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.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;

public class Codeforces {

    static double Phi = (1 + Math.sqrt(5)) / 2.0;
    static int MAX = -1 >>> 1;
    static long MODL = 1_000_000_007L;
    static int MOD = 1_000_000_007;
    static void no() throws IOException {println("NO");}
    static void yes() throws IOException {println("YES");}

    static boolean testCases = true;
    static boolean DEBUG = true;

    static void main() throws Exception {
        long k = nl();
        int level = 1;
        while(true) {
            long ls = levelSum(level);
            assert ls > 0;
            if(k > ls) {++level; k -= ls;}
            else {
                break;
            }
        }
        // digits lvl-1 done
        assert k > 0;
        // stuck at level digits
        int lo = 1;
        int hi = 9 * (int) Math.pow(10, level - 1);
        int mid;
        int ans = -1;
        while(lo <= hi) {
            mid = lo + (hi - lo >> 1);
            long pred = k - levelMidSum(level, mid);
            if(pred > 0) {
                lo = mid + 1;
                ans = mid;
            } else {
                hi = mid - 1;
            }
        }
        if(ans > -1) k -= levelMidSum(level, ans);
        println(finalAns(k));
    }
    static long finalAns(long k) throws Exception {
        long input = k;
        if(k < 10) {
            return k;
        }
        int d = 1;
        while(k > d * maxNumLevel(d)) {
            k -= d * maxNumLevel(d);
            ++d;
        }
        //answer is d digits number
        long base = (long) Math.pow(10, d - 1) + k / d;
        k %= d;
        // debug(input + " " + k + " " + base + " " + d);
        if(k == 0) {
            return (base - 1) % 10;
        } else {
            int kk = (int) k - 1;
            long ans = (base + "").charAt(kk) - '0';
            return ans;
        }
    }
    static long levelMidSum(int level, int mid) throws IOException {
        long lValue = level * ((mid * (mid + 1)) >> 1);
        long others = 0;
        for(int i = 1; i < level; ++i) {
            others += i * maxNumLevel(i);
        }
        return lValue + others * mid;
    }
    static long levelSum(int level) {
        long tCount = maxNumLevel(level);
        long lValue = level * ((tCount * (tCount + 1)) >> 1);
        long others = 0;
        for(int i = 1; i < level; ++i) {
            others += i * maxNumLevel(i);
        }
        return lValue + others * maxNumLevel(level);
    }    
    //ok
    static long maxNumLevel(int level) {
        return 9 * (long) Math.pow(10, level - 1);
    }
    public static void main(String[] args) throws Exception {
        long startPointTime = System.currentTimeMillis();
        scannerIn = System.in;
        printerBW = new BufferedWriter(new OutputStreamWriter(System.out));
        if (DEBUG && System.getProperty("ONLINE_JUDGE") == null) {
            HABLA = true;
            debug("Debugging enabled");
        }

        int t = testCases ? ni() : 1;
        int to = t;
        while (t-- > 0) {
            debug("Case #" + (to - t) + " ---------------- ");
            main();
        }
        long endTime = System.currentTimeMillis();
        float totalProgramTime = endTime - startPointTime;
        if (HABLA)
            debug("Execution time is " + totalProgramTime + " (" + (totalProgramTime / 1000) + "s)");
        close();
    }
    
 //IO Stuff
    private static boolean HABLA = false;
    private static byte[] scannerByteBuffer = new byte[1024]; // Buffer of Bytes
    private static int scannerIndex;
    private static InputStream scannerIn;
    private static int scannerTotal;
    private static BufferedWriter printerBW;

    private static int next() throws IOException { // Scan method used to scan buf
        if (scannerTotal < 0)
            throw new InputMismatchException();
        if (scannerIndex >= scannerTotal) {
            scannerIndex = 0;
            scannerTotal = scannerIn.read(scannerByteBuffer);
            if (scannerTotal <= 0)
                return -1;
        }
        return scannerByteBuffer[scannerIndex++];
    }

    static int ni() throws IOException {
        int integer = 0;
        int n = next();
        while (isWhiteSpace(n)) // Removing startPointing whitespaces
            n = next();
        int neg = 1;
        if (n == '-') { // If Negative Sign encounters
            neg = -1;
            n = next();
        }
        while (!isWhiteSpace(n)) {
            if (n >= '0' && n <= '9') {
                integer *= 10;
                integer += n - '0';
                n = next();
            } else
                throw new InputMismatchException();
        }
        return neg * integer;
    }

    static long nl() throws IOException {
        long integer = 0;
        int n = next();
        while (isWhiteSpace(n)) // Removing startPointing whitespaces
            n = next();
        int neg = 1;
        if (n == '-') { // If Negative Sign encounters
            neg = -1;
            n = next();
        }
        while (!isWhiteSpace(n)) {
            if (n >= '0' && n <= '9') {
                integer *= 10;
                integer += n - '0';
                n = next();
            } else
                throw new InputMismatchException();
        }
        return neg * integer;
    }

    static String line() throws IOException {
        StringBuilder sb = new StringBuilder();
        int n = next();
        while (isWhiteSpace(n))
            n = next();
        while (!isNewLine(n)) {
            sb.append((char) n);
            n = next();
        }
        return sb.toString();
    }

    private static boolean isNewLine(int n) {
        return n == '\n' || n == '\r' || n == -1;
    }

    private static boolean isWhiteSpace(int n) {
        return n == ' ' || isNewLine(n) || n == '\t';
    }

    static int[] nia(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        int[] array = new int[n];
        for (int i = 0; i < n; i++)
            array[i] = ni();
        return array;
    }

    static long[] nla(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        long[] array = new long[n];
        for (int i = 0; i < n; i++)
            array[i] = nl();
        return array;
    }

    static float[] nfa(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        float[] array = new float[n];
        for (int i = 0; i < n; i++)
            array[i] = nl();
        return array;
    }

    static double[] nda(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        double[] array = new double[n];
        for (int i = 0; i < n; i++)
            array[i] = nl();
        return array;
    }

    static <T> void print(T str) throws IOException {
        printerBW.append(str.toString());
        if (HABLA) flush();
    }

    static <T> void println() throws IOException {
        printerBW.append('\n');
        if (HABLA) flush();
    }

    static <T> void println(T str) throws IOException {
        if (str == null) {
            printerBW.append("null\n");
        } else {
            printerBW.append(str.toString());
            printerBW.append('\n');
            if (HABLA) flush();
        }
    }

    public static final String ANSI_RESET = "\u001B[0m";
    public static final String ANSI_DEBUG = "\u001B[33m";
    static <T> void debugl(T str) throws IOException {
        if (!HABLA) return;
        if (str == null) {
            printerBW.append(ANSI_DEBUG);
            printerBW.append("null");
            printerBW.append(ANSI_RESET);
        } else {
            printerBW.append(ANSI_DEBUG);
            printerBW.append(str.toString());
            printerBW.append(ANSI_RESET);
        }
        flush();
    }

    static void debug() throws IOException {
        if (!HABLA) return;
        printerBW.append('\n');
        flush();
    }
    static <T> void debug(T str) throws IOException {
        if (!HABLA) return;
        if (str == null) {
            printerBW.append(ANSI_DEBUG);
            printerBW.append("null\n");
            printerBW.append(ANSI_RESET);
        } else {
            printerBW.append(ANSI_DEBUG);
            printerBW.append(str.toString());
            printerBW.append(ANSI_RESET);
            printerBW.append('\n');
        }
        flush();
    }

    static void flush() throws IOException {
        printerBW.flush();
    }

    static void close() {
        try {
            printerBW.close();
        } catch (IOException e) {
            System.out.println(e.toString());
        }
    }
}