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 f {
	static long mod = (long)1e9+7;
	static int n, h;
	static int[] as;
public static void main(String[] args) throws IOException {
	input.init(System.in);
	PrintWriter out = new PrintWriter(System.out);
	n = input.nextInt();
	h = input.nextInt();
	as = new int[n];
	for(int i = 0; i<n; i++) as[i] = input.nextInt();
	memo = new long[n+1][n+1];
	for(long[] A : memo) Arrays.fill(A, -1);
	out.println(go(0, 0));
	out.close();
}
static long[][] memo;
static long go(int at, int depth)
{
	if(at == n) return depth == 0 ? 1 : 0;
	if(memo[at][depth] != -1) return memo[at][depth];
	long res = 0;
	if(as[at] + depth == h)
	{
		res += go(at+1, depth); // Change nothing here.
		if(depth > 0) res += depth * go(at+1, depth-1); // Make this an end point.
	}
	else if(as[at] + depth + 1 == h)
	{
		res += go(at+1, depth+1); // Make this a start point.
		res += (1+depth) * go(at+1, depth); // Make this a start and an end point.
	}
	return memo[at][depth] = res%mod;
}

public static class input {
	static BufferedReader reader;
	static StringTokenizer tokenizer;

	static void init(InputStream input) {
		reader = new BufferedReader(new InputStreamReader(input));
		tokenizer = new StringTokenizer("");
	}

	static String next() throws IOException {
		while (!tokenizer.hasMoreTokens())
			tokenizer = new StringTokenizer(reader.readLine());
		return tokenizer.nextToken();
	}

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

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

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

