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 sys
def func(x):
    x = x.split()
    if len(x) == 1:
        return int(x[0])
    x = [int(each) for each in x]
    return x
inputs = []
for line in sys.stdin:
    inputs += [line.split('\n')[0].strip()]
inputs = [func(each) for each in inputs]

for i in range(inputs[0]):
    n, k = inputs[i+1][0], inputs[i+1][1]
    low = 1
    high = n*k
    while low <= high:
        mid = low +(high - low)//2
        quotient = mid//n
        remaining_elem = mid - quotient
        if remaining_elem > k:
            high = mid - 1
        elif remaining_elem < k:
            low = mid + 1
        else:
            print(mid - (mid%n == 0))
            break