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:
import sys

def kth_termo(n, k, minimo, maximo):
    metade = (minimo + maximo) // 2
    kth = metade - (metade // n)

    if minimo > maximo:
        return metade + 1
    else:
        if (kth >= k):
            return kth_termo(n, k, minimo, metade - 1)
        elif (kth < k):
            return kth_termo(n, k, metade + 1, maximo)

minimo = 1
maximo = sys.maxsize
testes = int(raw_input())
resultados = []
for i in range(testes):
    n, k = map(int, raw_input().split())
    resultados.append(kth_termo(n, k, minimo, maximo))

for kth in resultados:
    print(kth)