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
import math
from collections import Counter,defaultdict
try: 
    sys.stdin = open('input.txt', 'r') 
    sys.stdout = open('output.txt', 'w')

except: 
    pass
    


def takeInput():
    return [int(x) for x in input().strip().split()]
 
        
t=int(input())
while t!=0:
    t-=1
    n,k=takeInput()
    if(k>n):
        ans=float("inf")
        rem=k//n
        count=k
        start=k
        end=2*k+1
        while start<=end:
            mid=start+(end-start)//2
            rem=mid-mid//n 
            if(rem>=k):
                ans=mid
                end=mid-1
            if(rem<k):
                start=mid+1
                
        print(ans)
    elif(k==n):
        print(k+1)
    else:
        print(k)