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 search(n, k, start, end):
    # print(n, k, start, end)
    middle = (start + end) // 2
    if start == end:
        return middle
    # We look at middle

    # print("middle :", middle)

    # Divisible by n = n, 2*n, 3*n, i*n where i*n <= middle
    div_by_n = middle // n
    not_div_by_n = (middle - (div_by_n * n)) + (div_by_n) * (n - 1)
    # print((middle - (div_by_n * n)), (div_by_n) * (n - 1))
    # print("div/not_div", div_by_n, not_div_by_n)
    if not_div_by_n > k:
        res = search(n, k, start, middle - 1)
    elif not_div_by_n < k:
        res = search(n, k, middle + 1, end)
    else:
        res = middle
    return res


T = int(input())
for t in range(T):
    n, k = list(map(int, input().split()))
    res = search(n, k, 0, 3 * k)
    if (res % n) == 0:
        res -= 1
    print(res)