The Fair Nut likes kvass very much. On his birthday parents presented him n kegs of kvass. There are v_i liters of kvass in the i-th keg. Each keg has a lever. You can pour your glass by exactly 1 liter pulling this lever. The Fair Nut likes this drink very much, so he wants to pour his glass by s liters of kvass. But he wants to do it, so kvass level in the least keg is as much as possible.

Help him find out how much kvass can be in the least keg or define it's not possible to pour his glass by s liters of kvass.

Input

The first line contains two integers n and s (1 ≤ n ≤ 10^3, 1 ≤ s ≤ 10^{12}) — the number of kegs and glass volume.

The second line contains n integers v_1, v_2, …, v_n (1 ≤ v_i ≤ 10^9) — the volume of i-th keg.

Output

If the Fair Nut cannot pour his glass by s liters of kvass, print -1. Otherwise, print a single integer — how much kvass in the least keg can be.

Examples

Input

3 3
4 3 5


Output

3


Input

3 4
5 3 4


Output

2


Input

3 7
1 2 3


Output

-1

Note

In the first example, the answer is 3, the Fair Nut can take 1 liter from the first keg and 2 liters from the third keg. There are 3 liters of kvass in each keg.

In the second example, the answer is 2, the Fair Nut can take 3 liters from the first keg and 1 liter from the second keg.

In the third example, the Fair Nut can't pour his cup by 7 liters, so the answer is -1.
import java.io.*;
import java.util.*;

public class Main {
    private static final int MAX = Integer.MAX_VALUE;
    private static final int MIN = Integer.MIN_VALUE;

    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        InputReader.OutputWriter out = new InputReader.OutputWriter(outputStream);
        Scanner scanner = new Scanner(System.in);

        int n = in.nextInt();
        long s = in.nextLong();
        int [] a = new int[n];
        long sum = 0;
        for (int i = 0; i < a.length; i++) {
            a[i] = in.nextInt();
            sum+=a[i];
        }
        if(sum < s) {
            out.println(-1);
        }
        else {
            int lo = 1;
            int hi = 1_000_000_000;
            while (lo<=hi) {
                int med = lo  + (hi-lo)/2;
                if (can(a,med,s)) {
                    lo = med + 1;
                }
                else {
                    hi = med - 1;
                }
            }
            out.println(hi);
        }
        out.flush();
    }
    private static boolean can(int [] a, int min, long s) {
        long sum = 0;
        for (int i = 0; i < a.length; i++) {
            if(a[i] < min) return false;
            sum+=a[i]-min;
        }
        return sum>=s;
    }
    private static int binarySearch(int [] a, int min) {
        int lo = 0;
        int hi = a.length - 1;
        while(lo<=hi) {
            int med = lo+(hi-lo)/2;
            if(min > a[med]) {
                lo = med + 1;
            }
            else {
                hi = med - 1;
            }
        }
        return lo;
    }
    private static int [] freq(char [] c) {
        int [] f = new int[26];
        for(char cc : c) {
            f[cc-'a']++;
        }
        return f;
    }
    private static void shuffle(int [] a) {
        for (int i = 0; i < a.length; i++) {
            int index = (int)(Math.random()*(i+1));
            int temp = a[index];
            a[index] = a[i];
            a[i] = temp;
        }
    }
    private static int lowerBound(int [] a, int target) {
        int lo = 0;
        int hi = a.length - 1;
        while (lo<=hi) {
            int med = lo + (hi-lo)/2;
            if(target >= a[med]) {
                lo = med + 1;
            }
            else {
                hi = med - 1;
            }
        }
        return lo;
    }
    static int numberOfSubsequences(String a, String b) {
        int [] dp = new int[b.length()+1];
        dp[0] = 1;
        for (int i = 0; i < a.length(); i++) {
            for (int j = b.length() - 1; j >=0;j--) {
                if(a.charAt(i) == b.charAt(j)) {
                    dp[j+1]+=dp[j];
                }
            }
        }
        return dp[dp.length - 1];
    }
    static long count(String a, String b)
    {
        int m = a.length();
        int n = b.length();

        // Create a table to store
        // results of sub-problems
        long lookup[][] = new long[m + 1][n + 1];

        // If first string is empty
        for (int i = 0; i <= n; ++i)
            lookup[0][i] = 0;

        // If second string is empty
        for (int i = 0; i <= m; ++i)
            lookup[i][0] = 1;

        // Fill lookup[][] in
        // bottom up manner
        for (int i = 1; i <= m; i++)
        {
            for (int j = 1; j <= n; j++)
            {
                // If last characters are
                // same, we have two options -
                // 1. consider last characters
                //    of both strings in solution
                // 2. ignore last character
                //    of first string
                if (a.charAt(i - 1) == b.charAt(j - 1))
                    lookup[i][j] = lookup[i - 1][j - 1] +
                            lookup[i - 1][j];

                else
                    // If last character are
                    // different, ignore last
                    // character of first string
                    lookup[i][j] = lookup[i - 1][j];
            }
        }

        return lookup[m][n];
    }
}
class Point {
    private int x;
    private int y;
    public int getX() {
        return x;
    }
    public int getY() {
        return y;
    }
    public Point(int x,int y) {
        this.x = x;
        this.y = y;
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (o == null || getClass() != o.getClass()) return false;
        Point point = (Point) o;
        return x == point.x &&
                y == point.y;
    }

    @Override
    public int hashCode() {
        return Objects.hash(x, y);
    }
}

class InputReader extends BufferedReader {
    StringTokenizer tokenizer;

    public InputReader(InputStream inputStream) {
        super(new InputStreamReader(inputStream), 32768);
    }

    public InputReader(String filename) {
        super(new InputStreamReader(Thread.currentThread().getContextClassLoader().getResourceAsStream(filename)));
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(readLine());
            } catch (IOException e) {
                throw new RuntimeException();
            }
        }
        return tokenizer.nextToken();
    }

    public Integer nextInt(){
        return Integer.valueOf(next());
    }
    public Long nextLong() {
        return  Long.valueOf(next());
    }
    public Double nextDouble() {
        return Double.valueOf(next());
    }
    static class OutputWriter extends PrintWriter {
        public OutputWriter(OutputStream outputStream) {
            super(outputStream);
        }

        public OutputWriter(Writer writer) {
            super(writer);
        }

        public OutputWriter(String filename) throws FileNotFoundException {
            super(filename);
        }

        public void close() {
            super.close();
        }
    }
}