KazaQ's Socks

KazaQ wears socks everyday.

At the beginning, he has $n$ pairs of socks numbered from $1$ to $n$ in his closets.

Every morning, he puts on a pair of socks which has the smallest number in the closets.

Every evening, he puts this pair of socks in the basket. If there are $n - 1$ pairs of socks in the basket now, lazy KazaQ has to wash them. These socks will be put in the closets again in tomorrow evening.

KazaQ would like to know which pair of socks he should wear on the $k$-th day.

The input consists of multiple test cases. (about $2000$)

For each case, there is a line contains two numbers $n, k$ $(2 \leq n \leq 10^9, 1 \leq k \leq 10^{18})$.

For each test case, output "Case #$x$: $y$" in one line (without quotes), where $x$ indicates the case number starting from $1$ and $y$ denotes the answer of corresponding case.

3 7
3 6
4 9

Case #1: 3
Case #2: 1
Case #3: 2

2017 Multi-University Training Contest - Team 1