Problem:
Score : 600 points

Problem Statement

AtCoDeer the deer has N cards with positive integers written on them. The number on the i-th card (1≤i≤N) is a_i.
Because he loves big numbers, he calls a subset of the cards good when the sum of the numbers written on the cards in the subset, is K or greater.

Then, for each card i, he judges whether it is unnecessary or not, as follows:

If, for any good subset of the cards containing card i, the set that can be obtained by eliminating card i from the subset is also good, card i is unnecessary.

Otherwise, card i is NOT unnecessary.

Find the number of the unnecessary cards. Here, he judges each card independently, and he does not throw away cards that turn out to be unnecessary.

Constraints

All input values are integers.

1≤N≤5000

1≤K≤5000

1≤a_i≤10^9 (1≤i≤N)

Partial Score

300 points will be awarded for passing the test set satisfying N,K≤400.

Input

The input is given from Standard Input in the following format:

N K
a_1 a_2 ... a_N

Output

Print the number of the unnecessary cards.

Sample Input 1

3 6
1 4 3

Sample Output 1

1

There are two good sets: {2,3} and {1,2,3}.

Card 1 is only contained in {1,2,3}, and this set without card 1, {2,3}, is also good. Thus, card 1 is unnecessary.

For card 2, a good set {2,3} without card 2, {3}, is not good. Thus, card 2 is NOT unnecessary.

Neither is card 3 for a similar reason, hence the answer is 1.

Sample Input 2

5 400
3 1 4 1 5

Sample Output 2

5

In this case, there is no good set. Therefore, all the cards are unnecessary.

Sample Input 3

6 20
10 4 3 10 25 2

Sample Output 3

3

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;

public class Main {
	public static void main(String[] args) throws IOException {
		proconScan proScan = new proconScan(" ");
		proScan.scan();
		Long nInteger = proScan.nextLong();
		Long kInteger = proScan.nextLong();
		ArrayList<Long> buf = new ArrayList<Long>();
		proScan.scan();
		for (int i = 0; i < nInteger; i++) {
			buf.add(proScan.nextLong());
		}
		Collections.sort(buf);
		Long ans = new Long(0);
		Long ans2 = new Long(0);
		Long temp = new Long(0);
		
		for (int i = buf.size() - 1; i >= 0; i--) {
			temp += buf.get(i);
			if (temp >= kInteger) {
				ans-=ans2;
				temp = new Long(0);
				ans2 = new Long(0);
			}else{
				ans++;
				ans2++;
			}
		}
		System.out.println(ans);
		proScan.proconEnd();
	}

}

class proconScan {
	private BufferedReader br;
	private String inLine;
	private String[] inString;
	private Integer idx;
	private String splitChar;

	public proconScan() {
		br = new BufferedReader(new InputStreamReader(System.in));
		idx = 0;
		splitChar = " ";
	}

	public proconScan(String split) {
		br = new BufferedReader(new InputStreamReader(System.in));
		idx = 0;
		splitChar = split;
	}

	public void proconEnd() throws IOException {
		// TODO 自動生成されたメソッド・スタブ
		br.close();
	}

	public String scan() throws IOException {
		idx = 0;
		inLine = br.readLine();
		inString = inLine.split(splitChar, 0);
		return inLine;
	}

	public Integer scanInteger1() throws IOException {
		scan();
		return Integer.parseInt(inString[0]);
	}

	public String backLine() {
		return inLine;
	}

	public String nextString() {
		return inString[idx++];
	}

	public String[] getString() {
		return inString;
	}

	public Long nextLong() {
		Long num;
		try {
			num = Long.parseLong(inString[idx++]);
		} catch (NumberFormatException e) {
			num = null;// TODO: handle exception
		}
		return num;
	}

	public Integer nextInteger() {
		Integer num;
		try {
			num = Integer.parseInt(inString[idx++]);
		} catch (NumberFormatException e) {
			num = null;// TODO: handle exception
		}
		return num;
	}

	public Integer[] getInteger() {
		Integer[] num = new Integer[this.getLen()];

		for (int i = 0; i < this.getLen(); i++) {
			num[i] = Integer.parseInt(inString[i]);
		}

		return num;
	}

	public Float nextFloat() {
		Float num;
		try {
			num = Float.parseFloat(inString[idx++]);
		} catch (NumberFormatException e) {
			num = null;// TODO: handle exception
		}
		return num;
	}

	public Float[] getFloat() {
		Float[] num = new Float[this.getLen()];

		for (int i = 0; i < this.getLen(); i++) {
			num[i] = Float.parseFloat(inString[i]);
		}

		return num;
	}

	public Integer getLen() {
		return inString.length;
	}

	public int[] getInt() {
		int[] num = new int[this.getLen()];

		for (int i = 0; i < this.getLen(); i++) {
			num[i] = Integer.parseInt(inString[i]);
		}

		return num;
	}

}