結果

問題 No.1396 Giri
コンテスト
ユーザー 箱星
提出日時 2021-02-14 22:03:42
言語 Kotlin
(2.1.0)
結果
AC  
実行時間 479 ms / 2,000 ms
コード長 4,200 bytes
コンパイル時間 14,518 ms
コンパイル使用メモリ 455,140 KB
実行使用メモリ 124,876 KB
最終ジャッジ日時 2024-07-22 09:45:09
合計ジャッジ時間 25,929 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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ファイルパターン 結果
sample AC * 3
other AC * 23
権限があれば一括ダウンロードができます

ソースコード

diff # 

import java.io.PrintWriter
import java.math.BigInteger
import java.util.*

// region ModInt
class ModInt(x: Long) {
    companion object {
        //const val MOD = 1000000007L
        const val MOD = 998244353L
    }

    constructor(y: Int) : this(y.toLong())

    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"
    }
}

fun Long.toModInt(): ModInt {
    return ModInt(this)
}

fun Int.toModInt(): ModInt {
    return ModInt(this)
}

const val fac_size = 600000
var fac_initialized = false
val arr_fac = Array(fac_size) { ModInt(1) }
val arr_invfac = Array(fac_size) { ModInt(1) }

fun facInitialize() {
    for (i in 1 until fac_size) {
        arr_fac[i] = arr_fac[i - 1] * ModInt(i)
    }
    arr_invfac[fac_size - 1] = arr_fac[fac_size - 1].inv()
    for (i in fac_size - 2 downTo 1) {
        arr_invfac[i] = arr_invfac[i + 1] * ModInt(i + 1)
    }
    fac_initialized = true
}

fun fac(n: Int): ModInt {
    if (!fac_initialized) facInitialize()
    return arr_fac[n]
}

fun fac(n: Long): ModInt {
    return fac(n.toInt())
}

fun invfac(n: Int): ModInt {
    if (!fac_initialized) facInitialize()
    return arr_invfac[n]
}

fun invfac(n: Long): ModInt {
    return invfac(n.toInt())
}

fun comb(n: Long, k: Long): ModInt {
    return if (k in 0..n) {
        if (!fac_initialized) facInitialize()
        arr_fac[n.toInt()] * arr_invfac[k.toInt()] * arr_invfac[(n - k).toInt()]
    } else {
        ModInt(0)
    }
}

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

fun PrintWriter.solve() {
    val n = nextLong()
    val isPrime = BooleanArray(n.toInt() + 2) { true }
    val pf = mutableMapOf<Long, Long>()
    for (i in 2..n) {
        if (!isPrime[i.toInt()]) continue
        var j = 2
        while (i * j <= n) {
            isPrime[(i * j).toInt()] = false
            j++
        }
        var exp = 1L
        var pow = i
        while (true) {
            if (pow * i <= n) {
                pow *= i
                exp++
            } else {
                break
            }
        }
        pf[i] = exp
    }

    // region prime factorization
    var number = (1..n).last { isPrime[it.toInt()] }
    var divisor = 2L
    while (divisor * divisor <= number) {
        var count = 0
        while (number % divisor == 0L) {
            number /= divisor
            count++
        }
        if (count > 0) {
            pf[divisor] = pf[divisor]!! - count
        }
        divisor++
    }
    if (number > 1) pf[number] = pf[number]!! - 1
    // endregion
    val num = pf.map { ModInt(it.key).pow(it.value) }.fold(ModInt(1), { x, y -> x * y })
    println(num)
}

fun main() {
    val writer = PrintWriter(System.out, false)
    writer.solve()
    writer.flush()
}

// region Scanner
private var st = StringTokenizer("")
private val br = System.`in`.bufferedReader()

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()
// endregion
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