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.*;
import java.util.*;

public class F implements Runnable {
	public static void main (String[] args) {new Thread(null, new F(), "_cf", 1 << 28).start();}

	int n, k;
	int[] a, diff;
	int[][][] dp;
	
	public void run() {
		FastScanner fs = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		System.err.println("");

		n = fs.nextInt(); k = fs.nextInt();
		a = fs.nextIntArray(n);
		Arrays.sort(a);
		dp = new int[n][n+1][k+1];
		for(int i = 0; i < n; i++) {
			for(int j = 0; j <= n; j++) {
				Arrays.fill(dp[i][j], -1);
			}
		}
		diff = new int[n];
		for(int i = 0; i < n-1; i++) diff[i] = a[i+1]-a[i];
		out.println(solve(0, 0, 0));
		
		out.close();
	}
	
	int solve(int idx, int numGroups, int imbal) {
		if(imbal > k) return 0;
//		System.out.println(idx + " " + numGroups + " " + imbal);
		if(idx == n) {
			if(numGroups > 0) return 0;
			return 1;
		}
		int ret = dp[idx][numGroups][imbal];
		if(ret != -1) return ret;
		int res = 0;
		
		//solo group
		res = add(res, solve(idx+1, numGroups, imbal+numGroups*diff[idx]));
		
		//start new group
		res = add(res, solve(idx+1, numGroups+1, imbal+(numGroups+1)*diff[idx]));
		
		//continue current groups
		if(numGroups > 0)
			res = add(res, mult(numGroups, solve(idx+1, numGroups, imbal+numGroups*diff[idx])));
		
		//end a current group
		if(numGroups > 0)
			res = add(res, mult(numGroups, solve(idx+1, numGroups-1, imbal + (numGroups-1)*diff[idx])));
		
		return dp[idx][numGroups][imbal] = res;
	}
	
	int MOD = (int)1e9+7;
	int add(int a, int b) {
		a += b;
		if(a >= MOD) a -= MOD;
		return a;
	}
	int mult(long a, long b) {
		a *= b;
		a %= MOD;
		return (int)a;
	}
	
	class FastScanner {
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;

		public FastScanner() {
			in = new BufferedInputStream(System.in, BS);
		}

		public FastScanner(String s) {
			try {
				in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
			}
			catch (Exception e) {
				in = new BufferedInputStream(System.in, BS);
			}
		}

		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}                
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}

		public int nextInt() {
			return (int)nextLong();
		}

		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}

		public double nextDouble() {
			double cur = nextLong();
			return c!='.' ? cur:cur+nextLong()/num;
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
		
		public int[] nextIntArray(int n) {
			int[] res = new int[n];
			for(int i = 0; i < n; i++) res[i] = nextInt();
			return res;
		}
		
	}

}