Bran and his older sister Arya are from the same house. Bran like candies so much, so Arya is going to give him some Candies.

At first, Arya and Bran have 0 Candies. There are n days, at the i-th day, Arya finds ai candies in a box, that is given by the Many-Faced God. Every day she can give Bran at most 8 of her candies. If she don't give him the candies at the same day, they are saved for her and she can give them to him later.

Your task is to find the minimum number of days Arya needs to give Bran k candies before the end of the n-th day. Formally, you need to output the minimum day index to the end of which k candies will be given out (the days are indexed from 1 to n).

Print -1 if she can't give him k candies during n given days.

Input

The first line contains two integers n and k (1 ≤ n ≤ 100, 1 ≤ k ≤ 10000).

The second line contains n integers a1, a2, a3, ..., an (1 ≤ ai ≤ 100).

Output

If it is impossible for Arya to give Bran k candies within n days, print -1.

Otherwise print a single integer — the minimum number of days Arya needs to give Bran k candies before the end of the n-th day.

Examples

Input

2 3
1 2


Output

2

Input

3 17
10 10 10


Output

3

Input

1 9
10


Output

-1

Note

In the first sample, Arya can give Bran 3 candies in 2 days.

In the second sample, Arya can give Bran 17 candies in 3 days, because she can give him at most 8 candies per day.

In the third sample, Arya can't give Bran 9 candies, because she can give him at most 8 candies per day and she must give him the candies within 1 day.
import java.io.IOException;

public class Kek
{
    static class Scan
    {
        final private int BUF_SIZE = 1 << 16;
        private int cur_size = 0;
        private int pointer = 0;
        private java.io.DataInputStream in;
        private byte buffer[] = new byte[BUF_SIZE];

        Scan(java.io.InputStream input)
        {
            in = new java.io.DataInputStream(input);
        }

        // fills the buffer with characters
        private void fill() throws java.io.IOException
        {
            cur_size = in.read(buffer, 0, BUF_SIZE);
            if (cur_size == -1) buffer[0] = 0;
            pointer = 0;
        }

        private byte read() throws java.io.IOException
        {
            if (pointer == cur_size) fill();
            return buffer[pointer++];
        }

        int readInt() throws java.io.IOException
        {
            int res = 0;
            byte c;
            while ((c = read()) <= ' ');
            boolean negate = c == '-';
            if (negate) c = read();
            while (c >= '0' && c <= '9')
            {
                res = res * 10 + c - '0';
                c = read();
            }
            return negate ? -res : res;
        }

        long readLong() throws java.io.IOException
        {
            long res = 0;
            byte c;
            while ((c = read()) <= ' ') ;
            boolean negate = c == '-';
            if (negate) c = read();
            while (c >= '0' && c <= '9') {
                res = res * 10 + c - '0';
                c = read();
            }
            return negate ? -res : res;
        }

        double readDouble() throws java.io.IOException
        {
            byte c;
            while ((c = read()) <= ' ');
            boolean negate = c == '-';
            if (negate)
                c = read();
            int power = 0;
            long res = 0;
            boolean dot_flag = false;
            for (;(c >= '0' && c <= '9') || c == '.'; c = read())
            {
                if (dot_flag)
                    power++;
                if (c == '.')
                    dot_flag = true;
                else
                    res = res * 10 + c - '0';
            }
            double ret = res / Math.pow(10, power);
            return negate ? -ret : ret;
        }

        // skip defines whether ' ', '\n', '\r' must be skipped in readChar method
        char readChar(boolean skip) throws java.io.IOException
        {
            if (skip)
            {
                byte c;
                while ((c = read()) == ' ' || c == '\n' || c == '\r');
                return (char) c;
            }
            return (char) read();
        }

        // skip defines whether current string must be skipped in readString and readText methods

        /* If exact length is known, in terms of efficiency
         it is better to specify it while using readText, readString and readWord methods */

        String readWord() throws java.io.IOException
        {
            byte c;
            while ((c = read()) == '\n' || c == ' ' || c == '\r');
            StringBuilder s = new StringBuilder();
            s.append((char)c);
            for (;(c = read()) != '\n' && c != ' ' && c != '\r' && c != 0; s.append((char)c));
            return s.toString();
        }

        String readWord(int LEN) throws java.io.IOException
        {
            byte[] s = new byte[LEN];
            byte c;
            while ((c = read()) == '\n' || c == ' ' || c == '\r');
            s[0] = c;
            for (int i = 1; (c = read()) != ' ' && c != '\n' && c != '\r' && c != 0; s[i++] = c);
            return new String(s);
        }

        String readString(boolean skip, int LEN) throws java.io.IOException
        {
            byte[] s = new byte[LEN];
            byte c;
            if (skip)
                while ((c = read()) != '\n');
            for (int i = 0; (c = read()) != '\n' && c != '\r' && c != 0; s[i++] = c);
            read();
            return new String(s);
        }

        String readString(boolean skip) throws java.io.IOException
        {
            StringBuilder s = new StringBuilder("");
            byte c;
            if (skip)
                while ((c = read()) != '\n');
            for (;(c = read()) != '\n' && c != '\r' && c != 0; s.append((char)c));
            read();
            return s.toString();
        }

        String readText(boolean skip, int LEN) throws java.io.IOException
        {
            byte[] s = new byte[LEN];
            byte c;
            if (skip)
                while ((c = read()) != '\n');
            for (int i = 0; (c = read()) != 0; s[i++] = c);
            return new String(s);
        }

        String readText(boolean skip) throws java.io.IOException
        {
            StringBuilder s = new StringBuilder("");
            byte c;
            if (skip)
                while ((c = read()) != '\n');
            for (;(c = read()) != 0; s.append((char)c));
            return s.toString();
        }
    }


    public static void main(String args[]) throws IOException
    {
        Scan in = new Scan(System.in);
        int n = in.readInt(), k = in.readInt(), l = 0;
        for (int i = 0; i < n; i++)
        {
            int a = in.readInt();
            if (a > 8)
            {
                k -= 8;
                l += a - 8;
            }
            else
            {
                k -= a;
                if (l != 0)
                {
                    k -= Math.min(8 - a, l);
                    l = Math.max(l - 8 + a, 0);
                }
            }
            if (k <= 0)
            {
                System.out.println(i + 1);
                return;
            }
        }
        System.out.println(-1);
    }
}