Uolevi and Maija are playing Wario kart, a popular racing game. So far Maija is having a perfect race while Uolevi is lagging behind.

The cars move normally at speed $100\ m/s$ but there are also $m$ boost pads numbered $1,\,2,\dots,\,m$, the $i$-th of which is located $a_i \times 100$ meters from the starting line. A boost pad doubles the car's speed for one second. When one boost is active, another one cannot be picked up. The racing track is circular and has length $n \times 100$ meters. Calculate Maija's position from the starting line $k$ seconds after the race started.

Input

First line contains three integers, $n,\,m,\,k$.

Second line contains $m$ distinct integers $a_1,\,a_2\,\dots,\,a_m$.

Output

Maija's distance from the starting line in meters

Constraints

• $1 \leq n \leq 10^5$
• $0 \leq m \leq n$
• $0 \leq k \leq 5 \times 10^5$
• $0 \leq a_i < n$
• $a_i < a_j$ if $i < j$
• All input values are integers

Example 1

Input:

10 2 2 
1 2

Output:

300

Example 2

Input:

5 3 15 
2 3 4

Output:

400

Example 3

Input:

1 0 1

Output:

0