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 delsfrom(a, b, delim):
    return delfromzero(b, delim) - delfromzero(a, delim)


def delfromzero(a, delim):
    return a // delim


for _ in range(int(input())):
    n, k = map(int, input().split())
    prev = k
    a = delfromzero(prev, n)
    next = prev + a
    s = a
    while a > 0:
        a = delsfrom(prev, next, n)
        prev = next
        next = prev + a
        s += a
    print(k + s)