalLength += length;
sequence += to_string(i);
lens.push_back(totalLength+lens.back());
}

int t,v;
cin >> t;
while(t--){
cin >> v;
int low = 0, high = 34999;
// bisect right to find next smaller sequence
while(low < high){
int mid = (low+high)/2+1;
if(lens[mid] >= v) high = mid-1;
else low = mid;
}
// n-th digit in sequence
printf("%c\n", sequence[v-lens[high]-1]);
}
}
``````
Copy The Code &

Input

cmd
2
8
3

Output

cmd
2
2