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:
from math import floor


def kth(n, k):
    return k - floor(k / n)


def solve(n, k):
    start = 0
    end = pow(10, 10)
    while start <= end:
        mid = start + (end - start) // 2
        if mid % n == 0:
            mid += 1
        check = kth(n, mid)
        if check == k:
            return mid
        elif check < k:
            start = mid + 1
        else:
            end = mid - 1

    result = [k]
    while floor(result[-1] / n) > 0:
        result.append(floor(result[-1] / n))

    result = sum(result)
    if result % n == 0:
        result += 1
    return result


if __name__ == "__main__":
    for i in range(int(input())):
        n, k = map(int, input().split())
        print(solve(n, k))