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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"sort"
	"strconv"
)

const pi = math.Pi

var mod int = pow(10, 9) + 7
var Umod uint64 = 1000000007
var ans, cnt int

func main() {
	reader.Split(bufio.ScanWords)
	N, _ := strconv.Atoi(read())
	K, _ := strconv.Atoi(read())
	a_f, a_r := make([]int, N+1), make([]int, N)
	for i := 1; i < N+1; i++ {
		t, _ := strconv.Atoi(read())
		a_f[i] = t
		a_r[i-1] = t
	}
	sort.Ints(a_f)
	sort.Sort(sort.Reverse(sort.IntSlice(a_r)))
	a_r = append(a_r[0:1], a_r[0:]...)
	a_r[0] = 0

	dp_f := make([][]bool, N+1)
	dp_r := make([][]bool, N+1)
	for i := 0; i < N+1; i++ {
		dp_f[i] = make([]bool, K+1)
		dp_r[i] = make([]bool, K+1)
	}
	dp_f[0][0] = true
	dp_r[0][0] = true
	// i文字目までで，値jを作れるか動的計画法で調査
	for i := 1; i < N+1; i++ {
		for j := 0; j < K+1; j++ {
			if 0 <= j-a_f[i] {
				dp_f[i][j] = dp_f[i][j] || dp_f[i-1][j-a_f[i]]
			}
			dp_f[i][j] = dp_f[i][j] || dp_f[i-1][j]
		}
	}
	// N-i文字目までで，値jを作れるか動的計画法で調査
	for i := 1; i < N+1; i++ {
		for j := 0; j < K+1; j++ {
			if 0 <= j-a_r[i] {
				dp_r[i][j] = dp_r[i][j] || dp_r[i-1][j-a_r[i]]
			}
			dp_r[i][j] = dp_r[i][j] || dp_r[i-1][j]
		}
	}
	// dpテーブルの累積和
	for i := 1; i < N+1; i++ {
		dp_ans := make([]bool, K+1)
		for j := 0; j < K+1; j++ {
			dp_ans[j] = dp_f[i-1][j] || dp_r[i-1][j]
		}

		// K-a[i] <= X < Kが存在するか調査
		for j := max(0, K-a_f[i]); j < K; j++ {
			if dp_ans[j] {
				break
			}
			if j == K-1 {
				cnt++
			}
		}
	}
	fmt.Println(cnt)
}

/*  ----------------------------------------  */

var reader = bufio.NewScanner(os.Stdin)

func read() string {
	reader.Scan()
	return reader.Text()
}

func lcm(x, y int) int {
	return (x / gcd(x, y)) * y
}

func gcd(x, y int) int {
	if x%y == 0 {
		return y
	} else {
		r := x % y
		return gcd(y, r)
	}
}

var fac [1000000]int
var finv [1000000]int
var inv [1000000]int

func combination_init() {
	fac[0], fac[1] = 1, 1
	finv[0], finv[1] = 1, 1
	inv[1] = 1

	// invは a^(-1) mod p
	// pをaで割ることを考える

	// p/a*(a) + p%a = p
	// p/a*(a) + p%a = 0          (mod p)
	// -p%a = p/a*(a)             (mod p)
	// -p%a *a^(-1)= p/a          (mod p)
	// a^(-1)= p/a * (-p%a)^(-1)  (mod p)
	// a^(-1) =

	for i := 2; i < 1000000; i++ {
		fac[i] = fac[i-1] * i % mod
		inv[i] = mod - inv[mod%i]*(mod/i)%mod
		finv[i] = finv[i-1] * inv[i] % mod
	}
}

func combination(x, y int) int {
	if x < y {
		return 0
	}
	if fac[0] != 1 {
		combination_init()
	}
	return fac[x] * (finv[y] * finv[x-y] % mod) % mod
	//return fac[x] / (fac[y] * fac[x-y])
}

func permutation(x, y int) int {
	if x < y {
		return 0
	}
	if fac[0] != 1 {
		combination_init()
	}
	return fac[x] * (finv[x-y] % mod) % mod
	//return fac[x] / fac[x-y]
}

func max(x ...int) int {
	var res int = x[0]
	for i := 1; i < len(x); i++ {
		res = int(math.Max(float64(x[i]), float64(res)))
	}
	return res
}

func min(x ...int) int {
	var res int = x[0]
	for i := 1; i < len(x); i++ {
		res = int(math.Min(float64(x[i]), float64(res)))
	}
	return res
}
func pow(x, y int) int { return int(math.Pow(float64(x), float64(y))) }
func abs(x int) int    { return int(math.Abs(float64(x))) }
func floor(x int) int  { return int(math.Floor(float64(x))) }
func ceil(x int) int   { return int(math.Ceil(float64(x))) }

type SortBy [][]int

func (a SortBy) Len() int           { return len(a) }
func (a SortBy) Swap(i, j int)      { a[i], a[j] = a[j], a[i] }
func (a SortBy) Less(i, j int) bool { return a[i][0] < a[j][0] }

type PriorityQueue []int

func (h PriorityQueue) Len() int            { return len(h) }
func (h PriorityQueue) Less(i, j int) bool  { return h[i] < h[j] }
func (h PriorityQueue) Swap(i, j int)       { h[i], h[j] = h[j], h[i] }
func (h *PriorityQueue) Push(x interface{}) { *h = append(*h, x.(int)) }
func (h *PriorityQueue) Pop() interface{} {
	old := *h
	n := len(old)
	x := old[n-1]
	*h = old[0 : n-1]
	return x
}