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 heapq

def solve():
    n, k = map(int, input().split())
    left = 0
    right = k * n
    while left <= right:
        mid = (left + right) // 2
        if mid % n == 0:
            mid += 1
        nth = mid - (mid // n)
        if nth == k:
            print(mid)
            return
        if nth > k:
            right = mid
        if nth < k:
            left = mid
    



if __name__ == "__main__":
    t = int(input())
    for _ in range(t):
        solve()