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 io
import os

from collections import Counter, defaultdict, deque


def solve(N, K):
    lo = 0
    hi = 2 * K + 1

    def rank(n):
        return n - (n // N)

    assert rank(lo) < K <= rank(hi)
    while hi - lo > 1:
        mid = (lo + hi) // 2
        if rank(mid) < K:
            lo = mid
        else:
            hi = mid
        assert rank(lo) < K <= rank(hi)
    assert lo + 1 == hi
    assert rank(lo) < K <= rank(hi)

    return hi


if __name__ == "__main__":
    input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

    T = int(input())
    for t in range(T):
        N, K = [int(x) for x in input().split()]
        ans = solve(N, K)
        print(ans)