結果

問題 No.1559 Next Rational
ユーザー 箱星
提出日時 2021-06-25 22:50:52
言語 Kotlin
(2.1.0)
結果
AC  
実行時間 286 ms / 2,000 ms
コード長 2,995 bytes
コンパイル時間 17,399 ms
コンパイル使用メモリ 446,144 KB
実行使用メモリ 54,484 KB
最終ジャッジ日時 2024-06-25 08:45:56
合計ジャッジ時間 19,868 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 15
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 #
プレゼンテーションモードにする

import java.io.PrintWriter
import java.lang.Exception
import java.util.*
data class Matrix(val a: ModInt, val b: ModInt, val c: ModInt, val d: ModInt)
fun product(x: Matrix, y: Matrix): Matrix {
    val a = x.a * y.a + x.b * y.c
    val b = x.a * y.b + x.b * y.d
    val c = x.c * y.a + x.d * y.c
    val d = x.c * y.b + x.d * y.d
    return Matrix(a, b, c, d)
}
fun pow(m: Matrix, n: Long): Matrix {
    if (n == 0L) {
        return Matrix(ModInt(1), ModInt(0), ModInt(0), ModInt(1))
    } else if (n == 1L) {
        return m
    }
    val x = pow(m, n / 2)
    val y = product(x, x)
    if (n % 2 == 0L) {
        return y
    } else {
        return product(y, m)
    }
}
fun PrintWriter.solve() {
    val n = nextLong()
    val a = nextLong()
    val b = nextLong()
    val k = nextLong()
    val c = ModInt(a * a + b * b + k) / ModInt(a * b)
    val m = pow(Matrix(c, ModInt(-1), ModInt(1), ModInt(0)), n - 1)
    println(m.c * b.toModInt() + m.d * a.toModInt())
}
// 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)
}
fun binomSimple(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 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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