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.math.BigInteger;
import java.util.*;


public class Main implements Runnable {

    int maxn = (int)1e3+111;
    int inf = (int)1e9;
    long mod = (long)1e9+7;
    int n,m,k;
    long a[] = new long[maxn];

    void solve() throws Exception {

        n = in.iInt();
        long s = in.lLong();

        for (int i=1; i<=n; i++) {
            a[i] = in.lLong();
        }

        long left = 0L;
        long right = Long.MAX_VALUE;
        long ans = -1;
        while (left<=right) {
            long mid = (left+right)/2L;
            if (checkMid(mid,s)) {
                left = mid + 1;
                ans = mid;
            } else {
                right = mid - 1;
            }
        }

        out.println(ans);
    }

    private boolean checkMid(long mid, long s) {
        long sum = 0L;
        for (int i=1; i<=n; i++) {
            if (a[i]-mid<0) return false;
            sum += Math.max(0L, a[i]-mid);
        }

        return (sum>=s);
    }

    class Pair {
        int x;
        int y;

        public Pair(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;
            Pair pair = (Pair) o;
            return x == pair.x &&
                    y == pair.y;
        }

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

    String fileInName = "";

    static Throwable throwable;
    public static void main (String [] args) throws Throwable {
        Thread thread = new Thread(null, new Main(), "", (1 << 26));
        thread.start();
        thread.join();
        thread.run();
        if (throwable != null)
            throw throwable;
    }

    FastReader in;
    PrintWriter out;

    public void run() {

        try {
            if (!fileInName.isEmpty()) {
                in = new FastReader(new BufferedReader(new FileReader(fileInName+".in")));
                out = new PrintWriter(new BufferedWriter(new FileWriter(fileInName+".out")));
            } else {
                in = new FastReader(new BufferedReader(new InputStreamReader(System.in)));
                out = new PrintWriter(System.out);
            }

            solve();
        } catch(Exception e) {
            throwable = e;
        } finally {
            out.close();
        }

    }

    class FastReader {
        BufferedReader bf;
        StringTokenizer tk = null;

        public FastReader(BufferedReader bf) {
            this.bf = bf;
        }

        public Integer iInt() throws Exception {
            return Integer.parseInt(sString());
        }

        public Long lLong() throws Exception {
            return Long.parseLong(sString());
        }

        public Double dDouble() throws Exception {
            return Double.parseDouble(sString());
        }

        public String sString () throws Exception {
            if (tk==null || !tk.hasMoreTokens()) {
                tk = new StringTokenizer(bf.readLine());
            }
            if (!tk.hasMoreTokens()) return sString();
            else
                return tk.nextToken();
        }
    }
}