Problem:
Score : 600 points

Problem Statement

Given are a sequence of N positive integers A_1, A_2, \ldots, A_N and another positive integer S.

For a non-empty subset T of the set \{1, 2, \ldots , N \}, let us define f(T) as follows:

f(T) is the number of different non-empty subsets \{x_1, x_2, \ldots , x_k \} of T such that A_{x_1}+A_{x_2}+\cdots +A_{x_k} = S.

Find the sum of f(T) over all 2^N-1 subsets T of \{1, 2, \ldots , N \}. Since the sum can be enormous, print it modulo 998244353.

Constraints

All values in input are integers.

1 \leq N \leq 3000

1 \leq S \leq 3000

1 \leq A_i \leq 3000

Input

Input is given from Standard Input in the following format:

N S
A_1 A_2 ... A_N

Output

Print the sum of f(T) modulo 998244353.

Sample Input 1

3 4
2 2 4

Sample Output 1

6

For each T, the value of f(T) is shown below. The sum of these values is 6.

f(\{1\}) = 0

f(\{2\}) = 0

f(\{3\}) = 1 (One subset \{3\} satisfies the condition.)

f(\{1, 2\}) = 1 (\{1, 2\})

f(\{2, 3\}) = 1 (\{3\})

f(\{1, 3\}) = 1 (\{3\})

f(\{1, 2, 3\}) = 2 (\{1, 2\}, \{3\})

Sample Input 2

5 8
9 9 9 9 9

Sample Output 2

0

Sample Input 3

10 10
3 1 4 1 5 9 2 6 5 3

Sample Output 3

3296

Solution in Kotlin (1.3.71) (judge verdict: Time Limit Exceeded)

import java.io.BufferedReader
import java.io.InputStream
import java.io.InputStreamReader
import java.io.PrintWriter
import java.lang.IllegalArgumentException
import java.lang.StringBuilder
import java.util.*

// ModInt
// region
class ModInt(x: Long) {

    companion object {
        const val MOD = 998244353L
    }

    val x = (x % MOD + MOD) % MOD

    operator fun plus(other: ModInt): ModInt {
        return ModInt(x + other.x)
    }

    operator fun minus(other: ModInt): ModInt {
        return ModInt(x - other.x)
    }

    operator fun times(other: ModInt): ModInt {
        return ModInt(x * other.x)
    }

    operator fun div(other: ModInt): ModInt {
        return this * other.inv()
    }

    fun pow(exp: Long): ModInt {
        if (exp == 0L) return ModInt(1L)
        var a = pow(exp shr 1)
        a *= a
        if (exp and 1L == 0L) return a
        return this * a
    }

    fun inv(): ModInt {
        return this.pow(MOD - 2)
    }

    override fun equals(other: Any?): Boolean {
        if (this === other) return true
        if (javaClass != other?.javaClass) return false

        other as ModInt

        if (x != other.x) return false

        return true
    }

    override fun hashCode(): Int {
        return x.hashCode()
    }

    override fun toString(): String {
        return "$x"
    }

}

val fac = mutableListOf<ModInt>()
val invfac = mutableListOf<ModInt>()

fun fact(n: Long, b: Boolean): ModInt {
    if (fac.count() == 0) {
        fac.add(ModInt(1))
        invfac.add(ModInt(1))
    }
    while (fac.count() <= n) {
        fac.add(fac.last() * ModInt(fac.count().toLong()))
        invfac.add(fac.last().inv())
    }
    return if (b) {
        fac[n.toInt()]
    } else {
        invfac[n.toInt()]
    }
}

fun comb(n: Long, k: Long): ModInt {
    return fact(n, true) * fact(k, false) * fact(n - k, false)
}

fun comb2(n: Long, k: Long): ModInt {
    var ans = ModInt(1)
    for (i in 0 until k) {
        ans = ans * ModInt(n - i) / ModInt(k - i)
    }
    return ans
}
// endregion

fun PrintWriter.solve(sc: FastScanner) {
    val n = sc.nextInt()
    val s = sc.nextInt()
    val a = Array(n) { sc.nextInt() }
    val dp = Array(n + 1) { Array(s + 1) { ModInt(0) } }
    dp[0][0] = ModInt(1)
    for (i in 0 until n) {
        for (k in n downTo 1) {
            for (j in 0..s) {
                if (j + a[i] <= s) {
                    dp[k][j+a[i]] += dp[k-1][j]
                } else {
                    break
                }
            }
        }
    }
    var ans = ModInt(0)
    for (i in 1..n) {
        ans += ModInt(2).pow(n.toLong() - i) * dp[i][s]
    }
    println(ans)
}

fun main(args: Array<String>) {
    val writer = PrintWriter(System.out, false)
    writer.solve(FastScanner(System.`in`))
    writer.flush()
}

class FastScanner(s: InputStream) {
    private var st = StringTokenizer("")
    private val br = BufferedReader(InputStreamReader(s))

    fun next(): String {
        while (!st.hasMoreTokens()) st = StringTokenizer(br.readLine())

        return st.nextToken()
    }

    fun nextInt() = next().toInt()
    fun nextLong() = next().toLong()
    fun nextLine() = br.readLine()
    fun nextDouble() = next().toDouble()
    fun ready() = br.ready()
}