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 PYTHON):

Solution:

def findIndex(num, div):
    return num - num / div

def binSearch(l, r, div, key):
    while 1:
        mid = l + r >> 1
        if l == mid:
            if findIndex(l, div) == key:
                return l
            else:
                return r
        elif findIndex(mid, div) < key:
            l = mid + 1
        else:
            r = mid
            
for tc in xrange(input()):
    N, K = map(int, raw_input().split())
    print binSearch(0, 10 ** 18, N, K)