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:
import math


def binary_search(n, k):
    l = 1
    r = 1e10
    m = -1
    res = -1
    while r >= l:
        m = l + math.trunc((r - l) / 2)
        if m - math.floor(m / n) >= k:
            r = m - 1
            if m%n != 0:
                res = m
        elif m - math.floor(m / n) < k:
            l = m + 1

    return res

t = int(input())
for i in range(t):
    n, k = [int(x) for x in input().split()]
    print(binary_search(n, k))