Problem: // We decided to drop the legend about the power sockets but feel free to come up with your own :^)

Define a chain: 

  * a chain of length 1 is a single vertex; 
  * a chain of length x is a chain of length x-1 with a new vertex connected to the end of it with a single edge. 



You are given n chains of lengths l_1, l_2, ..., l_n. You plan to build a tree using some of them.

  * Each vertex of the tree is either white or black. 
  * The tree initially only has a white root vertex. 
  * All chains initially consist only of white vertices. 
  * You can take one of the chains and connect any of its vertices to any white vertex of the tree with an edge. The chain becomes part of the tree. Both endpoints of this edge become black. 
  * Each chain can be used no more than once. 
  * Some chains can be left unused. 



The distance between two vertices of the tree is the number of edges on the shortest path between them.

If there is at least k white vertices in the resulting tree, then the value of the tree is the distance between the root and the k-th closest white vertex.

What's the minimum value of the tree you can obtain? If there is no way to build a tree with at least k white vertices, then print -1.

Input

The first line contains two integers n and k (1 ≤ n ≤ 2 ⋅ 10^5, 2 ≤ k ≤ 10^9) — the number of chains and the minimum number of white vertices a tree should have to have a value.

The second line contains n integers l_1, l_2, ..., l_n (3 ≤ l_i ≤ 2 ⋅ 10^5) — the lengths of the chains.

Output

Print a single integer. If there is no way to build a tree with at least k white vertices, then print -1. Otherwise, print the minimum value the tree can have.

Examples

Input


1 2
3


Output


2


Input


3 3
4 3 3


Output


3


Input


3 5
4 3 4


Output


4


Input


2 10
5 7


Output


-1

Note

<image>

You are allowed to not use all the chains, so it's optimal to only use chain of length 4 in the second example.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.text.*;

public class codeforces6 {
    void pre() throws Exception {}
    void solve(int TC) throws Exception {
        int N = ni();
        long K = nl();
        long[] L = new long[N];
        for (int i = 0; i < N; i++) L[i] = nl();
        Arrays.sort(L);
        for (int i = 0, j = N - 1; i < j; i++, j--) {
            long tmp = L[i];
            L[i] = L[j];
            L[j] = tmp;
        }

        int MAX = (int) 2e6;
        LazySegmentTree lst = new LazySegmentTree(MAX);
        lst.update(0, 0, 1);
        long ans = IINF;
        int cur = 0;
        for (int i = 0; i < N; i++) {
            while (lst.sum(cur, cur) == 0) cur++;

            lst.update(cur, cur, -1);
            if (L[i] % 2 == 1) {
                lst.update(cur + 2, (int)(cur + 2 + L[i] / 2 - 1), 2);
            } else {
                lst.update(cur + 2, (int)(cur + 2 + L[i] / 2 - 2), 2);
                lst.update((int)(cur + L[i] / 2 + 1), (int)(cur + L[i] / 2 + 1), 1);
            }
            ans = Math.min(ans, lst.kth(K - 1));
        }
        if (ans == IINF) ans = -1;
        pn(ans);
    }
    class LazySegmentTree {
        int m = 1;
        long[] t, lazy;
        public LazySegmentTree(int n) {
            while (m < n) m <<= 1;
            t = new long[m << 1];
            lazy = new long[m << 1];
        }
        private void push(int i, int ll, int rr) {
            if (lazy[i] != 0) {
                t[i] += lazy[i] * (rr - ll + 1);
                if (i < m) {
                    lazy[i << 1] += lazy[i];
                    lazy[i << 1 | 1] += lazy[i];
                }
                lazy[i] = 0;
            }
        }
        public void update(int l, int r, long x) {
            u(l, r, 0, m - 1, 1, x);
        }
        public long sum(int l, int r) {
            return s(l, r, 0, m - 1, 1);
        }

        private void u(int l, int r, int ll, int rr, int i, long x) {
            push(i, ll, rr);
            if (l == ll && r == rr) {
                lazy[i] += x;
                push(i, ll, rr);
                return;
            }
            int mid = (ll + rr) / 2;
            if (r <= mid) {
                u(l, r, ll, mid, i << 1, x);
                push(i << 1 | 1, mid + 1, rr);
            } else if (l > mid) {
                push(i << 1, ll, mid);
                u(l, r, mid + 1, rr, i << 1 | 1, x);
            } else {
                u(l, mid, ll, mid, i << 1, x);
                u(mid + 1, r, mid + 1, rr, i << 1 | 1, x);
            }
            t[i] = t[i << 1] + t[i << 1 | 1];
        }
        private long s(int l, int r, int ll, int rr, int i) {
            push(i, ll, rr);
            if (l == ll && r == rr) return t[i];
            int mid = (ll + rr) / 2;
            if (r <= mid) return s(l, r, ll, mid, i << 1);
            else if (l > mid) return s(l, r, mid + 1, rr, i << 1 | 1);
            else return s(l, mid, ll, mid, i << 1) + s(mid + 1, r, mid + 1, rr, i << 1 | 1);
        }
        private long kth(int ll, int rr, int i, long K) {
            if (ll == rr) return ll;
            int mid = (ll + rr) / 2;
            push(i << 1, ll, mid);
            push(i << 1 | 1, mid + 1, rr);
            if (K < t[i << 1]) return kth(ll, mid, i << 1, K);
            return kth(mid + 1, rr, i << 1 | 1, K - t[i << 1]);
        }
        public long kth(long K) {
            push(1, 0, m - 1);
            if (sum(0, m - 1) <= K) return IINF;
            return kth(0, m - 1, 1, K);
        }
    }
    void hold(boolean b) throws Exception {
        if (!b) throw new Exception("Hold right there, Sparky!");
    }
    void exit(boolean b) {
        if (!b) System.exit(0);
    }
    static void dbg(Object...o) {
        System.err.println(Arrays.deepToString(o));
    }
    final long IINF = (long) 1e17;
    final int INF = (int) 1e9 + 2;
    DecimalFormat df = new DecimalFormat("0.00000000000");
    double PI = 3.141592653589793238462643383279502884197169399, eps = 1e-8;
    static boolean multipleTC = false, memory = true, fileIO = false;
    FastReader in ;
    PrintWriter out;
    void run() throws Exception {
        long ct = System.currentTimeMillis();
        if (fileIO) { in = new FastReader("");
            out = new PrintWriter("");
        } else { in = new FastReader();
            out = new PrintWriter(System.out);
        }
        int T = multipleTC ? ni() : 1;
        pre();
        for (int t = 1; t <= T; t++) solve(t);
        out.flush();
        out.close();
        System.err.println(System.currentTimeMillis() - ct);
    }
    public static void main(String[] args) throws Exception {
        if (memory) new Thread(null, new Runnable() {
            public void run() {
                try {
                    new codeforces6().run();
                } catch (Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }, "1", 1 << 28).start();
        else new codeforces6().run();
    }
    int[][] make(int n, int e, int[] from, int[] to, boolean f) {
        int[][] g = new int[n][];
        int[] cnt = new int[n];
        for (int i = 0; i < e; i++) {
            cnt[from[i]]++;
            if (f) cnt[to[i]]++;
        }
        for (int i = 0; i < n; i++) g[i] = new int[cnt[i]];
        for (int i = 0; i < e; i++) {
            g[from[i]][--cnt[from[i]]] = to[i];
            if (f) g[to[i]][--cnt[to[i]]] = from[i];
        }
        return g;
    }
    int[][][] makeS(int n, int e, int[] from, int[] to, boolean f) {
        int[][][] g = new int[n][][];
        int[] cnt = new int[n];
        for (int i = 0; i < e; i++) {
            cnt[from[i]]++;
            if (f) cnt[to[i]]++;
        }
        for (int i = 0; i < n; i++) g[i] = new int[cnt[i]][];
        for (int i = 0; i < e; i++) {
            g[from[i]][--cnt[from[i]]] = new int[] {
                to[i], i, 0
            };
            if (f) g[to[i]][--cnt[to[i]]] = new int[] {
                from[i], i, 1
            };
        }
        return g;
    }
    int find(int[] set, int u) {
        return set[u] = (set[u] == u ? u : find(set, set[u]));
    }
    int digit(long s) {
        int ans = 0;
        while (s > 0) {
            s /= 10;
            ans++;
        }
        return ans;
    }
    long gcd(long a, long b) {
        return (b == 0) ? a : gcd(b, a % b);
    }
    int gcd(int a, int b) {
        return (b == 0) ? a : gcd(b, a % b);
    }
    int bit(long n) {
        return (n == 0) ? 0 : (1 + bit(n & (n - 1)));
    }
    void p(Object...o) {
        for (Object oo: o) out.print(oo + " ");
    }
    void pn(Object...o) {
        for (int i = 0; i < o.length; i++) out.print(o[i] + (i + 1 < o.length ? " " : "\n"));
    }
    void pni(Object...o) {
        for (Object oo: o) out.print(oo + " ");
        out.println();
        out.flush();
    }
    String n() throws Exception {
        return in.next();
    }
    String nln() throws Exception {
        return in.nextLine();
    }
    int ni() throws Exception {
        return Integer.parseInt( in .next());
    }
    long nl() throws Exception {
        return Long.parseLong( in .next());
    }
    double nd() throws Exception {
        return Double.parseDouble( in .next());
    }

    class FastReader {
        BufferedReader br;
        StringTokenizer st;
        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String s) throws Exception {
            br = new BufferedReader(new FileReader(s));
        }

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

        String nextLine() throws Exception {
            String str;
            try {
                str = br.readLine();
            } catch (IOException e) {
                throw new Exception(e.toString());
            }
            return str;
        }
    }
}