import java.io.PrintWriter import java.util.* fun PrintWriter.solve() { val numCases = nextInt() val b = arrayOf( arrayOf(1, 0, 0, 0, 1, 1), arrayOf(0, 1, 0, 1, 0, 1), arrayOf(0, 0, 1, 1, 1, 0), arrayOf(3, 0, 0, 0, 0, 0), arrayOf(0, 3, 0, 0, 0, 0), arrayOf(0, 0, 3, 0, 0, 0) ) case@ for (_i in 0 until numCases) { val n = nextLong() val mat = Matrix(b).pow(n).mat val p = mat[3][0] + ModInt(3) * mat[3][3] println(p / ModInt(3).pow(n + 1)) } } // region Matrix class Matrix(val mat: Array>) { private val n = mat.size constructor(a: Array>) : this(Array(a.size) { i -> Array(a.size) { j -> a[i][j].toModInt() } }) constructor(a: Array>) : this(Array(a.size) { i -> Array(a.size) { j -> a[i][j].toModInt() } }) operator fun plus(other: Matrix): Matrix { val b = mat.copyOf() for (i in 0 until n) { for (j in 0 until n) { b[i][j] += other.mat[i][j] } } return Matrix(b) } operator fun minus(other: Matrix): Matrix { val b = mat.copyOf() for (i in 0 until n) { for (j in 0 until n) { b[i][j] -= other.mat[i][j] } } return Matrix(b) } operator fun times(other: Matrix): Matrix { val b = zero(n).mat for (k in 0 until n) { for (i in 0 until n) { for (j in 0 until n) { b[i][j] += mat[i][k] * other.mat[k][j] } } } return Matrix(b) } fun pow(exp: Long): Matrix { if (exp == 0L) return e(n) var a = pow(exp shr 1) a *= a if (exp and 1L == 0L) return a return this * a } override fun toString(): String { return mat.joinToString("\n") { "[${it.joinToString()}]" } } } fun zero(n: Int): Matrix { return Matrix(Array(n) { Array(n) { ModInt(0) } }) } fun e(n: Int): Matrix { return Matrix(Array(n) { i -> Array(n) { j -> ModInt(if (i == j) 1 else 0) } }) } // endregion // region ModInt class ModInt(x: Long) { companion object { const val MOD = 1000000007L //const val MOD = 998244353L } constructor(y: Int) : this(y.toLong()) val x = (x % MOD + MOD) % MOD operator fun plus(other: ModInt): ModInt { return ModInt(x + other.x) } operator fun minus(other: ModInt): ModInt { return ModInt(x - other.x) } operator fun times(other: ModInt): ModInt { return ModInt(x * other.x) } operator fun div(other: ModInt): ModInt { return this * other.inv() } fun pow(exp: Long): ModInt { if (exp == 0L) return ModInt(1L) var a = pow(exp shr 1) a *= a if (exp and 1L == 0L) return a return this * a } fun inv(): ModInt { return this.pow(MOD - 2) } override fun equals(other: Any?): Boolean { if (this === other) return true if (javaClass != other?.javaClass) return false other as ModInt if (x != other.x) return false return true } override fun hashCode(): Int { return x.hashCode() } override fun toString(): String { return "$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() { Thread(null, { val writer = PrintWriter(System.out, !false) writer.solve() writer.flush() }, "solve", 1.shl(26)) .apply { setUncaughtExceptionHandler { _, e -> e.printStackTrace(); kotlin.system.exitProcess(1) } } .apply { start() }.join() } // 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