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 (Clang 3.8.0) (judge verdict: Wrong Answer)

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

int descending_compare(const void *a, const void *b){
    if (*(int*)a > *(int*)b){
        return -1;
    }else if (*(int*)a == *(int*)b){
        return 0;
    }else{
        return 1;
    }
}

int ascending_compare(const void *a, const void *b){
    if (*(int*)a < *(int*)b){
        return -1;
    }else if (*(int*)a == *(int*)b){
        return 0;
    }else{
        return 1;
    }
}

// array pointer = *a, num of element = n, key key
int lower_bound(int *a, int n, int key){
    int ng, mid, ok;
    ng = -1, ok = n-1;
    while (abs(ok - ng) > 1){
        mid = (ok + ng) / 2;
        if (key <= a[mid]){
            ok = mid;
        }else{
            ng = mid;
        }
    }
    if (a[ok] >= key)return ok;
    return n;
}

//greatest common divisor
unsigned long gcd(unsigned long x, unsigned long y){
    if (y == 0){ 
        return x;
    }else if (x > y){
        return gcd(y, x % y);
    }else{
        return gcd(x, y % x);
    }
}

unsigned long lcm(unsigned long x, unsigned long y){
    unsigned long g = gcd(x, y);
    return x*y/g;

}



long long factorial(int x){
    long long rtn = 1;
    int i;
    for (i = x; i > 1; i--){
        rtn = (rtn*i);
    }
    return rtn;
}




/*unsigned long long pascal[100][100] = {0};
void make_pascal(void){
    for (int i = 0; i < 100; i++){
        pascal[i][0] = 1;
    }
    pascal[1][1] = 1;
    for (int i = 2; i < 100; i++){
        for (int j = 1; j < 100; j++){
           pascal[i][j] = (pascal[i-1][j-1]+pascal[i-1][j]) % mod;
        }
    }
}*/
long long mod = 1000000007;

//x ^ n
long long mod_pow(long long x, long long n){
    long long res = 1;
    for(int i = 0;i < 60; i++){
        if(n >> i & 1) res = res * x % mod;
        x = x * x % mod;
    }
    return res;
}

/*int struct_ascending_compare(const void *p, const void *q) {
    return ((structname*)p)->member - ((strcutname*)q)->member;
}*/


int field[3][3];
int tate[3][2];
int yoko[2][3];
int total;

int dfs(int level){
    int chokudai = 0;
    if (level == 9){
        for (int i = 0; i < 3; i++){
            for (int j = 0; j < 2; j++){
                if (field[i][j] == field[i][j+1]){
                    chokudai += tate[i][j];
                }
            }
        }
        for (int i = 0; i < 2; i++){
            for (int j = 0; j < 3; j++){
                if (field[i][j] == field[i+1][j]){
                    chokudai += yoko[i][j];
                }
            }
        }
        return chokudai;
    }

    //空いているマスにlevelに応じて書き込む
    int tmp;
    int max = -1;
    int min = total + 1;
    for (int i = 0; i < 3; i++){
        for (int j = 0; j < 3; j++){
            if (field[i][j] == 0){
                if (level % 2){
                    field[i][j] = -1;
                    tmp = dfs(level+1);
                    field[i][j] = 0;
                    min = min>tmp?tmp:min;
                }else{
                    field[i][j] = 1;
                    tmp = dfs(level+1);
                    field[i][j] = 0;
                    max = max<tmp?tmp:max;
                }
            }
        }
    }
    if (level % 2){
        return min;
    }else{
        return max;
    }
}

int dp[5005];
int a[5005];
int n, k;

int check(int mid){
    memset(dp, 0, sizeof(dp));
    dp[0] = 1;

    for (int i = 0; i < n; i++){
        for (int j = 5000; j >= 0; j--){
            if (i != mid && j - a[i] >= 0 && dp[j-a[i]]){
                dp[j] = 1;
                if (i != mid && dp[j-a[i]] && j < k && j >= k-a[mid]) return 0;
            }
        }
    }

    return 1;
}


int main(void){
    scanf("%d %d", &n, &k);
    for (int i = 0; i < n; i++){
        scanf("%d", &a[i]);
    }

    qsort(a, n, sizeof(int), ascending_compare);

    int ng, mid, ok;
    ok = n, ng = -1;
    while (abs(ok - ng) > 1){
        mid = (ok + ng) / 2;
        if (!(mid >= k) && check(mid)){
            ng = mid;
        }else{
            ok = mid;
        }
    }
}