And Then There Was One

Let's play a stone-removal game.

Initially, as shown in Figure 1, $n$ stones numbered from $1$ to $n$ are arranged clockwise in a circle. Two numbers $k$ and $m$ are also given. Starting from this arrangement, remove the stones one at a time according to the rules below, until only one stone remains.

• Step 1: remove stone $m$.
• Step $i$ (for $i \ge 2$): starting from the position of the stone removed in step $(i-1)$, remove the $k$-th stone clockwise among the remaining stones. That is, skip $k-1$ stones and remove the next one; stones that have already been removed are not counted while skipping.

Carry out step 1, step 2, step 3, and so on in order until a single stone is left. That last stone is the answer.

For example, as in Figure 1, when $n = 8$, $k = 5$, $m = 3$ the answer is $1$.

Figure 1: Game Example

• Initial state: 8 stones are placed clockwise.
• Step 1: since $m = 3$, stone 3 is removed.
• Step 2: starting from 3 and with $k = 5$, skip stones 4, 5, 6, 7 (four stones) and remove stone 8.
• Step 3: starting from 8, skip stones 1, 2, 4, 5 and remove stone 6. Note that stone 3 is ignored (it is already removed, so it is not counted among the skipped stones).
• Steps 4-7: continue until only one stone remains.
• Finally, the remaining stone is 1, so the answer is 1.

The input consists of several data lines; each data line contains three numbers:

n k m

The line after the last data line contains three zeros. Each number satisfies the following ranges.

$2 \le n \le 10000$, $1 \le k \le 10000$, $1 \le m \le n$

The number of data lines is fewer than 100.

For each data line, output the number of the last remaining stone.