You are given two positive integers n and s. Find the maximum possible median of an array of n non-negative integers (not necessarily distinct), such that the sum of its elements is equal to s.

A median of an array of integers of length m is the number standing on the ⌈ {m/2} ⌉-th (rounding up) position in the non-decreasing ordering of its elements. Positions are numbered starting from 1. For example, a median of the array [20,40,20,50,50,30] is the ⌈ m/2 ⌉-th element of [20,20,30,40,50,50], so it is 30. There exist other definitions of the median, but in this problem we use the described definition.

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows.

Each test case contains a single line with two integers n and s (1 ≤ n, s ≤ 10^9) — the length of the array and the required sum of the elements.

Output

For each test case print a single integer — the maximum possible median.

Example

Input


8
1 5
2 5
3 5
2 1
7 17
4 14
1 1000000000
1000000000 1


Output


5
2
2
0
4
4
1000000000
0

Note

Possible arrays for the first three test cases (in each array the median is underlined):

  * In the first test case [\underline{5}] 
  * In the second test case [\underline{2}, 3] 
  * In the third test case [1, \underline{2}, 2] 
// हर हर महादेव
import java.util.*;
import java.lang.*;
import java.io.*;
import java.text.DecimalFormat;

public final class Solution {

    static int inf = Integer.MAX_VALUE;
    static int mod = 1000000000 + 7;


  
    static void ne(Scanner sc, BufferedWriter op) throws Exception {
    int n=sc.nextInt();
    int s=sc.nextInt();
    if(n>s){
        int mid=(int)Math.ceil((double)n/2.0)-1;
      if(n-mid>s){
          op.write(0+"\n");
      }else{
          int ans=s/(n-mid);
          op.write(ans+"\n");
      }

    }else{
            int mid=(int)Math.ceil((double)n/2.0)-1;
        int ans=s/(n-mid);
        op.write(ans+"\n");
    }
    
         
    }
    static int gcd(int a, int b){
        if(a==0) return b;
        return gcd(b%a,a);
    }
    

    public static void main(String[] args) throws Exception {
        BufferedWriter op = new BufferedWriter(new OutputStreamWriter(System.out));
        Scanner sc = new Scanner(System.in);

        int t = sc.nextInt();
        while (t-- > 0) {
            ne(sc, op);
            // op.flush();
        }
        op.flush();
    }

    static void print(Object o) {
        System.out.println(String.valueOf(o));
    }

}

class pair {
    int xx;

    int yy;

    pair(int xx, int yy) {
        this.xx = xx;
        this.yy = yy;
    }
}

class sortY implements Comparator<pair> {
    public int compare(pair p1, pair p2) {
        if (p1.yy > p2.yy) {
            return 1;
        } else if (p1.yy == p2.yy) {
            if (p1.xx > p2.xx) {
                return 1;
            } else if (p1.xx < p2.xx) {
                return -1;
            }
            return 0;

        }
        return -1;
    }
}

class sortX implements Comparator<pair> {
    public int compare(pair p1, pair p2) {
        if (p1.xx > p2.xx) {
            return 1;
        } else if (p1.xx == p2.xx) {
            if (p1.yy > p2.yy) {
                return 1;
            } else if (p1.yy < p2.yy) {
                return -1;
            }
            return 0;

        }
        return -1;
    }
}

class debug {

    static void print1d(long[] arr) {
        System.out.println();
        for (int i = 0; i < arr.length; i++) {
            System.out.print(arr[i] + " ");
        }

    }

    static void print1d(int[] arr) {
        System.out.println();
        for (int i = 0; i < arr.length; i++) {
            System.out.print(arr[i] + " ");
        }

    }

    static void print1d(boolean[] arr) {
        System.out.println();
        for (int i = 0; i < arr.length; i++) {
            System.out.println(i + "= " + arr[i] + " ");
        }

    }

    static void print2d(int[][] arr) {
        System.out.println();
        int n = arr.length;
        int n2 = arr[0].length;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n2; j++) {
                System.out.print(arr[i][j] + " ");
            }
            System.out.println();
        }

    }

    static void print2d(long[][] arr) {
        System.out.println();
        int n = arr.length;
        int n2 = arr[0].length;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n2; j++) {
                System.out.print(arr[i][j] + " ");
            }
            System.out.println();
        }

    }

}

class Reader {
    final private int BUFFER_SIZE = 1 << 16;
    private DataInputStream din;
    private byte[] buffer;
    private int bufferPointer, bytesRead;

    public Reader() {
        din = new DataInputStream(System.in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public Reader(String file_name) throws IOException {
        din = new DataInputStream(new FileInputStream(file_name));
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public String readLine() throws IOException {
        byte[] buf = new byte[64]; // line length
        int cnt = 0, c;
        while ((c = read()) != -1) {
            if (c == '\n') {
                if (cnt != 0) {
                    break;
                } else {
                    continue;
                }
            }
            buf[cnt++] = (byte) c;
        }
        return new String(buf, 0, cnt);
    }

    public int nextInt() throws IOException {
        int ret = 0;
        byte c = read();
        while (c <= ' ') {
            c = read();
        }
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');

        if (neg)
            return -ret;
        return ret;
    }

    public long nextLong() throws IOException {
        long ret = 0;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');
        if (neg)
            return -ret;
        return ret;
    }

    public double nextDouble() throws IOException {
        double ret = 0, div = 1;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();

        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');

        if (c == '.') {
            while ((c = read()) >= '0' && c <= '9') {
                ret += (c - '0') / (div *= 10);
            }
        }

        if (neg)
            return -ret;
        return ret;
    }

    private void fillBuffer() throws IOException {
        bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
        if (bytesRead == -1)
            buffer[0] = -1;
    }

    private byte read() throws IOException {
        if (bufferPointer == bytesRead)
            fillBuffer();
        return buffer[bufferPointer++];
    }

    public void close() throws IOException {
        if (din == null)
            return;
        din.close();
    }
}