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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

import java.util.*
import kotlin.*

import java.io.InputStream
import java.lang.NumberFormatException
import java.lang.StringBuilder


fun main(args: Array<String>) {
    Program().solve()
}

class Program {
    fun solve() {
        val sc = FastScanner()
        val n = sc.nextInt()
        val k = sc.nextInt()
        val a = (1..n).map { sc.nextInt() }

        // a[i]が必要になる条件
        // a[i]を含む良い集合の総和 - a[i] < kになる良い集合が存在する

        // [0,i)で作れる値 (i,n)で作れる値を持っておく [
        // 前 f 後ろ b
        // f + b < k <= f + b + a[i]
        // k - f - a[i] <= b < k - f
        //

        val f = Array(n) { Array(k + 1) { false } }
        f[0][0] = true
        for (i in 0 until n - 1) {
            for (j in 0..k) {
                if (f[i][j]) {
                    f[i + 1][j] = true
                    f[i + 1][Math.min(k, j + a[i])] = true
                }
            }
        }



        val b = Array(n) { SegmentTree({ l, r -> l + r }, 0) }
        b[n - 1][0] = 1

        for (i in n - 1 downTo 1) {
            for (j in 0..k) {
                if (b[i][j] == 1) {
                    b[i - 1][j] = 1
                    b[i - 1][Math.min(k, j + a[i])] = 1
                }
            }
        }

        var ans = n

        for (i in 0 until n) {
            var flag = false
            for (j in 0 until k) {
                if (f[i][j] && b[i].query(k - j - a[i], k - j) > 0) {
                    flag = true
                    break
                }
            }
            if (flag) ans--
        }

        println(ans)
    }
}

class SegmentTree<T>(private val op: (T, T) -> T, private val id: T) {
    companion object {
        const val size = 1 shl 13
    }

    @Suppress("UNCHECKED_CAST")
    private val array = Array<Any?>(size * 2) { id } as Array<T>

    operator fun get(i: Int) = array[i + size]
    operator fun set(i: Int, n: T) = update(i, n)

    fun update(i: Int, n: T) {
        var index = i + size
        array[index] = n
        while (index > 1) {
            index /= 2
            array[index] = op(array[index * 2], array[index * 2 + 1])
        }
    }

    private fun query(left: Int, right: Int, k: Int, l: Int, r: Int): T {
        if (left <= l && r <= right) {
            return array[k]
        }

        if (r <= left || right <= l) {
            return id
        }

        return op(query(left, right, k * 2, l, (l + r) / 2), query(left, right, k * 2 + 1, (l + r) / 2, r))
    }

    fun query(left: Int, right: Int) = query(left, right, 1, 0, size)
}


class FastScanner {
    companion object {
        val input: InputStream = System.`in`
        val buffer = ByteArray(1024) { 0 }
        fun isPrintableChar(c: Int): Boolean = c in 33..126
    }

    var ptr = 0
    var buflen = 0
    private fun hasNextByte(): Boolean {
        if (ptr < buflen) {
            return true
        } else {
            ptr = 0
            buflen = input.read(buffer)
            if (buflen <= 0) {
                return false
            }
        }
        return true
    }

    private fun readByte(): Int = if (hasNextByte()) buffer[ptr++].toInt() else -1

    private fun skipUnprintable() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr].toInt())) ptr++
    }

    fun hasNext(): Boolean {
        skipUnprintable()
        return hasNextByte()
    }

    fun next(): String {
        if (!hasNext()) throw NoSuchElementException()
        val sb = StringBuilder()
        var b = readByte()
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b)
            b = readByte()
        }
        return sb.toString()
    }

    fun nextInt(): Int {
        if (!hasNext()) throw NoSuchElementException()
        var n = 0
        var b = readByte()
        // '-' = 45
        val minus = b == 45
        if (minus) {
            b = readByte()
        }

        // '0' = 48 '9' = 57
        if (b !in 48..57) {
            throw NumberFormatException()
        }

        while (true) {
            if (b in 48..57) {
                n *= 10
                n += b - 48
            } else if (b == -1 || !isPrintableChar(b)) {
                return if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun nextLong(): Long {
        if (!hasNext()) throw NoSuchElementException()
        var n = 0L
        var b = readByte()
        // '-' = 45
        val minus = b == 45
        if (minus) {
            b = readByte()
        }

        // '0' = 48 '9' = 57
        if (b !in 48..57) {
            throw NumberFormatException()
        }

        while (true) {
            if (b in 48..57) {
                n *= 10
                n += b - 48
            } else if (b == -1 || !isPrintableChar(b)) {
                return if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun nextDouble(): Double = next().toDouble()
}