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..." 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, ..., 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.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 500) — the number of queries.

The i-th of the following q lines contains one integer k_i (1 ≤ k_i ≤ 10^9) — the description of the corresponding query.

Output

Print q lines. In the i-th line print one digit x_i (0 ≤ x_i ≤ 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.

Examples

Input


5
1
3
20
38
56


Output


1
2
5
2
0


Input


4
2132
506
999999999
1000000000


Output


8
2
9
8

Note

Answers on queries from the first example are described in the problem statement.
import java.io.*; 
import java.math.*;
import java.util.*;
 
public class Main {
	//static final long MOD = 998244353;
	static final long MOD = 1000000007;
	static boolean[] visited;
    public static void main(String[] args) throws IOException {
        FastScanner sc=new FastScanner();
        int Q = sc.nextInt();
        HashSet<Integer> tens = new HashSet<Integer>();
        for (int i = 0; i <= 5; i++)
        	tens.add((int)Math.pow(10,i));
        
        int n = 0;
        int d = 0;
        int[] places = new int[21837];
        places[0] = 0;
        for (int i = 1; i < places.length; i++) {
        	if (tens.contains(i))
        		d++;
        	n += d;
        	places[i] = places[i-1] + n;
        }
        StringBuilder str = new StringBuilder();
        for (int i = 1; i < places.length; i++) {
        	str.append(i);
        }
        StringBuilder ans = new StringBuilder();
        for (int q = 0; q < Q; q++) {
        	int index = sc.nextInt();
        	int pos = 0;
        	int num = 0;
        	int low = 0;
        	int high = places.length-1;
        	while (low < high) {
        		int mid = (low+high)/2;
        		if (places[mid] >= index) {
        			high = mid;
        		} else {
        			low = mid+1;
        		}
        	}
        	num = low;
        	pos = index-places[low-1];
        	ans.append(str.charAt(pos-1) + "\n");
        }
        System.out.print(ans);
    }

    public static int gcd(int a, int b) {
    	if (b == 0)
    		return a;
    	else
    		return gcd(b,a%b);
    }
    
    public static int[][] sort(int[][] array) {
    	//Sort an array (immune to quicksort TLE)
		Random rgen = new Random();
		for (int i = 0; i < array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    int[] temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
		Arrays.sort(array, new Comparator<int[]>() {
			  @Override
        	  public int compare(int[] arr1, int[] arr2) {
	        	    if (arr1[0] != arr2[0])
	        	    	return arr1[0]-arr2[0];
	        	    else
	        	    	return arr1[1]-arr2[1];
	         }
		});
		return array;
	}
    
    static class FastScanner { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastScanner() { 
            br = new BufferedReader(new InputStreamReader(System.in)); 
        } 
  
        String next() { 
            while (st == null || !st.hasMoreElements()) { 
                try { 
                    st = new StringTokenizer(br.readLine());
                } catch (IOException  e) { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() { 
            String str = ""; 
            try { 
                str = br.readLine(); 
            } catch (IOException e) {
                e.printStackTrace(); 
            } 
            return str; 
        }
    }
}