Let’s play a stone removing game.Initially, *n* stones are arranged on a circle and numbered 1, …, *n* clockwise (Figure 1). You are also given two numbers *k* and *m*. From this state, remove stones one by one following the rules explained below, until only one remains. In step 1, remove stone *m*. In step 2, locate the *k*-th next stone clockwise from *m* and remove it. In subsequent steps, start from the slot of the stone removed in the last step, make *k* hops clockwise on the remaining stones and remove the one you reach. In other words, skip (*k* − 1) remaining stones clockwise and remove the next one. Repeat this until only one stone is left and answer its number. For example, the answer for the case *n* = 8, *k* = 5, *m* = 3 is 1, as shown in Figure 1.

Figure 1: An example game

Initial state | Step 1 | Step 2 | Step 3 | Step 4 |

Step 5 | Step 6 | Step 7 | Final state |

The input consists of multiple datasets each of which is formatted as follows.*n* *k* *m*The last dataset is followed by a line containing three zeros. Numbers in a line are separated by a single space. A dataset satisfies the following conditions.2 ≤ *n* ≤ 10000, 1 ≤ *k* ≤ 10000, 1 ≤ *m* ≤ *n*The number of datasets is less than 100.

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