A14129 | Cat Cycle

Suppose you are living with two cats: A and B. There are $n$ napping spots where both cats usually sleep.

Your cats like to sleep and also like all these spots, so they change napping spot each hour cyclically:

- Cat A changes its napping place in order: $n, n - 1, n - 2, \dots, 3, 2, 1, n, n - 1, \dots$ In other words, at the first hour it's on the spot $n$ and then goes in decreasing order cyclically;
- Cat B changes its napping place in order: $1, 2, 3, \dots, n - 1, n, 1, 2, \dots$ In other words, at the first hour it's on the spot $1$ and then goes in increasing order cyclically.

The cat B is much younger, so they have a strict hierarchy: A and B don't lie together. In other words, if both cats'd like to go in spot $x$ then the A takes this place and B moves to the next place in its order (if $x < n$ then to $x + 1$ , but if $x = n$ then to $1$ ). Cat B follows his order, so it won't return to the skipped spot $x$ after A frees it, but will move to the spot $x + 2$ and so on.

Calculate, where cat B will be at hour $k$ ?

The first line contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases.

The first and only line of each test case contains two integers $n$ and $k$ ( $2 \le n \le 10^9$ ; $1 \le k \le 10^9$ ) — the number of spots and hour $k$ .

For each test case, print one integer — the index of the spot where cat B will sleep at hour $k$ .