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.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.*;

/** Built using CHelper plug-in Actual solution is at the top */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solution solver = new Solution();
        boolean multipleTC = true;
        int testCount = multipleTC ? Integer.parseInt(in.next()) : 1;
        for (int i = 1; i <= testCount; i++) solver.solve(in, out, i);
        out.close();
    }

    static class Solution {
        PrintWriter out;
        InputReader in;

        public void solve(InputReader in, PrintWriter out, int test) {
            this.out = out;
            this.in = in;
            int n = ni(), s = ni();
            pn(s / (n / 2 + 1));
        }

        static final Comparator<Pair> com = Comparator.comparingInt(o -> o.wt);

        String n() {
            return in.next();
        }

        int ni() {
            return in.nextInt();
        }

        long nl() {
            return in.nextLong();
        }

        void pn(long zx) {
            out.println(zx);
        }

        void pn(String sz) {
            out.println(sz);
        }

        void pn(double dx) {
            out.println(dx);
        }

        class Pair {
            int u, v, wt;

            Pair(int u, int v, int wt) {
                this.u = u;
                this.v = v;
                this.wt = wt;
            }
        }
    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new UnknownError();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new UnknownError();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public String next() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));

            return res.toString();
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}
