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] 
"""
from functools import reduce
import statistics
import numpy as np
import itertools
import statistics
import operator
import decimal
sys.setrecursionlimit(10 ** 6 + 1)
MAX = sys.maxsize
"""
# from time import time
import math
import os
import sys
# from math import *
from io import BytesIO, IOBase
from collections import Counter, deque
# from bisect import bisect_right, insort_right
BUFSIZE = 8192
import array


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")

sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
getint = lambda: int(sys.stdin.readline().rstrip("\r\n"))
getints = lambda: map(int, sys.stdin.readline().rstrip("\r\n").split())
lgetints = lambda: list(map(int, sys.stdin.readline().rstrip("\r\n").split()))
getstrs = lambda: map(str, sys.stdin.readline().rstrip("\r\n").split())


# d is a dictionary min val of d is
# d = { 1 : 2, 4 : 5, 3 : 0}
# min(d.values())
# ans = 0

# def gcd(a, b):
#     if a == 0:
#         return b
#     else:
#         return gcd(b % a, a)

# def fact(num):
#     cnt = 0
#     for x in range(1, int(math.sqrt(num)) + 1):
#         if num % x == 0:
#             cnt = x
#             # if num // x == x:
#                 # cnt += 1
#             # else:
#                 # cnt += 2
#     return cnt

# def isPrime(num):
#     if num == 2:
#         return True
#     elif num % 2 == 0:
#         return False
#     else:
#         i = 3
#         while i * i <= num:
#             if num % i == 0:
#                 return False
#             i += 2
#         return True

# def power(x, y):
#     res = 1
#     x = x
#     while y > 0:
#         if y & 1:
#             res = res * x
#         x = x * x
#         y = y >> 1
#     return res

def prog_name():
    # A
    n, s = getints()
    if n == 1:
        print(s)
    else:
        if n > s:
            print(0)
        else:
            n = n // 2 + 1
            print(s // n)


    
    # print()
def main ():
    # init = time()
    # T = getint()
    T = getint()
    for unique in range(T):
        # print("Case #"+str(unique+1)+":", end = " ")
        # print()
        prog_name()
    # print(time() - init)


if __name__ == "__main__":
    main()