import scala.io.StdIn.* import ModInt.* object ModInt: opaque type ModInt = Long extension (value: Long) inline def asModInt(using inline mod: Int): ModInt = value % mod extension (value: Int) inline def asModInt(using inline mod: Int): ModInt = value % mod trait Converter[T]: inline def convert(value: T)(using inline mod: Int): ModInt inline given Converter[Int] with override inline def convert(value: Int)(using inline mod: Int) = value.asModInt inline given Converter[Long] with override inline def convert(value: Long)(using inline mod: Int) = value.asModInt inline given Converter[ModInt] with override inline def convert(value: ModInt)(using inline mod: Int) = value extension (modInt: ModInt) inline def asLong(using inline mod: Int): Long = (modInt + mod) % mod inline def asInt(using inline mod: Int): Int = asLong.toInt inline def inverse(using inline mod: Int): ModInt = modInt.powMod(mod - 2) inline def powMod(exp: Long)(using inline mod: Int): ModInt = var result = 1L var base = modInt var e = exp while e > 0 do if (e & 1) == 1 then result = result * base % mod base = base * base % mod e >>= 1 result inline def powMod(exp: Int)(using inline mod: Int): ModInt = powMod(exp.toLong) extension [L: Converter, R: Converter] (left: L) inline def +(right: R)(using inline mod: Int): ModInt = (summon[Converter[L]].convert(left) + summon[Converter[R]].convert(right)).asModInt inline def -(right: R)(using inline mod: Int): ModInt = (summon[Converter[L]].convert(left) - summon[Converter[R]].convert(right)).asModInt inline def *(right: R)(using inline mod: Int): ModInt = (summon[Converter[L]].convert(left) * summon[Converter[R]].convert(right)).asModInt inline def /(right: R)(using inline mod: Int): ModInt = (summon[Converter[L]].convert(left) * summon[Converter[R]].convert(right).inverse).asModInt type Matrix = Array[Array[ModInt]] extension (left: Matrix) inline infix def *(right: Matrix)(using inline mod: Int): Matrix = val row = left.length val column = right(0).length val mid = right.length Array.tabulate(row){i => Array.tabulate(column){j => (0 until mid).foldLeft(0.asModInt){(acc, k) => acc + left(i)(k) * right(k)(j)} }} extension (matrix: Matrix) inline def pow(exp: Long)(using inline mod: Int): Matrix = val size = matrix.length var result = Array.tabulate(size){i => Array.tabulate(size){j => if i == j then 1.asModInt else 0.asModInt}} var base = matrix var e = exp while e > 0 do if (e & 1) == 1 then result = result * base base = base * base e = e >> 1 result @main def main = inline given mod: Int = 1000000007 val Array(a, b) = readLine().split(' ').map(_.toInt.asModInt) val n = readLine().toInt val time = Array.fill(n){readLine().toLong} val initial = Array.tabulate(3){i => if i == 2 then Array(0.asModInt) else Array(1.asModInt)} val oddOperation = Array(Array(1.asModInt, 0.asModInt, 0.asModInt), Array(0.asModInt, 1.asModInt, 0.asModInt), Array(a, b, 1.asModInt)) val evenOperation = Array(Array(0.asModInt, 0.asModInt, 1.asModInt), Array(1.asModInt, 0.asModInt, 0.asModInt), Array(0.asModInt, 0.asModInt, 0.asModInt)) val result = Array.fill(n){0} for (t, i) <- time.zipWithIndex do val operation = if t % 2 == 0 then (evenOperation * oddOperation).pow(t / 2) else oddOperation * (evenOperation * oddOperation).pow(t / 2) val lastState = operation * initial result(i) = lastState.flatten.reduce(_ + _).asInt println(result.mkString("\n"))