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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
const int INF = 1e9;
const ll LINF = 1e18;
template<class S,class T> ostream &operator << (ostream& out,const pair<S,T>& o){
    out << "(" << o.first << "," << o.second << ")"; return out;
}

/*
<url:https://arc070.contest.atcoder.jp/tasks/arc070_b>
問題文============================================================
 シカのAtCoDeerくんは正整数が書かれたカードを N 枚持っています。i(1≦i≦N) 枚目に書かれている数は ai です。
 AtCoDeerくんは大きい数が好きなので、
 カードに書かれた数の総和が K 以上になるようなカードの部分集合をよい集合と呼びます。
 
 そして、各カード i に対して、そのカードが不必要かどうかを次のように判定します。
 
 「カード i を含む任意のよい集合に対して、その集合からカード i を除いたものもよい集合」ならカード i は不必要
 それ以外の場合は、不必要でない
 
 不必要なカードの枚数を求めてください。
 ただし、それぞれの判定は独立に行われ、不必要だからと言ってカードが途中で捨てられたりすることはありません。

 入力は全て整数
 1≦N≦5000
 1≦K≦5000
 1≦ai≦10^9(1≦i≦N)
=================================================================

解説=============================================================

================================================================
*/
ll N,K;
vector<ll> a;
ll solve(){
    ll res = 0;
    cin >> N >> K;
    a.resize(N); for(auto &in:a) cin >> in;
    sort(a.begin(),a.end());
    vector<int> f(N,true);
    int l = 0,r = 0;
    ll sum = 0;
    while(true){
        while(r < N && sum < K){ sum += a[r++];}
        if(sum < K){ break; }
        if(sum - a[l] < K){
            for(int i = l; i <= r;i++) f[i] = false;
        }
        sum -= a[l++];
    }
    res = accumulate(f.begin(),f.end(),0);
    return res;
}
int main(void) {
	cin.tie(0); ios::sync_with_stdio(false);
    cout << solve() << endl;
	return 0;
}