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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <math.h>
#include <string.h>
#include <stdlib.h>

#define llong long long
#define fr(i,l,r) for(i=(l);i<(r);i++)
#define min(p,q) ((p)<(q)?(p):(q))
#define max(p,q) ((p)>(q)?(p):(q))
#define INF 1000000000000//10^12


struct heap_t{
	int idnum;
	int atai;
}heap[5010];

int sz=-1;

void push(int x,int y){
	//自分のノード番号
	int i;
	sz++;
	i=sz;
	
	while(i>0){
		//親のノード番号
		int p=(i-1)/2;
		//もう逆転していないなら抜ける
		if(heap[p].atai<=x) break;
		//親のノードの数字を下ろして、自分は上に
		heap[i]=heap[p];
		i=p;
	}
	heap[i].atai=x;
	heap[i].idnum=y;
}

int pop(){
	int ret;
	int a,b;
	int x,y;
	int i;
	//最小値
	ret=heap[0].atai;
	//根に持ってくる値
	x=heap[sz].atai;
	y=heap[sz].idnum;
	sz=sz-1;
	//根からおろしていく
	i=0;
	while(i*2+1<=sz){
		a=i*2+1;
		b=i*2+2;
		if(b<sz&&heap[b].atai<heap[a].atai) a=b;
		//もう逆転していないなら終わり
		if(heap[a].atai>=x) break;
		//子の数字を持ち上げる
		heap[i]=heap[a];
		i=a;
	}
	heap[i].atai=x;
	heap[i].idnum=y;
	
	return ret;
}


int main(void)
{
	//変数の宣言
	int n,m;
	int a[5010];
	int noneed[5010];
	
	//よく使う変数
	int i,j,k,l;
	int flag=0;
	int ans=0;
	int count=0;
	int temp,temp1,temp2;
	int max,min;
//	int len;
	int sum=0;
	//データの読み込み
	scanf("%d %d",&n,&m);
	
	for(i=0;i<n;i++){
		scanf("%d",&a[i]);
	}
	
	for(i=0;i<5000;i++){
		noneed[i]=1;
	}
	
	
//	printf("nは%dです\n", n);
//	printf("データの読み込み終了\n");
	//実際の処理
	
	for(i=0;i<n;i++){
		temp=i;
		sum=0;
		while(sum<m&&temp<n){
			push(a[temp],temp);
			sum=sum+a[temp];
			temp++;
		}
	//	printf("l=%d,r=%d\n",i,temp-1);
		if(sum<m) break;
		
		for(j=i;j<temp;j++){//roop数あってる？
			sum=sum-heap[0].atai;
			if(sum<m){
				noneed[heap[0].idnum]=0;
			}
			sum=sum+heap[0].atai;
			pop();
		}
		
	}
	
	for(i=0;i<n;i++){
		ans=ans+noneed[i];
	}
	
	
//	printf("計算部分終了\n");
	//出力
	
	printf("%d",ans);
	
//	printf("結果の出力終了\n");
	
	return 0;
	
}