Problem: There are n students in a class working on group projects. The students will divide into groups (some students may be in groups alone), work on their independent pieces, and then discuss the results together. It takes the i-th student ai minutes to finish his/her independent piece.

If students work at different paces, it can be frustrating for the faster students and stressful for the slower ones. In particular, the imbalance of a group is defined as the maximum ai in the group minus the minimum ai in the group. Note that a group containing a single student has an imbalance of 0. How many ways are there for the students to divide into groups so that the total imbalance of all groups is at most k?

Two divisions are considered distinct if there exists a pair of students who work in the same group in one division but different groups in the other.

Input

The first line contains two space-separated integers n and k (1 ≤ n ≤ 200, 0 ≤ k ≤ 1000) — the number of students and the maximum total imbalance allowed, respectively.

The second line contains n space-separated integers ai (1 ≤ ai ≤ 500) — the time it takes the i-th student to complete his/her independent piece of work.

Output

Print a single integer, the number of ways the students can form groups. As the answer may be large, print its value modulo 109 + 7.

Examples

Input

3 2
2 4 5


Output

3


Input

4 3
7 8 9 10


Output

13


Input

4 0
5 10 20 21


Output

1

Note

In the first sample, we have three options: 

  * The first and second students form a group, and the third student forms a group. Total imbalance is 2 + 0 = 2. 
  * The first student forms a group, and the second and third students form a group. Total imbalance is 0 + 1 = 1. 
  * All three students form their own groups. Total imbalance is 0. 



In the third sample, the total imbalance must be 0, so each student must work individually.

Solution (in JAVA):

Solution:

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

public class GroupProjects {
	public static void main(String[] args) {
		Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		int n = in.nextInt();
		int k = in.nextInt();
		int[] a = getIntArr(in, n);
		long r = solve(n, k, a);
		System.out.println(r);
		in.close();
	}

	private static long solve(int n, int k, int[] a) {
		Arrays.sort(a);
		long[][] prev = new long[n + 1][k + 1];
		prev[0][0] = 1;
		for (int i = 1; i <= n; i++) {
			long[][] cur = new long[n + 1][k + 1];
			int d = 0;
			if (i > 1) {
				d = a[i - 1] - a[i - 2];
			}
			for (int j = 0; j <= i; j++) {
				int dj = d * j;
				for (int l = 0; l <= k - dj; l++) {
					// i as single group
					cur[j][l + dj] = add(cur[j][l + dj], prev[j][l]);
					long dlj = mul(prev[j][l], j);
					// put i in one of the open groups
					cur[j][l + dj] = add(cur[j][l + dj], dlj);
					// add i to new group
					if (j < n) {
						cur[j + 1][l + dj] = add(cur[j + 1][l + dj], prev[j][l]);
					}
					// close a group
					if (j > 0) {
						cur[j - 1][l + dj] = add(cur[j - 1][l + dj], dlj);
					}
				}
			}
			prev = cur;
		}
		long r = 0;
		for (int i = 0; i <= k; i++) {
			r = add(r, prev[0][i]);
		}
		return r;
	}

	static long mod = 1000000007;

	static long add(long a, long b) {
		long r = a + b;
		if (r < 0) {
			r += mod;
		}
		return r % mod;
	}

	static long mul(long a, long b) {
		return (a * b) % mod;
	}

	int gcd(int a, int b) {
		if (b == 0) {
			return a;
		} else {
			return gcd(b, a % b);
		}
	}

	static String str(int[] a) {
		String[] str = new String[a.length];
		for (int i = 0; i < a.length; i++) {
			str[i] = a[i] + "";
		}
		return String.join(" ", str);
	}

	static int[] getIntArr(Scanner in, int size) {
		int[] arr = new int[size];
		for (int i = 0; i < size; i++) {
			arr[i] = in.nextInt();
		}
		return arr;
	}

	static int[][] getIntArr(Scanner in, int row, int col) {
		int[][] arr = new int[row][];
		for (int i = 0; i < row; i++) {
			arr[i] = getIntArr(in, col);
		}
		return arr;
	}

	static char[] getCharArr(Scanner in, int size) {
		char[] arr = in.next().toCharArray();
		return arr;
	}

	static String[] getStringArr(Scanner in, int size) {
		String[] arr = new String[size];
		for (int i = 0; i < size; i++) {
			arr[i] = in.next();
		}
		return arr;
	}

	static Map<Integer, List<Integer>> getEdges(Scanner in, int size, boolean directed) {
		Map<Integer, List<Integer>> edges = new HashMap<>();
		for (int i = 0; i < size; i++) {
			int from = in.nextInt();
			int to = in.nextInt();
			if (!edges.containsKey(from)) {
				edges.put(from, new ArrayList<Integer>());
			}
			edges.get(from).add(to);
			if (!directed) {
				if (!edges.containsKey(to)) {
					edges.put(to, new ArrayList<Integer>());
				}
				edges.get(to).add(from);
			}

		}
		return edges;
	}
}