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: Wrong Answer)

#pragma region GNUC
//https://yukicoder.me/wiki/auto_vectorization
#ifdef __GNUC__
#pragma GCC optimize ("O3")
#pragma GCC target ("avx")
#endif
#pragma endregion
#define _USE_MATH_DEFINES
#pragma region include
#include <iostream>
#include <iomanip>
#include <stdio.h>

#include <sstream>
#include <algorithm>
#include <cmath>

#include <string>
#include <cstring>
#include <vector>
#include <tuple>

#include <queue>
#include <complex>
#include <set>
#include <map>
#include <stack>
#include <list>

#include <fstream>
#include <random>
#pragma endregion //#include
/////////
#define REP(i, x, n) for(int i = x; i < n; ++i)
#define rep(i,n) REP(i,0,n)
/////////
#pragma region typedef
typedef long long LL;
typedef long double LD;
typedef unsigned long long ULL;
#pragma endregion //typedef
////定数
const int INF = (int)1e9;
const int MOD = (int)1e9+7;
const LL LINF = (LL)1e18;
const double PI = acos(-1.0);
const double EPS = 1e-9;
/////////
using namespace::std;
/////////
#pragma region Math
// 最大公約数
template<class T>
inline T gcd(T a, T b){return b ? gcd(b, a % b) : a;}
//inline T gcd(T a, T b){return b == 0 ? a : gcd(b, a % b);}

// 最小公倍数
template<class T>
inline T lcm(T a, T b){return a / gcd(a, b) * b;}
//inline T lcm(T a, T b){return a * b / gcd(a, b);}

//繰り返し二乗法
template<class T,class S>
T powMod(T num,int n,S mod=MOD){
	if( n == 0 ){
		return (T)1;
	}
	T mul = num;
	T ans = (T)1;
	while(n){
		if( n&1){
			ans = (ans*mul)%mod;
		}
		mul = (mul*mul)%mod;
		n >>= 1;
	}
	return ans;
}
#pragma endregion //math
#pragma region
template<class T>
void UNIQUE(vector<T>& vec){
	sort(vec.begin(),vec.end());
	vec.erase(unique(vec.begin(),vec.end()),vec.end() );
}
#pragma endregion // sort erase unique
////////////////////////////////
#pragma region 
long long  bitcount64(long long bits)
{
    bits = (bits & 0x5555555555555555) + (bits >> 1 & 0x5555555555555555);
    bits = (bits & 0x3333333333333333) + (bits >> 2 & 0x3333333333333333);
    bits = (bits & 0x0f0f0f0f0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f0f0f0f0f);
    bits = (bits & 0x00ff00ff00ff00ff) + (bits >> 8 & 0x00ff00ff00ff00ff);
    bits = (bits & 0x0000ffff0000ffff) + (bits >>16 & 0x0000ffff0000ffff);
    return (bits & 0x00000000ffffffff) + (bits >>32 & 0x00000000ffffffff);
}
#pragma endregion //その他
////////////////////////////////
struct edge{int to;LL cost;};
edge make_edge(int to,LL cost){
	edge ret = {to,cost};
	return ret;
}
#pragma region //グラフ
void dijkstra(int root,int V,vector<LL>& dist,
	vector< vector<edge> > G	){
	priority_queue<pair<LL,int>,vector<pair<LL,int> >,greater<pair<LL,int> > > que;
	dist.assign(V,LINF);
	dist[root] = 0;
	que.push(pair<LL,int>(0,root));//距離、頂点番号

	while( !que.empty() ){
		pair<LL,int> p = que.top();que.pop();
		int v = p.second;
		if( dist[v] < p.first ) continue;
		for(int i=0;i < (int)G[v].size();++i){
			edge e = G[v][i];
			if( dist[e.to] > dist[v] + e.cost ){
				dist[e.to] = dist[v] + e.cost;
				que.push(pair<LL,int>(dist[e.to],e.to));
			}
		}
	}
}
#pragma endregion //ダイクストラ法:O(|E|log|V|)
#pragma region //グラフ
void warshall_floyd(vector<vector<LL> >& dist,int V,const LL INF=LINF){
	for(int k=0;k<V;++k){
		for(int i=0;i<V;++i){
			if( dist[i][k] >= INF ) continue;
			for(int j=0;j<V;++j){
				if( dist[k][j] >= INF )continue;
				dist[i][j] = min(dist[i][j],dist[i][k]+dist[k][j]);
			}
		}
	}
}
#pragma endregion //ワーシャルフロイド:O(|V|**3)
#pragma region //グラフ
bool is_bipartite(int v,int c,vector< vector<int> >& G,vector<int>& Color){
	Color[v] = c;
	for(int i=0;i < (int)G[v].size();++i){//隣接グラフ
		if(Color[ G[v][i] ] == c ) return false;
		if(Color[ G[v][i] ] == 0 && 
			!is_bipartite(G[v][i],-c,G,Color)
			){
				return false;
		}
	}
	return true;
}
bool is_bipartite(int Root,vector< vector<int> >& Graph){
	int GraphSize = Graph.size();
	vector<int> Color(GraphSize,0);
	const int ColorNo = 1;
	return is_bipartite(Root,ColorNo,Graph,Color);
}
#pragma endregion //二部グラフチェック is_bipartite(root,GraphList)
#pragma region 
//http://sugarknri.hatenablog.com/entry/2016/07/16/165715
//LL inv[1000010];
void makeinv(vector<LL>& inv,const LL P){
	int i;
	inv = vector<LL>(1000010,0);
	inv[1]=1;
	for(i=2;i<=1000000;i++){
		inv[i] = inv[P%i] * (P-P/i)%P;//OVF
	}
}

ULL nCk(ULL N,ULL k){
	static vector<LL> inv;
	if( inv.size() == 0 ){
		makeinv(inv,MOD);
	}
	k = min(k,N-k);
	if( k == 0 ){return 1;}
	if( k == 1 ){return N%MOD;}
	ULL ret = 1;
	for(int i=1;i<=k;++i){
		ret *= ((N+1-i)*inv[i])%MOD;//OVF
		ret %= MOD;
	}
	return ret;
}
#pragma endregion //組み合わせnCk(,10^5)
#pragma region CGL
class Point{
public:
	double x,y;
	Point(double x=0,double y=0):x(x),y(y){}

	Point	operator +	(Point p){return Point(add(x,p.x),add(y,p.y));}
	void	operator +=	(Point p){x=add(x,p.x);y=add(y,p.y);}
	Point	operator -	(Point p){return Point(add(x,-p.x),add(y,-p.y));}
	void	operator -=	(Point p){x=add(x,-p.x);y=add(y,-p.y);}
	Point	operator *	(double a){return Point(x*a,y*a);}
	double	operator *	(Point p){return dot(p);}
	Point	operator /	(double a){return Point(x/a,y/a);}

	double norm(){return sqrt(x*x+y*y);}
	double dot(Point p){return add(x*p.x,y*p.y);}
	double rot(Point p){return add(x*p.y,-y*p.x);}
	double add(double a,double b){
		double EPS = 1e-10;
		if( abs(a+b) < EPS*(abs(a)+abs(b)) ){
			return 0;
		}
		return a+b;
	}
};
istream& operator>>(istream& in,Point& P){
	in >> P.x >> P.y;
	return in;
}

//線分で表した直線の交差判定
bool is_cross(Point p1,Point p2,Point q1,Point q2){
	double res = (p2-p1).rot(q2-q1);
	return  res != 0;//平行なら0
}

//線分p1-p2上に点qがあるか判定
bool on_seg(Point p1,Point p2,Point q){
	return (p1-q).rot(p2-q) == 0 && (p1-q).dot(p2-q) <= 0;
}
//直線p1-p2と直線q1-q2の交点
Point intersection(Point p1,Point p2,Point q1,Point q2){
	return p1+(p2-p1)*((q2-q1).rot(q1-p1)/(q2-q1).rot(p2-p1));
}

//線分p1-p2,と線分q1-q2の交差判定
//line segment:線分
bool LSI(Point p1,Point p2,Point q1,Point q2){
	if( (p2-p1).rot(q1-p1) * (p2-p1).rot(q2-p1) < 0 ){
		if( (q2-q1).rot(p1-q1) * (q2-q1).rot(p2-q1) < 0 ){
			return true;
		}
	}
	return false;
}

enum PointPotion{ON_SEGMENT,COUNTER_CLOCKWISE,ONLINE_BACK,CLOCKWISE,ONLINE_FRONT};
PointPotion ccw(Point A,Point B,Point C){
	B -= A;C -=A;
	if( B.rot(C) > 0 ) return COUNTER_CLOCKWISE;
	if( B.rot(C) < 0 ) return CLOCKWISE;
	if( B.dot(C) < 0 ) return ONLINE_BACK;
	if( B.norm() < C.norm() ) return ONLINE_FRONT;
	return ON_SEGMENT;
}
#pragma endregion //class Point
#pragma region DSL
#pragma region DSL
class UnionFind{
public:
	int cNum;//要素数
	vector<int> parent;
	vector<int> count;
	vector< vector<int> > GList;
	UnionFind(int n){
		cNum = n;
		parent = vector<int>(n);
		count = vector<int>(n,1);
		GList.resize(n);
		for(int i=0;i<n;++i){
			parent[i] = i;
			GList[i].push_back(i);
		}
	}
	int find(int x){
		if( parent[x] == x ){return x;}
		return parent[x] = find( parent[x] );
	}
	bool same(int x,int y){return find(x) == find(y);}
	int Count(int x){return count[find(x)];}
	void add(int x,int y){//union
		x = find(x);
		y = find(y);
		if( x==y )return;
		parent[x] = y;
		count[y] += count[x];
		if( GList[y].size() < GList[x].size() ){
			swap(GList[x],GList[y]);
		}
		GList[y].insert( GList[y].end(),
			GList[x].begin(),GList[x].end() );
	}
};
#pragma endregion //UnionFind
#pragma region DSL
class segment{
	int n;
	int OTHER_VAL;
	int NUM_NULL;
	vector< int > dat;
public:
	int getN(){return n;}
	void init(int size,int num=INF,int num_null=-1){//N:要素数,最大値
		OTHER_VAL = num;
		NUM_NULL = num_null;
		n = 2;
		while(n < size ){
			n <<= 1;
		}
		dat.assign(n<<1, OTHER_VAL );
	}
	void init(vector<int> vec,int size,int num=INF){
		OTHER_VAL = num;
		n = 2;
		while(n < size ){
			n <<= 1;
		}
		dat.assign(n<<1,OTHER_VAL );
		for(int i=0;i<size;++i){
			update(i,vec[i]);
		}
	}
	int SELECT(int L,int R){
		return min(L,R);
	}
	void update(int i,int x){
		i += n;
		while(i){
			dat[i] = SELECT(dat[i],x);
			i >>= 1;
		}
	}
	void update(int X,int Y,int VAL){
		//全体の範囲は閉区間、
		update(1,0,n-1,X,Y,VAL);
	}
private:
	void update(int t,int L,int R,int X,int Y,int VAL){
		//親から子へ進んでいく
		if( L == X && R == Y){
			dat[t] = VAL;
		}else{
			int mid = (L+R)/2;
			if( dat[t] != NUM_NULL ){//値の伝播
				dat[t*2+0] = dat[t];
				dat[t*2+1] = dat[t];
				dat[t] = NUM_NULL;
			}
			if( Y <= mid ){
				update(t*2+0,L,mid,X,Y,VAL);
			}else if( X > mid ){
				update(t*2+1,mid+1,R,X,Y,VAL);
			}else{
				update(t*2+0,L,mid,X,mid,VAL);
				update(t*2+1,mid+1,R,mid+1,Y,VAL);
			}
		}
	}
public:
	//query(a,b,0,0,n)//[a,b)半開区間
	int query(int a,int b){
		return query(a,b,1,0,n);//n==getNを使う
	}
private:
	int query(int a,int b,int k,int l,int r){
		if(r<=a || b<=l)return OTHER_VAL;//交差しない
		if(a<=l && r<=b && dat[k]!=NUM_NULL)return dat[k];

		int res = OTHER_VAL;
		int mid = (l+r)>>1;
		if( a < mid ) res = SELECT(res,query(a,b,k*2+0,l,mid) );
		if( mid < b ) res = SELECT(res,query(a,b,k*2+1,mid,r) );
		return res;
	}
};
#pragma endregion //segment tree
#pragma region DSL
class BITree{//1-index
	int N;
	vector<LL> bit;
public:
	BITree(int n){
		N = n;
		bit = vector<LL>(N+1,0);//1-index
	}
	void add(int a,int w){
		for(int i=a;i<=N;i += i & -i){
			bit[i] += w;
		}
	}
	LL sum(int a){//[1,a)の和
		LL ret = 0;
		for(int i=a; i > 0; i -= i & -i){
			ret += bit[i];
		}
		return ret;
	}
};
#pragma endregion //BIndexTree
#pragma endregion //

#pragma region
//辞書順で比較
bool cmp_x(const Point& p,const Point& q){
	if( p.x != q.x ) return p.x < q.x;
	return p.y < q.y;
}

//凸包を求める
vector<Point> convex_hull(vector<Point> ps,int n){
	sort(ps.begin(),ps.end(), cmp_x);
	int k = 0;//凸包の頂点数
	vector<Point> qs(n*2);//構築中の凸包
	//下側の凸包の作成
	for(int i=0;i<n;++i){
		while(k>1 && (qs[k-1]-qs[k-2]).rot(ps[i]-qs[k-1]) <=0){
			k--;
		}
		qs[k++] = ps[i];
	}
	//上側凸包の作成
	for(int i=n-2,t=k;i>=0;i--){
		while(k>t && (qs[k-1]-qs[k-2]).rot(ps[i]-qs[k-1]) <=0){
			k--;
		}
		qs[k++] = ps[i];
	}
	qs.resize(k-1);
	return qs;
}
#pragma endregion //凸包
#pragma region 
template<class T,class U>
istream& operator>>(istream& in,pair<T,U>& P){
	in >> P.first >> P.second;
	return in;
}
#pragma endregion //cin pair<T,U>

#pragma region 
//行列の積
template<class T>
vector< vector<T> > operator*( vector<vector<T> >& A,vector< vector<T> >& B){
	LL mod = MOD;
	int R = A.size();
	int cen = A[0].size();
	int C = B[0].size();
	vector< vector<T> > ans(R,vector<T>(C,0) );
	for(int row=0;row<R;++row){
		for(int col=0;col<C;++col){
			for(int inner=0;inner< cen;++inner){
				ans[row][col] = (ans[row][col] + A[row][inner]*B[inner][col])%mod;
				//ans[row][col] = (ans[row][col] + A[row][inner]*B[inner][col]);
			}
		}
	}
	return ans;
}

template<class T>
vector< vector<T> > powMod(vector< vector<T> > mat,LL N){
	int R = mat.size();
	int C = mat[0].size();
	//R==C
	vector< vector<T> > I(R,vector<T>(C,0));//単位元
	for(int i=0;i<R && i<C;++i){
		I[i][i] = 1;
	}
	if( N == 0 ){
		return I;
	}
	vector< vector<T> > mul(R,vector<T>(C)),ans(R,vector<T>(C));
	ans = I;
	mul = mat;
	while(N){
		if( N & 1 ){
			ans = ans*mul;
		}
		N >>= 1;
		mul = mul*mul;
	}
	return ans;
}
#pragma endregion //行列

#pragma region
#pragma endregion //

////////////////////

void solve(){
	int N;//カード枚数
	int K;//閾値
	cin >> N >> K;
	
	vector<int> A(N);
	LL sum = 0;
	for(int i=0;i<N;++i){
		cin >> A[i];
	}
	sort(A.begin(),A.end());
	int pos = 0;
	while(pos < N && sum<K){
		sum += A[pos];
		++pos;
	}
	if( sum < K ){
		cout << N << endl;
		return;
	}

	int L = 0;//K>=1
	int R = pos-1;
	int Mid = (L+R)/2;
	while(R-L>1){//使わない数index
		Mid = (L+R)/2;
		if( K<=A[Mid] ){
			R = Mid;
			continue;
		}
		
		vector< bool > dp(K,false);
		dp[0] = true;
		for(int i=0;i<N;++i){
			if( i == Mid ) continue;
			for(int j=K-1;j>=0;--j){
				if( dp[j] == false)continue;
				if( A[i] + j >= K ) continue;
				dp[ A[i] + j ] = true;
			}
		}
		bool flag = false;
		
		for(int in=K-A[Mid];in<K;++in){
			if( dp[in] ){
				flag = true;
				break;
			}
		}
		if( flag == false ){
			L = Mid;
		}else{
			R = Mid;
		}
	}
	
	cout << Mid << endl;
}

#pragma region main
signed main(void){
	std::cin.tie(0);
	std::ios::sync_with_stdio(false);
	std::cout << std::fixed;//小数を10進数表示
	cout << setprecision(16);//小数点以下の桁数を指定
	
	solve();
}
#pragma endregion //main()