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
# sys.setrecursionlimit(10**9)
t=int(input())

def bs(l,h,n,k):
	if(l<=h):
		m=(l+h)//2
		# print(m)
		# if(m%n!=0):
		temp=m-(m//n)
		if(temp==k ):
			if(m%n!=0):
				return m
			return bs(l,m-1,n,k)
		if(temp<k):
			return bs(m+1,h,n,k)
		else:
			return bs(l,m-1,n,k)
		# else:
		# 	z1=bs(l,m-1,n,k)

for i1 in range(t):
	n,k=map(int,input().split(" "))
	m=10**30
	z=bs(0,m,n,k)
	print(z)