Peter has a sequence of integers a1, a2, ..., an. Peter wants all numbers in the sequence to equal h. He can perform the operation of "adding one on the segment [l, r]": add one to all elements of the sequence with indices from l to r (inclusive). At that, Peter never chooses any element as the beginning of the segment twice. Similarly, Peter never chooses any element as the end of the segment twice. In other words, for any two segments [l1, r1] and [l2, r2], where Peter added one, the following inequalities hold: l1 ≠ l2 and r1 ≠ r2.

How many distinct ways are there to make all numbers in the sequence equal h? Print this number of ways modulo 1000000007 (109 + 7). Two ways are considered distinct if one of them has a segment that isn't in the other way.

Input

The first line contains two integers n, h (1 ≤ n, h ≤ 2000). The next line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 2000).

Output

Print a single integer — the answer to the problem modulo 1000000007 (109 + 7).

Examples

Input

3 2
1 1 1


Output

4


Input

5 1
1 1 1 1 1


Output

1


Input

4 3
3 2 1 1


Output

0
import java.io.*;
import java.util.*;

public class D {

    final static long MOD = 1000000007;

    void solve() throws IOException {
        in = new InputReader("__std");
        out = new OutputWriter("__std");

        int n = in.readInt();
        int h = in.readInt();
        int[] a = new int[n];
        for (int i = 0; i < n; ++i) {
            a[i] = in.readInt();
            if (a[i] > h) {
                out.println(0);
                exit();
            }
        }
        long[][] d = new long[2][h + 1];
        int k = 0;
        d[k][0] = 1;
        for (int i = 0; i < n; ++i) {
            int l = h - a[i];
            // the same
            d[1 - k][l] = (d[1 - k][l] + d[k][l]) % MOD;
            if (l > 0) {
                // start and end
                d[1 - k][l - 1] = (d[1 - k][l - 1] + d[k][l - 1]) % MOD;
                // start one
                d[1 - k][l] = (d[1 - k][l] + d[k][l - 1]) % MOD;
                // stop one
                d[1 - k][l - 1] = (d[1 - k][l - 1] + d[k][l] * l % MOD) % MOD;
                // stop and start
                d[1 - k][l - 1] = (d[1 - k][l - 1] + d[k][l - 1] * (l - 1) % MOD) % MOD;
            }
            Arrays.fill(d[k], 0);
            k = 1 - k;
        }
        out.println(d[k][0]);

        exit();
    }

    void exit() {
        //System.err.println((System.currentTimeMillis() - startTime) + " ms");
        out.close();
        System.exit(0);
    }

    InputReader in;
    OutputWriter out;

    //long startTime = System.currentTimeMillis();

    public static void main(String[] args) throws IOException {
        new D().solve();
    }

    class InputReader {

        private InputStream stream;

        private byte[] buffer = new byte[1024];
        private int pos, len;

        private int cur;

        private StringBuilder sb = new StringBuilder(32);

        InputReader(String name) throws IOException {
            if (name.equals("__std")) {
                stream = System.in;
            } else {
                stream = new FileInputStream(name);
            }
            cur = read();
        }

        private int read() throws IOException {
            if (len == -1) {
                throw new EOFException();
            }
            if (pos >= len) {
                pos = 0;
                len = stream.read(buffer);
                if (len == -1) return -1;
            }
            return buffer[pos++];
        }

        char readChar() throws IOException {
            if (cur == -1) {
                throw new EOFException();
            }
            char res = (char) cur;
            cur = read();
            return res;
        }

        int readInt() throws IOException {
            if (cur == -1) {
                throw new EOFException();
            }
            while (whitespace()) {
                cur = read();
            }
            if (cur == -1) {
                throw new EOFException();
            }
            int sign = 1;
            if (cur == '-') {
                sign = -1;
                cur = read();
            }
            int res = 0;
            while (!whitespace()) {
                if (cur < '0' || cur > '9') {
                    throw new NumberFormatException();
                }
                res *= 10;
                res += cur - '0';
                cur = read();
            }
            return res * sign;
        }

        long readLong() throws IOException {
            if (cur == -1) {
                throw new EOFException();
            }
            return Long.parseLong(readToken());
        }

        double readDouble() throws IOException {
            if (cur == -1) {
                throw new EOFException();
            }
            return Double.parseDouble(readToken());
        }

        String readLine() throws IOException {
            if (cur == -1) {
                throw new EOFException();
            }
            sb.setLength(0);
            while (cur != -1 && cur != '\r' && cur != '\n') {
                sb.append((char) cur);
                cur = read();
            }
            if (cur == '\r') {
                cur = read();
            }
            if (cur == '\n') {
                cur = read();
            }
            return sb.toString();
        }

        String readToken() throws IOException {
            if (cur == -1) {
                throw new EOFException();
            }
            while (whitespace()) {
                cur = read();
            }
            if (cur == -1) {
                throw new EOFException();
            }
            sb.setLength(0);
            while (!whitespace()) {
                sb.append((char) cur);
                cur = read();
            }
            return sb.toString();
        }

        boolean whitespace() {
            return cur == ' ' || cur == '\t' || cur == '\r' || cur == '\n' || cur == -1;
        }

        boolean eof() {
            return cur == -1;
        }
    }

    class OutputWriter {

        private PrintWriter writer;

        OutputWriter(String name) throws IOException {
            if (name.equals("__std")) {
                writer = new PrintWriter(System.out);
            } else {
                writer = new PrintWriter(name);
            }
        }

        void print(String format, Object ... args) {
            writer.print(new Formatter(Locale.US).format(format, args));
        }

        void println(String format, Object ... args) {
            writer.println(new Formatter(Locale.US).format(format, args));
        }

        void print(Object value) {
            writer.print(value);
        }

        void println(Object value) {
            writer.println(value);
        }

        void println() {
            writer.println();
        }

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