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] 
import java.io.BufferedReader;
import java.io.File;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.StringTokenizer;

public class Main {
    static int mod = 1000_000_007;
    static long mod1 = 998244353;
    static boolean memory = false;
    static FastScanner f;
    static PrintWriter pw;
    static double eps = 1e-6;
    static int oo = (int) 1e9;

    public static void solve() throws Exception {
        // Add your code here
        long n = f.nl();
        long s = f.nl();

        if (n == 1) {
            pn(s);
            return;
        }
        
        long lo = 0 , hi = n;
        long t = n - ((n + 1) / 2) + 1;
        long ans = 0;
        while (lo <= hi) {
            long mid = lo + ((hi - lo) / 2);
            if (mid * t <= s) {
                ans = mid;
                lo = mid + 1;
            }
            else {
                hi = mid - 1;
            }
        }
        pn(ans);
    }

    public static void main(String[] args) throws Exception {
        if (memory)
            new Thread(null, new Runnable() {
                public void run() {
                    try {
                        new Main().run();
                    } catch (Exception e) {
                        e.printStackTrace();
                        System.exit(1);
                    }
                }
            }, "", 1 << 28).start();
        else
            new Main().run();
    }

    void run() throws Exception {
        if (System.getProperty("ONLINE_JUDGE") == null) {
            f = new FastScanner("");
            File file = new File("!out.txt");
            pw = new PrintWriter(file);
        } else {
            f = new FastScanner();
            pw = new PrintWriter(System.out);
        }

        int t = f.ni();
        int tt = 1;
        while (t-- > 0) {
            // p("Case #" + (tt++) + ": ");
            solve();
        }

        pw.flush();
        pw.close();
    }

    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(String str) throws Exception {
            try {
                br = new BufferedReader(new FileReader("!a.txt"));
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int ni() throws IOException {
            return Integer.parseInt(next());
        }

        public long nl() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nd() throws IOException {
            return Double.parseDouble(next());
        }

    }

    public static void pn(Object... o) {
        for (int i = 0; i < o.length; ++i)
            pw.print(o[i] + (i + 1 < o.length ? " " : "\n"));
    }

    public static void p(Object... o) {
        for (int i = 0; i < o.length; ++i)
            pw.print(o[i] + (i + 1 < o.length ? " " : ""));
    }

    public static void pni(Object... o) {
        for (Object obj : o)
            pw.print(obj + " ");
        pw.println();
        pw.flush();
    }

    public static void sort(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a)
            l.add(i);
        Collections.sort(l);
        for (int i = 0; i < a.length; ++i)
            a[i] = l.get(i);
    }

    public static void sort(long[] a) {
        ArrayList<Long> l = new ArrayList<>();
        for (long i : a)
            l.add(i);
        Collections.sort(l);
        for (int i = 0; i < a.length; ++i)
            a[i] = l.get(i);
    }
}