import java.io.ByteArrayInputStream import java.io.ByteArrayOutputStream import java.io.PrintStream import kotlin.math.ceil fun main() = if (localEnv && execChecker) checker() else contest296a() fun contest296a() = solve() @OptIn(ExperimentalStdlibApi::class) private fun solve() = Messiah_contest296a(MOD).exec { repeat(readInt()) { val (a0, a1, a2) = readLong(3).sorted() val y = readLong() val (gcd, s, t) = extensionGcd(a0, a1) val a0d = a0 / gcd val a1d = a1 / gcd var answer = 0L for (yd in y downTo 0 step a2) { if (yd % gcd != 0L) continue val ydd = yd / gcd // val kMin = (-s * ydd).divCeil(a1d) val kMin = ceil((-s * ydd).toDouble() / a1d).toLong() val kMax = t * ydd / a0d val count = kMax - kMin + 1L answer += count answer %= MOD } println(answer) } } fun Long.divCeil(b: Long): Long { check(b != 0L) return if (this > 0 && b > 0) (this + b - 1) / b else { this / b + if (this % b != 0L && this < 0 && b < 0) 1 else 0 } } /** * `[a]x + [b]y = gcd(a, b)` となる [a] と [b] の最大公約数と解 x, y を求める * @return */ private fun extensionGcd(a: Long, b: Long): Triple { var ar = a var br = b var x0 = 1L var x1 = 0L var y0 = 0L var y1 = 1L while (br != 0L) { val q = ar / br val r = ar % br val x2 = x0 - q * x1 val y2 = y0 - q * y1 run { ar = br; br = r; x0 = x1; x1 = x2; y0 = y1; y1 = y2 } } return Triple(ar, x0, y0) } private const val MOD = 1_000_000_007 // region kokokara template dayo (^o^) private const val execChecker = false private val localEnv = runCatching { "ENABLE_DEBUG_MODE_FOR_COMPETITIVE_PROGRAMING" in System.getenv() }.getOrNull() ?: false private fun checker() = Messiah_contest296a(MOD).exec { debugln("#######################################################") debugln("############### executing check mode. ###############") debugln("#######################################################") fun getOutPut(input: String, action: () -> Unit): String { System.setIn(ByteArrayInputStream(input.toByteArray())) val sysOut = ByteArrayOutputStream() System.setOut(PrintStream(sysOut)) action() return sysOut.toString() } val wrongCases = mutableSetOf>() while (wrongCases.size < 10) { /* examples val randomString = (1..20).map { ('a'..'z').random() }.joinToString("") val randomNum = Random.nextInt(0,2000) */ val n = 0 val input = buildString { appendln(n) } val solve = getOutPut(input, ::solve) val greedy = getOutPut(input, ::greedy) if (solve != greedy && wrongCases.add(listOf(solve, greedy))) { debugln("#################### wrong case: ${wrongCases.size} ####################") debugln("input:") debugln(input) debugln("solve:") debugln(solve) debugln("greedy:") debugln(greedy) } } } private fun greedy() = Messiah_contest296a(MOD).exec { TODO() } @Suppress("ClassName", "unused", "FunctionName", "PropertyName") private class Messiah_contest296a(private val mod: Int) { ////////////////////////////////////////////////// // IO ////////////////////////////////////////////////// private val input = System.`in` private val buffer = ByteArray(1024) private var pointer = 0 private var bufferLength = 0 private val sb = StringBuilder() private fun Byte.isPrintable() = this in 33..126 private fun Byte.isNumeric() = this in '0'.toByte()..'9'.toByte() private fun Byte.toNumVal() = if (this.isNumeric()) this - '0'.toByte() else error("$this is not numeric") private val lineSeparator: String = System.lineSeparator() private fun hasNextByte(): Boolean { return if (pointer < bufferLength) true else { pointer = 0 bufferLength = input.read(buffer) bufferLength > 0 } } private fun readByte(): Byte = if (hasNextByte()) buffer[pointer++] else -1 private fun skipUnprintable() = run { while (hasNextByte() && !buffer[pointer].isPrintable()) pointer++ } private fun hasNext(): Boolean = run { skipUnprintable() }.run { hasNextByte() } private fun hasNextOrError() = if (!hasNext()) error("has no next element.") else Unit fun readString(): String { hasNextOrError() val sb = StringBuilder() var b = readByte() while (b.isPrintable()) { sb.appendCodePoint(b.toInt()) b = readByte() } return sb.toString() } fun readLong(): Long { hasNextOrError() var n = 0L var negative = false var b = readByte() if (b == '-'.toByte()) { negative = true b = readByte() } if (!b.isNumeric()) error("$b is not numeric.") while (true) { when { b.isNumeric() -> n = n * 10 + b.toNumVal() b.toInt() == -1 || !b.isPrintable() -> return if (negative) -n else n else -> error("failed to parse. [n=$n, b=$b]") } b = readByte() } } fun readInt() = readLong() .let { if (it in Int.MIN_VALUE..Int.MAX_VALUE) it.toInt() else error("$it is not in range of Int.") } fun readIntAsIndex() = readInt().dec() fun readDouble(): Double { hasNextOrError() var n = 0.0 var div = 1.0 var negative = false var b = readByte() if (b == '-'.toByte()) { negative = true b = readByte() } do n = n * 10 + b.toNumVal() while (run { b = readByte() }.run { b.isNumeric() }) if (b == '.'.toByte()) { while (run { b = readByte() }.run { b.isNumeric() }) n += b.toNumVal() / (run { div *= 10 }.run { div }) } return if (negative) -n else n } fun readString(size: Int): Array = Array(size) { readString() } @Suppress("UNUSED_PARAMETER") fun readChars(h: Int, w: Int): Array = Array(h) { readString().toCharArray() } fun readLong(size: Int): LongArray = LongArray(size) { readLong() } fun readLong(h: Int, w: Int): Array = Array(h) { readLong(w) } fun readInt(size: Int): IntArray = IntArray(size) { readInt() } fun readInt(h: Int, w: Int): Array = Array(h) { readInt(w) } fun readIntAsIndex(size: Int): IntArray = IntArray(size) { readIntAsIndex() } fun readIntAsIndex(h: Int, w: Int): Array = Array(h) { readIntAsIndex(w) } fun readDouble(size: Int): DoubleArray = DoubleArray(size) { readDouble() } fun readDouble(h: Int, w: Int): Array = Array(h) { readDouble(w) } fun readBooleanWithSeparator(size: Int, trueElement: String): BooleanArray = BooleanArray(size) { readString() == trueElement } fun readBooleanWithSeparator(h: Int, w: Int, trueElement: String): Array = Array(h) { readBooleanWithSeparator(w, trueElement) } @Suppress("UNUSED_PARAMETER") fun readBooleanWithoutSeparator(size: Int, trueElement: Char): BooleanArray = readString().map { it == trueElement }.toBooleanArray() fun readBooleanWithoutSeparator(h: Int, w: Int, trueElement: Char): Array = Array(h) { readBooleanWithoutSeparator(w, trueElement) } fun println(): Unit = run { sb.append(lineSeparator) } fun print(any: Any): Unit = run { sb.append(any.toString()) } fun println(any: Any): Unit = run { sb.append(any.toString() + lineSeparator) } fun flush() = run { kotlin.io.println(sb); sb.clear() } fun debugln(any: Any): Unit = run { if (localEnv) System.err.println(any) } fun debugln(): Unit = run { if (localEnv) System.err.println() } fun debugln(action: () -> Unit): Unit = run { if (localEnv) action() } fun exec(action: Messiah_contest296a.() -> Unit) { var t: Throwable? = null Thread(null, { action() }, "solve", 128 * 1024 * 1024) .apply { setUncaughtExceptionHandler { _, t1 -> t = t1 } } .apply { start() }.join() t?.let { throw it } kotlin.io.print(sb) } fun readLine(): Nothing = error("readLine is disabled.") ////////////////////////////////////////////////// // MOD ////////////////////////////////////////////////// fun Long.invertMod(): Long = invGcd(this).second fun Long.safeMod(): Long = (this % MOD).let { if (it < 0) it + MOD else it } fun Long.modPow(p: Long): Long { var x = this % MOD var y = p var result = 1L while (y > 0) { if (y % 2 == 1L) result = (result * x) % MOD y = y shr 1 x = (x * x) % MOD } return result } fun Long.modPow(p: Long, m: Int): Long { var x = this % m var y = p var result = 1L while (y > 0) { if (y % 2 == 1L) result = (result * x) % m y = y shr 1 x = (x * x) % m } return result } fun invGcd(a: Long): Pair { val am = a.safeMod() if (a == 0L) return MOD.toLong() to 0L var s = MOD.toLong() var t = am var m0 = 0L var m1 = 1L while (t != 0L) { val u = s / t s -= t * u m0 -= m1 * u var temp = s s = t t = temp temp = m0 m0 = m1 m1 = temp } if (m0 < 0) m0 += MOD / s return s to m0 } ////////////////////////////////////////////////// // Misc ////////////////////////////////////////////////// /** * `n.indices()` is sugar syntax of `0 until n`. */ val Int.indices: IntRange get() = 0 until this /** * `[index] in [this]` is sugar syntax of `index in 0 until [this]`. */ operator fun Int.contains(index: Int): Boolean = index in this.indices /** * `[this].mapIndices { transform }` is sugar syntax of `(0 until [this]).map{ transform(it) }`. */ inline fun Int.mapIndices(transform: (Int) -> R): List = this.indices.map(transform) /** * `[this].mapIndices(x) { transform }` is sugar syntax of * `(0 until [this]).map{ y1-> (0 until [x]).map { x1-> transform(y1,x1) } }`. */ inline fun Int.mapIndices(x: Int, transform: (Int, Int) -> R): List> = this.mapIndices { y1 -> x.mapIndices { x1 -> transform(y1, x1) } } /** * `[this].mapIndices(x) { transform }` is sugar syntax of * `(0 until [this]).map{ y1-> (0 until [x]).map { x1-> transform(y1,x1) } }`. */ inline fun Int.flatMapIndices(x: Int, transform: (Int, Int) -> R): List = this.indices.flatMap { y1 -> x.mapIndices { x1 -> transform(y1, x1) } } /** * `[this].forEachIndices { transform }` is sugar syntax of `(0 until [this]).map{ transform(it) }`. */ inline fun Int.forEachIndices(transform: (Int) -> Unit): Unit = this.indices.forEach(transform) /** * `[this].forEachIndices(x) { transform }` is sugar syntax of * `(0 until [this]).map{ y1-> (0 until [x]).map { x1-> transform(y1,x1) } }`. */ inline fun Int.forEachIndices(x: Int, transform: (Int, Int) -> Unit): Unit = this.forEachIndices { y1 -> x.forEachIndices { x1 -> transform(y1, x1) } } /** * get characters numeric value. * e.g.: '0' to 0 */ fun Char.toNumericValue(): Int = this - '0' fun Char.caseToIndexedValue(): Int = this - 'a' // fun Char.isLowerCase() = this in 'a'..'z' // // fun Char.isUpperCase() = this in 'A'..'Z' /** * make triple. e.g.:`1 to 2 to 3` */ infix fun Pair.to(c: C): Triple = Triple(this.first, this.second, c) fun YesNo(b: Boolean): String = if (b) Yes else No val Yes = "Yes" val No = "No" fun YES_NO(b: Boolean): String = if (b) YES else NO val YES = "YES" val NO = "NO" fun IntArray.swap(a: Int, b: Int): Unit = run { val temp = this[a]; this[a] = this[b]; this[b] = temp } fun LongArray.swap(a: Int, b: Int): Unit = run { val temp = this[a]; this[a] = this[b]; this[b] = temp } fun CharArray.swap(a: Int, b: Int): Unit = run { val temp = this[a]; this[a] = this[b]; this[b] = temp } fun Array.swap(a: Int, b: Int): Unit = run { val temp = this[a]; this[a] = this[b]; this[b] = temp } fun MutableList.swap(a: Int, b: Int): Unit = run { val temp = this[a]; this[a] = this[b]; this[b] = temp } fun IntArray.changeMinOf(i: Int, v: Int): Unit = run { this[i] = kotlin.math.min(this[i], v) } fun IntArray.changeMaxOf(i: Int, v: Int): Unit = run { this[i] = kotlin.math.max(this[i], v) } fun LongArray.changeMinOf(i: Int, v: Long): Unit = run { this[i] = kotlin.math.min(this[i], v) } fun LongArray.changeMaxOf(i: Int, v: Long): Unit = run { this[i] = kotlin.math.max(this[i], v) } /** * same usage as `IntArray.scan`, but it will faster than that. */ inline fun IntArray.scanArray(initial: Int, operation: (acc: Int, Int) -> Int): IntArray { val accumulator = IntArray(this.size + 1).apply { this[0] = initial } for (i in this.indices) accumulator[i + 1] = operation(accumulator[i], this[i]) return accumulator } /** * same usage as `LongArray.scan`, but it will faster than that. */ inline fun LongArray.scanArray(initial: Long, operation: (acc: Long, Long) -> Long): LongArray { val accumulator = LongArray(this.size + 1).apply { this[0] = initial } for (i in this.indices) accumulator[i + 1] = operation(accumulator[i], this[i]) return accumulator } /** * same usage as `IntArray.scanReduce`, but it will faster than that. */ inline fun IntArray.scanReduceArray(operation: (acc: Int, Int) -> Int): IntArray { val accumulator = IntArray(this.size).apply { this[0] = this@scanReduceArray[0] } for (i in 1..this.lastIndex) accumulator[i] = operation(accumulator[i - 1], this[i]) return accumulator } /** * same usage as `LongArray.scanReduce`, but it will faster than that. */ inline fun LongArray.scanReduceArray(operation: (acc: Long, Long) -> Long): LongArray { val accumulator = LongArray(this.size).apply { this[0] = this@scanReduceArray[0] } for (i in 1..this.lastIndex) accumulator[i] = operation(accumulator[i - 1], this[i]) return accumulator } } // endregion kokomade template dayo (^o^)