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 binary_search(left,right,n,k):
    if(left>right):
        return
    mid=(left+right)//2
    if(mid-mid//n==k and mid%n!=0):
        return mid
    elif(mid-mid//n==k and mid%n==0):
        return mid-1
    if(mid-mid//n>k):
        return binary_search(left,mid-1,n,k)
    return binary_search(mid+1,right,n,k)

t=int(input())
for you in range(t):
    l=input().split()
    n=int(l[0])
    k=int(l[1])
    print(binary_search(1,10**18,n,k))