import java.util.* fun main() { val ONE = ModInt(1) val (n, m) = readLine()!!.split(" ").map(String::toInt) var a = readLine()!!.splitToSequence(" ").map(String::toInt).toSortedSet() val frac = Array(m+1) {ONE} for (i in 2..frac.lastIndex) { frac[i] = frac[i-1] * i } val finv = Array(m+1) {ONE / frac[it]} val prs = IntArray(m+1) var newcomer: SortedSet = sortedSetOf(0) for (s in 1 until m) { a = a.subSet(0, m-newcomer.first()+1) val tmp = newcomer newcomer = sortedSetOf() for (ai in a) { for (t in tmp) { val nxt = ai + t if (nxt < s) continue else if (nxt <= m) { if (prs[nxt] == 0) { newcomer.add(nxt) prs[nxt] = s } } else break } } if (newcomer.isEmpty()) break } var ans = if (prs[m] == 0) ONE else ModInt(2) for (c in 1 until m) { if (prs[c] == 0) continue ans += frac[m-prs[c]] * finv[c-prs[c]] * finv[m-c] } println(ans) } class ModInt { val v: Long constructor(v: Int) { this.v = when { v >= 0 -> v % MOD else -> (v % MOD) + MOD } } constructor(v: Long) { this.v = when { v >= 0 -> v % MOD else -> (v % MOD) + MOD } } override fun toString() = v.toString() fun toInt() = v.toInt() fun toLong() = v override fun equals(other: Any?): Boolean { return if (other is ModInt) v == other.v else false } override fun hashCode() = 31 * 17 + v.hashCode() operator fun unaryPlus() = this operator fun unaryMinus() = ModInt(-this.v) private operator fun plus(o: Long) = ModInt(this.v + o) operator fun plus(o: ModInt) = this.plus(o.v) operator fun plus(o: Int) = this.plus(o.toLong()) private operator fun minus(o: Long) = ModInt(this.v - o) operator fun minus(o: ModInt) = this.minus(o.v) operator fun minus(o: Int) = this.minus(o.toLong()) private operator fun times(o: Long) = ModInt(this.v * o) operator fun times(o: ModInt) = this.times(o.v) operator fun times(o: Int) = this.times(o.toLong()) operator fun div(o: ModInt) = this.times(o.pow(MOD - 2)) operator fun div(o: Int) = this.times(o.powMod(MOD - 2)) operator fun inc() = this.plus(1) operator fun dec() = this.minus(1) fun pow(e: Long): ModInt { assert(e >= 0) if (this.v == 1L) return ModInt(1) var ans = ModInt(1) var b = this; var e = e while (e != 0L) { if (e % 2 == 1L) ans *= b b *= b e /= 2 } return ans } fun pow(e: Int) = pow(e.toLong()) companion object { const val MOD = 998244353L } } fun Long.powMod(e: Long) = ModInt(this).pow(e) fun Long.powMod(e: Int) = ModInt(this).pow(e.toLong()) fun Int.powMod(e: Long) = ModInt(this).pow(e) fun Int.powMod(e: Int) = ModInt(this).pow(e.toLong())