Problem: You are given two positive integers n and k. Print the k-th positive integer that is not divisible by n.

For example, if n=3, and k=7, then all numbers that are not divisible by 3 are: 1, 2, 4, 5, 7, 8, 10, 11, 13 .... The 7-th number among them is 10.

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases in the input. Next, t test cases are given, one per line.

Each test case is two positive integers n (2 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 10^9).

Output

For each test case print the k-th positive integer that is not divisible by n.

Example

Input


6
3 7
4 12
2 1000000000
7 97
1000000000 1000000000
2 1


Output


10
15
1999999999
113
1000000001
1

Solution (in PYTHON3):

Solution:
def notDiv(divisor, kthDiv, begin, end):
    half = (begin + end) // 2
    aux = half - (half // divisor)

    if begin > end:
        return begin

    if kthDiv <= aux:
        return notDiv(divisor, kthDiv, begin, half - 1)

    return notDiv(divisor, kthDiv, half + 1, end)


minimum = 1
maximum = 10000000000000
numTestCases = int(input())
for i in range(numTestCases):
    n, k = input().split()
    n = int(n)
    k = int(k)
    result = notDiv(n, k, minimum, maximum)
    print(result)