Circular Seats

Version: Phuoc Hung OJ Extended

Problem Statement

There are $M$ seats arranged in a circle and numbered from $1$ to $M$. Seat $1$ follows seat $M$. A student starts at seat $S$ and moves to the next seat clockwise at each step. Determine the seat after exactly $T$ steps.

Input

One line contains three integers $M$, $S$, and $T$.

Output

Print the seat number after exactly $T$ steps.

Subtasks

• Subtask 1 (30 points):
  • $1 \le S \le M \le 10^6$.
  • $0 \le T \le 10^6$.
• Subtask 2 (70 points):
  • $1 \le S \le M \le 10^{18}$.
  • $0 \le T \le 10^{18}$.

Examples

Example 1

Input

8 3 0

Output

3

Explanation

No move is made, so the student remains at seat $3$.

Example 2

Input

8 3 6

Output

1

Explanation

Starting from seat $3$, six moves visit $4,5,6,7,8,1$, so the final seat is $1$.

Example 3

Input

100 100 1

Output

1

Explanation

Seat $1$ follows seat $100$, so one step leads to seat $1$.