DZY has a hash table with p buckets, numbered from 0 to p - 1. He wants to insert n numbers, in the order they are given, into the hash table. For the i-th number xi, DZY will put it into the bucket numbered h(xi), where h(x) is the hash function. In this problem we will assume, that h(x) = x mod p. Operation a mod b denotes taking a remainder after division a by b.

However, each bucket can contain no more than one element. If DZY wants to insert an number into a bucket which is already filled, we say a "conflict" happens. Suppose the first conflict happens right after the i-th insertion, you should output i. If no conflict happens, just output -1.

Input

The first line contains two integers, p and n (2 ≤ p, n ≤ 300). Then n lines follow. The i-th of them contains an integer xi (0 ≤ xi ≤ 109).

Output

Output a single integer — the answer to the problem.

Examples

Input

10 5
0
21
53
41
53


Output

4


Input

5 5
0
1
2
3
4


Output

-1
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.Reader;
import java.util.StringTokenizer;

public class CFFF_A
{
    public static void main(String[] args)
    {
        Scanner in = new Scanner();

        int p = in.nextInt();
        int n = in.nextInt();
        int [] nums = new int[n];
        boolean [] filled = new boolean [p];
        boolean okay = true;
        for (int i = 0; i < n; i++)
        {
            nums[i] = in.nextInt();
        }

        for (int i = 0; i < n; i++)
        {
            int hashed = nums[i] % p;
            if (filled[hashed])
            {
                okay = false;
                System.out.println(i + 1);
                break;
            }
            else
            {
                filled[hashed] = true;
            }
        }

        if (okay)
        {
            System.out.println("-1");
        }
    }


    // -----------Pair class for comparisons--------------
    public static class Pair
        implements Comparable<Pair>
    {
        int x, y;


        public Pair(int x, int y)
        {
            this.x = x;
            this.y = y;
        }


        @Override
        public int compareTo(Pair o)
        {
            return Integer.compare(this.x, o.x);
        }


        @Override
        public int hashCode()
        {
            return x ^ y;
        }


        @Override
        public boolean equals(Object o)
        {
            Pair p = (Pair)o;
            return p.x == x && p.y == y;
        }
    }


    // -----------Scanner class for faster input----------
    /*
     * Provides similar API as java.util.Scanner but does not use regular
     * expression engine.
     */
    public static class Scanner
    {
        BufferedReader  br;
        StringTokenizer st;


        public Scanner(Reader in)
        {
            br = new BufferedReader(in);
        }


        public Scanner()
        {
            this(new InputStreamReader(System.in));
        }


        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }


        int nextInt()
        {
            return Integer.parseInt(next());
        }


        long nextLong()
        {
            return Long.parseLong(next());
        }


        double nextDouble()
        {
            return Double.parseDouble(next());
        }


        // Slightly different from java.util.Scanner.nextLine(),
        // which returns any remaining characters in current line,
        // if any.
        String readNextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
    // --------------------------------------------------------
}
