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:
# all my editorials are at http://interview.solutions
for testcase in range(int(input())):
    n, k = map(int, input().split())

    def f(x):
        # Among {1, 2, ..., x}, how many are
        # not divisible by n?
        return x - x // n

    # f is a monotone increasing function, and
    # we want to know the first x so that f(x) = k.
    lo, hi = 0, 10 ** 12
    while lo < hi:
        mi = lo + hi >> 1
        if f(mi) < k:
            lo = mi + 1
        else:
            hi = mi
    print(lo)