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
t = int(input())
for _ in range(t):
    n,k = tuple([int(i) for i in input().split()])
    ub = k*n
    lb = 1
    for x in range(2*math.ceil(math.log(ub-lb,2))+20):
        nb = (ub+lb)//2
        if nb-(nb//n) ==k:
            
            ub = nb
            lb = nb
            break
        if nb-(nb//n) >k:
            ub = nb
        else:
            lb = nb
    if (ub-1)-((ub-1)//n) == k:
        print(ub-1)
    elif ub-(ub//n) == k:
        print(ub)
    elif (ub+1)-((ub+1)//n) == k:
        print(ub+1)