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.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class B {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            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();
        }

        ArrayList<Integer> readIntArrayList(int n) {
            ArrayList<Integer> a = new ArrayList<>();
            for (int i = 0; i < n; i++)
                a.add(nextInt());
            return a;
        }

        ArrayList<Long> readLongArrayList(int n) {
            ArrayList<Long> a = new ArrayList<>();
            for (int i = 0; i < n; i++)
                a.add(nextLong());
            return a;
        }

        int[] readIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        long[] readLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }

        char[] readCharArray(int n) {
            char[] a = new char[n];
            for (int i = 0; i < n; i++)
                a[i] = next().charAt(0);
            return a;
        }

        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;
        }
    }

    static Boolean[] sieveOfEratosthenes(int n, Boolean[] prime) {
        for (int i = 0; i <= n; i++)
            prime[i] = true;

        for (int p = 2; p * p <= n; p++) {
            // If prime[p] is not changed, then it is a
            // prime
            if (prime[p] == true) {
                // Update all multiples of p
                for (int i = p * p; i <= n; i += p)
                    prime[i] = false;
            }
        }
        return prime;

        // Print all prime numbers
    }

    static int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    static int isPrime(int n) {
        for (int i = 2; i * i <= n; i++) {
            if (n % i == 0) {
                return i;
            }
        }
        return -1;
    }

    static void p(String s) {
        System.out.print(s);
    }

    static void pln(String s) {
        System.out.println(s);
    }

    static String ts(int x) {
        return Integer.toString(x);
    }

    static int[] randomArray(int n) {
        Random r = new Random();
        int[] ar = new int[n];
        for (int i = 0; i < n; i++)
            ar[i] = r.nextInt(n + 1);
        return ar;

    }

    public static void main(String[] args) {

        FastReader fr = new FastReader();
        int t = fr.nextInt();
        while (t-- > 0) {
            int n = fr.nextInt();
            int s = fr.nextInt();

            int index = (int) Math.ceil((double) n / (double) 2);

            int diff = n - index + 1;
            System.out.println(s / diff);

        }
    }

}
