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 q6 {
	static int mod=(int)(1e9+7);
	public static void main(String[] args) throws Exception
	{
		InputReader in=new InputReader(System.in);
		PrintWriter pw=new PrintWriter(System.out);
		int n=in.nextInt();
		int m=in.nextInt();
		int[] a=new int[n+1];
		for(int i=1;i<=n;i++)
		{
			a[i]=in.nextInt();
		}
		Arrays.sort(a);
		
		long[][][] dp=new long[2][n+1][m+1];
		dp[0][0][0]=1;
		//dp[i][j][k] currenty adding i'th element number of oprn group is j and their total imbalance is k
		for(int f=1;f<=n;f++)
		{
			int cu=f&1;
			int pr=(cu^1);
			for(int j=0;j<=n;j++)
			{
				for(int k=0;k<=m;k++)
				{
					/*//create new group total imbalance doesn't change
					if(j+1<=n)
					{
						int add=(j)*(a[i]-a[i-1]);
						if(k+add<=m)
						{
						dp[i][j+1][k+add]+=dp[i-1][j][k];
						}
					}
					//decrese size of one set
					if(j-1>=0)
					{
						int add=(a[i]-a[i-1]);
						if(k+add<=m)
						{
							dp[i][j-1][k+add]+=j*dp[i-1][j][k];
						}
					}
					//add element to any of open set
					int add=(j)*(a[i]-a[i-1]);
					if(k+add<=m)
					{
						dp[i][j][k+add]+=dp[i-1][j][k];
					}*/
					long ans=0;
					int prev=k-(j-1)*(a[f]-a[f-1]);
					if(prev>=0 && j-1>=0 )
					{
						ans+=dp[pr][j-1][prev];
						ans%=mod;
					}
					prev=k-(j)*(a[f]-a[f-1]);
					if(prev>=0)
					{
					ans+=(dp[pr][j][prev]*1l*(j+1));
					ans%=mod;
					
					}
					if(j+1<=n)
					{
						 prev=k-(j+1)*(a[f]-a[f-1]);
						 if(prev>=0 && prev<=m)
						 {
							 ans+=dp[pr][j+1][prev]*1l*(j+1);
							 ans%=mod;
						 }
						
					}
					dp[cu][j][k]=ans%mod;
					
					
					
					
					
					
					
				
					
					
					
				}
			}
			for(int i=0;i<=n;i++)
			{
				for(int j=0;j<=m;j++)
				{
					dp[pr][i][j]=0;
				}
			}
		}
		long ans=0;
		for(int i=0;i<=m;i++)
		{
			ans+=dp[n&1][0][i];
			ans%=mod;
		}
		pw.println(ans%mod);

		
		
		pw.close();
	}
	
	
	
	
	
	
	
	
	 static class InputReader {

		private InputStream stream;
		private byte[] buf = new byte[8192];
		private int curChar;
		private int snumChars;
		private SpaceCharFilter filter;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		public int snext() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int nextInt() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}

			int res = 0;

			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));

			return res * sgn;
		}
		
		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}

			long res = 0;

			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));

			return res * sgn;
		}
		
		public String readString() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}

}