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
import sys

t = int(input())
while t:
    t -= 1
    n, k = [int(x) for x in input().split()]
    l, r = 1, 10**10
    while r - l > 1:
        m = (r + l) >> 1
        if m - m//n <= k:
            l = m
        else:
            r = m
    while (l - 1) - (l - 1)//n == k:
        l -= 1
    print(l)