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: Accepted)

#include<bits/stdc++.h>
using namespace std;
using ll = long long;
template<class T> using vt = vector<T>;
template<class T> using vvt = vector<vt<T>>;
template<class T> using ttt = tuple<T,T>;
using tii = tuple<int,int>;
using vi = vector<int>;
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define pb push_back
#define mt make_tuple
#define ALL(a) (a).begin(),(a).end()
#define FST first
#define SEC second
#define DEB cerr<<"!"<<endl
#define SHOW(a,b) cerr<<(a)<<" "<<(b)<<endl
#define DIV int(1e9+7)
const int INF = (INT_MAX/2);
const ll LLINF = (LLONG_MAX/2);
const double eps = 1e-8;
//const double PI = M_PI;  
inline ll pow(ll x,ll n,ll m){ll r=1;while(n>0){if((n&1)==1)r=r*x%m;x=x*x%m;n>>=1;}return r%m;}
inline ll lcm(ll d1, ll d2){return d1 / __gcd(d1, d2) * d2;}
/* Coding space */
bool dp1[5001][5001] = {};
bool dp2[5001][5001] = {};
int main(){
  int n,k; cin >> n >> k;
  vi in(n);
  rep(i,n) cin >> in[i];

  rep(i,n+1)  dp1[i][0] = 1,dp2[i][0] = 1;
  rep(i,n)rep(j,k){
    if(dp1[i][j]){
      dp1[i+1][j] = 1;
      if(j + in[i] <= k)
        dp1[i+1][j+in[i]] = 1;
    }
  }
  for(int i = n; i > 0; i--)rep(j,k){
    if(dp2[i][j]){
      dp2[i-1][j] = 1;
      if(j + in[i-1] <= k)
        dp2[i-1][j+in[i-1]] = 1;
    }
  }
  int ans = n;
  rep(i,n){
    [&](){
    set<int> table;
    //rep(j,k+1) cerr << i << " " << j << " " << dp2[i+1][j] << endl;
    rep(j,k+1) if(dp2[i+1][j]) table.insert(j);
    rep(j,k+1){
      if(dp1[i][j]){
        auto itr = table.lower_bound(k - (j + in[i]));
        if(itr != table.end() && *itr + j < k){
          //cerr << i << " " << j << endl;
          ans--;
          return;
        }
      }
    }
    }();
  }
  cout << ans << endl;
}