Mr. Chanek opened a letter from his fellow, who is currently studying at Singanesia. Here is what it says.

Define an array b (0 ≤ b_i < k) with n integers. While there exists a pair (i, j) such that b_i ≠ b_j, do the following operation:

  * Randomly pick a number i satisfying 0 ≤ i < n. Note that each number i has a probability of 1/n to be picked. 
  * Randomly Pick a number j satisfying 0 ≤ j < k. 
  * Change the value of b_i to j. It is possible for b_i to be changed to the same value. 



Denote f(b) as the expected number of operations done to b until all elements of b are equal. 

You are given two integers n and k, and an array a (-1 ≤ a_i < k) of n integers. 

For every index i with a_i = -1, replace a_i with a random number j satisfying 0 ≤ j < k. Let c be the number of occurrences of -1 in a. There are k^c possibilites of a after the replacement, each with equal probability of being the final array.

Find the expected value of f(a) modulo 10^9 + 7. 

Formally, let M = 10^9 + 7. It can be shown that the answer can be expressed as an irreducible fraction p/q, where p and q are integers and q not ≡ 0 \pmod{M}. Output the integer equal to p ⋅ q^{-1} mod M. In other words, output such an integer x that 0 ≤ x < M and x ⋅ q ≡ p \pmod{M}.

After reading the letter, Mr. Chanek gave the task to you. Solve it for the sake of their friendship!

Input

The first line contains two integers n and k (2 ≤ n ≤ 10^5, 2 ≤ k ≤ 10^9). 

The second line contains n integers a_1, a_2, …, a_n (-1 ≤ a_i < k).

Output

Output an integer denoting the expected value of f(a) modulo 10^9 + 7.

Examples

Input


2 2
0 1


Output


2


Input


2 2
0 -1


Output


1


Input


3 3
0 1 1


Output


12


Input


3 3
-1 -1 -1


Output


11


Input


10 9
-1 0 -1 1 1 2 2 3 3 3


Output


652419213
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        FFindingExpectedValue solver = new FFindingExpectedValue();
        solver.solve(1, in, out);
        out.close();
    }

    static class FFindingExpectedValue {
        MOD mod = new MOD();

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt(), k = in.nextInt();
            int[] f = new int[n + 1];
            f[1] = 1000000006;
            int d = f[1];
            for (int a = 1; a < n; a++) {
                d = mod.subtract(mod.multiply(mod.multiply(d, a), k - 1), n);
                d = mod.multiply(d, mod.inverse(n - a));
                f[a + 1] = mod.add(f[a], d);
            }
            HashMap<Integer, Integer> hm = new HashMap<>();
            for (int i = 0; i < n; i++) {
                int u = in.nextInt();
                hm.put(u, hm.getOrDefault(u, 0) + 1);
            }
            int init = 0, fin = f[n];
            int t = hm.getOrDefault(-1, 0);
            int[] c = new int[t + 1];
            int h = mod.power(mod.subtract(1, mod.inverse(k)), t);
            int r = mod.inverse(k - 1);
            int R = 1, C = 1;
            for (int i = 0; i <= t; i++) {
                c[i] = mod.multiply(R, C);
                R = mod.multiply(R, r);
                C = mod.multiply(C, t - i);
                C = mod.multiply(C, mod.inverse(i + 1));
            }
            hm.remove(-1);
            int[] answers = new int[n + 1];
            Arrays.fill(answers, -1);

            for (int b : hm.keySet()) {
                int a = hm.get(b);
                if (answers[a] == -1) {
                    answers[a] = 0;
                    for (int i = 0; i <= t; i++) {
                        answers[a] = mod.add(answers[a], mod.multiply(c[i], f[a + i]));
                    }
                }
                init = mod.add(init, answers[a]);
            }
            int x = 0;
            for (int i = 0; i <= t; i++) {
                x = mod.add(x, mod.multiply(c[i], f[i]));
            }
            init = mod.add(init, mod.multiply(k - hm.size(), x));
            out.println(mod.subtract(mod.multiply(init, h), fin));
        }

    }

    static class MOD {
        static final int modulo = 1000000007;

        public int add(int x, int y) {
            x += y;
            if (x >= modulo) x -= modulo;
            return x;
        }

        public int subtract(int x, int y) {
            x -= y;
            if (x < 0) x += modulo;
            return x;
        }

        public int multiply(int x, int y) {
            return (int) ((x * 1L * y) % modulo);
        }

        public int power(int x, long y) {
            int ans = 1;
            for (; y > 0; y >>= 1, x = (int) ((x * 1L * x) % modulo))
                if (y % 2 == 1) ans = (int) ((ans * 1L * x) % modulo);
            return ans;
        }

        public int inverse(int x) {
            return power(x, modulo - 2);
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void println(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
            writer.print('\n');
        }

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

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

