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 binsearch_divisibility(n: int, k: int) -> int:
    l,r = 1,sys.maxsize
    key = 0

    while l <= r:
        m = l + (r-l)//2

        not_divisible_tillmid = m - m//n

        if not_divisible_tillmid > k:
            r = m - 1
        elif not_divisible_tillmid == k:
            key = m
            r = m - 1
        else: #not_divisible_tillmid < k
            l = m + 1
    
    return key

if __name__ == "__main__":
    t = int(input())
    for _ in range(t):
        n,k = map(int, input().split())
        print(binsearch_divisibility(n,k))