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 kth_search(low, high, n, k):
  mid = (low + high) // 2
  count = mid - mid // n # Há count números não divisíveis por n até mid
  
  if low > high: # O resultado é o valor em low
    return int(low)
  
  if count >= k:
    return kth_search(low, mid - 1, n, k)
  else:
    return kth_search(mid + 1, high, n, k)

t = int(input())
for i in range(t):
  n, k = map(int, input().split())
  print(kth_search(1, 1e12, n, k))