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 gcd(a, b): 
	if a == 0: 
		return b 
	return gcd(b % a, a) 

def divTermCount(a, num): 

	return num-(num // a )


def findNthTerm(a, n): 

	low = 1; high = sys.maxsize 

	while low < high: 
		mid = low + (high - low) // 2

		if divTermCount(a, mid) < n: 
			low = mid + 1

		else: 
			high = mid 
	return low


for _ in range(int(input())):
    a,n=map(int,input().split())
    #if a%2==0:
    ans=findNthTerm(a,n)
    
    print(ans)