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 math
t = int(input())
for _ in range(t):
    n, k = map(int, input().split())
    cur = 1
    if(n > k):
        print(k)
    else:
        lo = ((math.ceil(k/(n-1)) - 1) * n) + 1
        hi = ((math.ceil(k/(n-1)) - 1) * n)  + n
        while (lo <= hi):
            mid = (lo+hi)>>1
            if (mid - (mid//n) == k):
                print(mid)
                break
            if (mid - (mid//n) > k):
                hi = mid-1
            else:
                lo = mid+1