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 find_not_divisible(n, k, start_at, end_at):
    half = (start_at + end_at) // 2
    not_divisibles = half - (half // n)

    if start_at > end_at:
        return start_at
    if k <= not_divisibles:
        return find_not_divisible(n, k, start_at, half - 1)

    return find_not_divisible(n, k, half + 1, end_at)


n_tests = int(input())
MIN_VALUE, MAX_VALUE = 1, 10000000000000

for i in range(n_tests):
    n, k = map(int, input().split())
    print(find_not_divisible(n, k, MIN_VALUE, MAX_VALUE))