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 sys
input = lambda : sys.stdin.readline().strip()
t = int(input())
while t:
    t-=1
    n,k = map(int,input().split())
    if k==1:
        print(1)
        continue
    lo = 1
    hi = 2*(10**9)
    while lo<hi:
        mi = (lo+hi)//2
        v = mi//n
        v = mi-v
        if v<k:
            lo = mi+1 
        else:
            hi = mi
    print(lo)