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 Main{
    final boolean isFileIO = false; 
    BufferedReader in;
    PrintWriter out;
    StringTokenizer st = new StringTokenizer("");
    String delim = " ";

    public static void main(String[] args) throws IOException {
        Main m = new Main();
        m.initIO();
        m.solve();
        m.in.close();
        m.out.close();
    }

    public void initIO() throws IOException {
        if(!isFileIO) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt"); 
        }
    }
  
    String nextToken() throws IOException {
        if(!st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken(delim);
    }
 
    String readLine() throws IOException {
        return in.readLine();
    }

    int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    public void solve() throws IOException {        
        int n, h;
        n = nextInt(); h = nextInt();
        int[] a = new int[n];
        for(int i = 0; i < n; i++)
            a[i] = nextInt();
        long[][] dp = new long[n][n + 1];
        if(a[0] == h - 1) {
            dp[0][0] = 1;
            dp[0][1] = 1;
        }
        if(a[0] == h) {
            dp[0][0] = 1;
        }
        long mod = 1_000_000_007;
        for(int i = 1; i < n; i++) {
            for(int j = 0; j <= n; j++) {
                if(a[i] + j == h) {
                    dp[i][j] = ((j - 1 >= 0 ? dp[i - 1][j - 1] : 0) + dp[i - 1][j]) % mod;
                }
                if(a[i] + j == h - 1) {
                    dp[i][j] = ((j + 1 <= n ? dp[i - 1][j + 1] : 0) * (j + 1) + dp[i - 1][j] * j + dp[i - 1][j]) % mod;
                }
            }
        }
        out.println(dp[n - 1][0]);
    }
}
