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:
def check(m, n, k):
    c = m // n
    k -= (n - 1) * c    
    k -= m % n
    return k <= 0

t = int(input())
for _ in range(t):
    n, k = tuple([int(e) for e in input().split()])
    b = 1
    e = int(10e9)
    while b < e:
        m = (b + e) // 2
        if check(m, n, k):
            e = m
        else:
            b = m + 1
    
    if check(e, n, k):
        print(e)
    else:
        print(e - 1)