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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Runtime.Remoting.Contexts;
class Simple {
    private int N, K;
    private int[] a;
    void Solve() {
        //input
        N = io.Int;
        K = io.Int;
        a = new int[N];
        for(int i = 0; i < N; ++i) a[i] = io.Int;
        //cal
        Func <int, bool> check = (n) => {
            if(a[n] > K) return true;
            var dp = new bool[K];
            dp[0] = true;
            for(int i = 0; i < N; ++i) {
                if(i == n) continue;
                for(int j = K - 1; j >= 0; --j) 
                    if(dp[j] && j + a[i] < K)
                        dp[j + a[i]] = true;
            }
            for(int i = K - a[n]; i < K; ++i) 
                if(dp[i]) return true;
            return false;
        };
        Array.Sort(a);
        var ans = search(a, -1, N, check);
        //ret
        Console.WriteLine(ans);
    }
    int search(int[] arr, int ng, int ok, Func <int, bool> f) {
        while(Math.Abs(ok - ng) > 1) {
            var mid = (ok + ng) / 2;
            if(f(mid)) ok = mid;
            else ng = mid;
        }
        return ok;
    }
    SimpleIO io = new SimpleIO();
    public static void Main(string[] args) => new Simple().Stream();
    private void Stream() {
        //var exStdIn = new System.IO.StreamReader("stdin.txt");
        //System.Console.SetIn(exStdIn);
        Solve();
        io.Flush();
    }
}
class SimpleIO {
    string[] _nextBuffer;
    int _bufferCnt;
    char[] cs = new char[] {' ', '"', ','};
    StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
    public SimpleIO() {
        _nextBuffer = new string[0];
        _bufferCnt = 0;
        Console.SetOut(sw);
    }
    public string Next() {
        if(_bufferCnt < _nextBuffer.Length) return _nextBuffer[_bufferCnt++];
        var st = Console.ReadLine();
        while(st == "") st = Console.ReadLine();
        if(st != null) _nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        else st = "";
        _bufferCnt = 0;
        return _nextBuffer[_bufferCnt++];
    }
    public string String => Next();
    public char Char => char.Parse(String);
    public int Int => int.Parse(String);
    public long Long => long.Parse(String);
    public double Double => double.Parse(String);
    public void Flush() { Console.Out.Flush(); }
}
static class NumericEx {
    public static string pad0 <T>(this T v, int n) { return v.ToString().PadLeft(n, '0'); }
    public static double RoundOff(this double v, int n) { return Math.Round(v, n - 1, MidpointRounding.AwayFromZero); }
    public static bool Odd(this int v) { return v % 2 != 0; }
    public static bool Odd(this long v) { return v % 2 != 0; }
    public static void REP(this int v, Action <int> act) {
        for(int i = 0; i < v; ++i) act(i);
    }
    public static void REPR(this int v, Action <int> act) {
        for(int i = v - 1; i >= 0; --i) act(i);
    }
}