Adilbek's house is located on a street which can be represented as the OX axis. This street is really dark, so Adilbek wants to install some post lamps to illuminate it. Street has n positions to install lamps, they correspond to the integer numbers from 0 to n - 1 on the OX axis. However, some positions are blocked and no post lamp can be placed there.

There are post lamps of different types which differ only by their power. When placed in position x, post lamp of power l illuminates the segment [x; x + l]. The power of each post lamp is always a positive integer number.

The post lamp shop provides an infinite amount of lamps of each type from power 1 to power k. Though each customer is only allowed to order post lamps of exactly one type. Post lamps of power l cost a_l each.

What is the minimal total cost of the post lamps of exactly one type Adilbek can buy to illuminate the entire segment [0; n] of the street? If some lamps illuminate any other segment of the street, Adilbek does not care, so, for example, he may place a lamp of power 3 in position n - 1 (even though its illumination zone doesn't completely belong to segment [0; n]).

Input

The first line contains three integer numbers n, m and k (1 ≤ k ≤ n ≤ 10^6, 0 ≤ m ≤ n) — the length of the segment of the street Adilbek wants to illuminate, the number of the blocked positions and the maximum power of the post lamp available.

The second line contains m integer numbers s_1, s_2, ..., s_m (0 ≤ s_1 < s_2 < ... s_m < n) — the blocked positions.

The third line contains k integer numbers a_1, a_2, ..., a_k (1 ≤ a_i ≤ 10^6) — the costs of the post lamps.

Output

Print the minimal total cost of the post lamps of exactly one type Adilbek can buy to illuminate the entire segment [0; n] of the street.

If illumintaing the entire segment [0; n] is impossible, print -1.

Examples

Input

6 2 3
1 3
1 2 3


Output

6


Input

4 3 4
1 2 3
1 10 100 1000


Output

1000


Input

5 1 5
0
3 3 3 3 3


Output

-1


Input

7 4 3
2 4 5 6
3 14 15


Output

-1
import java.util.*;
import java.lang.*;
import java.math.*;
import java.io.*;
 
public class cf5 implements Runnable{    
	
	final static long mod = (long)1e9 + 7; 
	
	public void run() {
	    
		InputReader s = new InputReader(System.in);
		PrintWriter w = new PrintWriter(System.out);

		int n = s.nextInt(), m = s.nextInt(), k = s.nextInt();
		
		int[] blk = new int[n];
		
		for(int i = 1; i <= m; i++)
			blk[s.nextInt()] = 1;
		
		int[] pre = new int[n]; pre[0] = -1;
		
		for(int i = 1; i < n; i++) {
			
			if(blk[i - 1] == 0)
				pre[i] = i - 1;
			else
				pre[i] = pre[i - 1];
		}
		
		long[] lamps = new long[k + 1];
		Arrays.fill(lamps, 1);
		
		for(int i = 1; i <= k; i++) {
			
			if(blk[0] == 1) {
				lamps[i] = -1; continue;
			}
			
			int j = i;
			
			while(j < n) {
				
				if(blk[j] == 1 && pre[j] <= j - i) {
					lamps[i] = -1; break;
				}
				
				if(blk[j] == 1)
					j = pre[j]; 
				
				lamps[i]++; j += i;
			}
			
		}
		
		long res = Long.MAX_VALUE;
		
		for(int i = 1; i <= k; i++) {
			
			long x = s.nextLong();
			
			if(lamps[i] == -1)
				continue;
			
			res = Math.min(x * lamps[i], res);
		}
		
		if(res == Long.MAX_VALUE)
			w.println(-1);
		else
			w.println(res);
		
		w.close();
	}
	
	static class InputReader {
		
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
		
		public InputReader(InputStream stream)
		{
			this.stream = stream;
		}
		
		public int read()
		{
			if (numChars==-1) 
				throw new InputMismatchException();
			
			if (curChar >= numChars)
			{
				curChar = 0;
				try 
				{
					numChars = stream.read(buf);
				}
				catch (IOException e)
				{
					throw new InputMismatchException();
				}
				
				if(numChars <= 0)				
					return -1;
			}
			return buf[curChar++];
		}
	 
		public String nextLine()
		{
			BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
			String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
		}
		public int nextInt()
		{
			int c = read();
			
			while(isSpaceChar(c)) 
				c = read();
			
			int sgn = 1;
			
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			
			int res = 0;
			do 
			{
				if(c<'0'||c>'9') 
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			while (!isSpaceChar(c)); 
			
			return res * sgn;
		}
		
		public long nextLong() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			long res = 0;
			
			do 
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			while (!isSpaceChar(c));
				return res * sgn;
		}
		
		public double nextDouble() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') 
			{
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, nextInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') 
			{
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) 
				{
					if (c == 'e' || c == 'E')
						return res * Math.pow(10, nextInt());
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}
		
		public String readString() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = read();
			} 
			while (!isSpaceChar(c));
			
			return res.toString();
		}
	 
		public boolean isSpaceChar(int c) 
		{
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	 
		public String next() 
		{
			return readString();
		}
		
		public interface SpaceCharFilter 
		{
			public boolean isSpaceChar(int ch);
		}
	}
    
	public static void main(String args[]) throws Exception
	{
		new Thread(null, new cf5(),"cf5",1<<26).start();
	}
}   