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 <string.h>
#include <stdlib.h>
#include <math.h>
#include <stdlib.h>
#include <stdbool.h>
#define MOD 1000000007
void input_array(int how_data,long *data);
int get_random(int min, int max);
int factorial(int n);
int fibonacci(int n);
int qsort_09(const int *sys1 , const int *sys2);
int qsort_90(const int *sys1 , const int *sys2);

long souwa=0;

int main(void){
    long how_card,border;
    scanf("%ld %ld",&how_card,&border);
    if(border==0){
        printf("%ld\n",how_card);
        return 0;
    }
    long data[how_card];
    input_array(how_card,data);
    qsort(data,how_card,sizeof(long),(int (*)(const void *,const void *))qsort_09);
    int ans=0;
    int loop1;
    // 2 3 4 10 10 25
    // k=20
    // したから総和見て行って最初に20突破→5番目
    // 1 3 4
    // k=6
    // 1 1 3 4 5
    // k=2
    souwa=0;
    loop1=0;
    while(souwa<border){
        souwa+=data[loop1];
        loop1++;
        if(loop1>how_card){
            printf("%ld\n",how_card);
            return 0;
        }
    }
    //printf("now=%d wa=%ld\n",loop1,souwa);
    int loop2;
    for(loop2=0;loop2<loop1;loop2++){
        if(souwa-data[loop2]>=border)ans++;
    }

    //if(ans==0)ans=how_card;
    printf("%d\n",ans);
    return 0;
    
    
    
}


//how_data個の配列data[]に標準入力
//input_array(how_data,data);
void input_array(int how_data,long *data){
    int loop;
    for(loop=0;loop<how_data;loop++){
        scanf("%ld",&data[loop]);
        //souwa+=data[loop];
    }
}

int get_random(int min, int max){   //指定の範囲から乱数を1つ返すやつ
    //srand((unsigned int)time(0));   //現在時刻で疑似乱数初期化
    rand();rand();rand();rand();    //乱数を空打ち
    return (rand()%(max+1-min))+min;
}


int factorial(int n){//n!のMOD10^9+7を返すやつ
    unsigned long long int ret=1;
    for(int i=1;i<=n;i++)ret=(ret*i)%1000000007;
    return (int)ret;
}

int qsort_09(const int *sys1 , const int *sys2){ //小さいのが上にくるやつ
    //qsort(data,how_data,sizeof(int),(int (*)(const void *,const void *))qsort_09);
    if(*sys1<*sys2){
        return -1;
    }else if(*sys1==*sys2){
        return 0;
    }else{
        return 1;
    }
}

int qsort_90(const int *sys1 , const int *sys2){ //大きいのが上にくるやつ
    //qsort(data,how_data,sizeof(int),(int (*)(const void *,const void *))qsort_90);
    if(*sys1<*sys2){
        return 1;
    }else if(*sys1==*sys2){
        return 0;
    }else{
        return -1;
    }
}
int fibonacci(int n){
    switch(n){
        case 0:return 0;
        case 1:return 1;
        default :return fibonacci(n-1)+fibonacci(n-2);
    }
}