結果
| 問題 | No.3376 Rectangle in Circle |
| コンテスト | |
| ユーザー |
 seekworser
|
| 提出日時 | 2026-03-19 03:02:20 |
| 言語 | Nim (2.2.6) |
| 結果 |
AC
|
| 実行時間 | 141 ms / 2,000 ms |
| コード長 | 35,654 bytes |
| 記録 | |
| コンパイル時間 | 4,695 ms |
| コンパイル使用メモリ | 102,420 KB |
| 実行使用メモリ | 16,256 KB |
| 最終ジャッジ日時 | 2026-03-19 03:02:31 |
| 合計ジャッジ時間 | 9,617 ms |
|
ジャッジサーバーID （参考情報） |
judge1_0 / judge2_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 20 |
ソースコード
import macros;macro ImportExpand(s:untyped):untyped = parseStmt($s[2])
# source: https://github.com/kemuniku/cplib/tree/main/src/cplib/tmpl/citrus.nim
ImportExpand "cplib/tmpl/citrus" <=== "when not declared CPLIB_TMPL_CITRUS:\n const CPLIB_TMPL_CITRUS* = 1\n {.warning[UnusedImport]: off.}\n {.hint[XDeclaredButNotUsed]: off.}\n import os\n import algorithm\n import sequtils\n import tables\n import macros\n import std/math\n import sets\n import strutils\n import strformat\n import sugar\n import streams\n import deques\n import bitops\n import heapqueue\n import options\n import hashes\n const MODINT998244353* = 998244353\n const MODINT1000000007* = 1000000007\n when not declared CPLIB_UTILS_CONSTANTS:\n const CPLIB_UTILS_CONSTANTS* = 1\n const INF32*: int32 = 1001000027.int32\n const INF64*: int = int(3300300300300300491)\n \n const INFL = INF64\n type double* = float64\n let readNext = iterator(getsChar: bool = false): string {.closure.} =\n while true:\n var si: string\n try: si = stdin.readLine\n except EOFError: yield \"\"\n for s in si.split:\n if getsChar:\n for i in 0..<s.len():\n yield s[i..i]\n else:\n if s.isEmptyOrWhitespace: continue\n yield s\n proc input*(t: typedesc[string]): string = readNext()\n proc input*(t: typedesc[char]): char = readNext(true)[0]\n proc input*(t: typedesc[int]): int = readNext().parseInt\n proc input*(t: typedesc[float]): float = readNext().parseFloat\n macro input*(t: typedesc, n: varargs[int]): untyped =\n var repStr = \"\"\n for arg in n:\n repStr &= &\"({arg.repr}).newSeqWith \"\n parseExpr(&\"{repStr}input({t})\")\n macro input*(ts: varargs[auto]): untyped =\n var tupStr = \"\"\n for t in ts:\n tupStr &= &\"input({t.repr}),\"\n parseExpr(&\"({tupStr})\")\n macro input*(n: int, ts: varargs[auto]): untyped =\n for typ in ts:\n if typ.typeKind != ntyAnything:\n error(\"Expected typedesc, got \" & typ.repr, typ)\n parseExpr(&\"({n.repr}).newSeqWith input({ts.repr})\")\n proc `fmtprint`*(x: int or string or char or bool): string = return $x\n proc `fmtprint`*(x: float or float32 or float64): string = return &\"{x:.16f}\"\n proc `fmtprint`*[T](x: seq[T] or Deque[T] or HashSet[T] or set[T]): string = return x.toSeq.join(\" \")\n proc `fmtprint`*[T, N](x: array[T, N]): string = return x.toSeq.join(\" \")\n proc `fmtprint`*[T](x: HeapQueue[T]): string =\n var q = x\n while q.len != 0:\n result &= &\"{q.pop()}\"\n if q.len != 0: result &= \" \"\n proc `fmtprint`*[T](x: CountTable[T]): string =\n result = x.pairs.toSeq.mapIt(&\"{it[0]}: {it[1]}\").join(\" \")\n proc `fmtprint`*[K, V](x: Table[K, V]): string =\n result = x.pairs.toSeq.mapIt(&\"{it[0]}: {it[1]}\").join(\" \")\n proc print*(prop: tuple[f: File, sepc: string, endc: string, flush: bool], args: varargs[string, `fmtprint`]) =\n for i in 0..<len(args):\n prop.f.write(&\"{args[i]}\")\n if i != len(args) - 1: prop.f.write(prop.sepc) else: prop.f.write(prop.endc)\n if prop.flush: prop.f.flushFile()\n proc print*(args: varargs[string, `fmtprint`]) = print((f: stdout, sepc: \" \", endc: \"\\n\", flush: false), args)\n const LOCAL_DEBUG{.booldefine.} = false\n macro getSymbolName(x: typed): string = x.toStrLit\n macro debug*(args: varargs[untyped]): untyped =\n when LOCAL_DEBUG:\n result = newNimNode(nnkStmtList, args)\n template prop(e: string = \"\"): untyped = (f: stderr, sepc: \"\", endc: e, flush: true)\n for i, arg in args:\n if arg.kind == nnkStrLit:\n result.add(quote do: print(prop(), \"\\\"\", `arg`, \"\\\"\"))\n else:\n result.add(quote do: print(prop(\": \"), getSymbolName(`arg`)))\n result.add(quote do: print(prop(), `arg`))\n if i != args.len - 1: result.add(quote do: print(prop(), \", \"))\n else: result.add(quote do: print(prop(), \"\\n\"))\n else:\n return (quote do: discard)\n proc `%`*(x: SomeInteger, y: SomeInteger): int =\n result = x mod y\n if y > 0 and result < 0: result += y\n if y < 0 and result > 0: result += y\n proc `//`*(x: SomeInteger, y: SomeInteger): int =\n result = x div y\n if y > 0 and result * y > x: result -= 1\n if y < 0 and result * y < x: result -= 1\n proc `^`*(x: SomeInteger, y: SomeInteger): int = x xor y\n proc `&`*(x: SomeInteger, y: SomeInteger): int = x and y\n proc `|`*(x: SomeInteger, y: SomeInteger): int = x or y\n proc `>>`*(x: SomeInteger, y: SomeInteger): int = x shr y\n proc `<<`*(x: SomeInteger, y: SomeInteger): int = x shl y\n proc `%=`*(x: var SomeInteger, y: SomeInteger): void = x = x % y\n proc `//=`*(x: var SomeInteger, y: SomeInteger): void = x = x // y\n proc `^=`*(x: var SomeInteger, y: SomeInteger): void = x = x ^ y\n proc `&=`*(x: var SomeInteger, y: SomeInteger): void = x = x & y\n proc `|=`*(x: var SomeInteger, y: SomeInteger): void = x = x | y\n proc `>>=`*(x: var SomeInteger, y: SomeInteger): void = x = x >> y\n proc `<<=`*(x: var SomeInteger, y: SomeInteger): void = x = x << y\n proc `[]`*(x, n: int): bool = (x and (1 shl n)) != 0\n proc `[]=`*(x: var int, n: int, i: bool) =\n if i: x = x or (1 << n)\n else: (if x[n]: x = x xor (1 << n))\n proc pow*(a, n: int, m = INF64): int =\n var\n rev = 1\n a = a\n n = n\n while n > 0:\n if n % 2 != 0: rev = (rev * a) mod m\n if n > 1: a = (a * a) mod m\n n >>= 1\n return rev\n when not declared CPLIB_MATH_ISQRT:\n const CPLIB_MATH_ISQRT* = 1\n proc isqrt*(n: int): int =\n var x = n\n var y = (x + 1) shr 1\n while y < x:\n x = y\n y = (x + n div x) shr 1\n return x\n \n proc chmax*[T](x: var T, y: T): bool {.discardable.} = (if x < y: (x = y; return true; ) return false)\n proc chmin*[T](x: var T, y: T): bool {.discardable.} = (if x > y: (x = y; return true; ) return false)\n proc `max=`*[T](x: var T, y: T) = x = max(x, y)\n proc `min=`*[T](x: var T, y: T) = x = min(x, y)\n proc at*(x: char, a = '0'): int = int(x) - int(a)\n proc Yes*(b: bool = true): void = print(if b: \"Yes\" else: \"No\")\n proc No*(b: bool = true): void = Yes(not b)\n proc YES_upper*(b: bool = true): void = print(if b: \"YES\" else: \"NO\")\n proc NO_upper*(b: bool = true): void = Yes_upper(not b)\n const DXY* = [(0, -1), (0, 1), (-1, 0), (1, 0)]\n const DDXY* = [(1, -1), (1, 0), (1, 1), (0, -1), (0, 1), (-1, -1), (-1, 0), (-1, 1)]\n macro exit*(statement: untyped): untyped = (quote do: (`statement`; quit()))\n proc initHashSet[T](): Hashset[T] = initHashSet[T](0)\n"
# source: https://github.com/kemuniku/cplib/tree/main/src/cplib/convolution/convolution.nim
ImportExpand "cplib/convolution/convolution" <=== "when not declared CPLIB_CONVOLUTION_CONVOLUTION:\n const CPLIB_CONVOLUTION_CONVOLUTION* = 1\n import bitops\n import sequtils\n import std/math\n when not declared CPLIB_MODINT_MODINT:\n const CPLIB_MODINT_MODINT* = 1\n when not declared CPLIB_MODINT_MODINT_BARRETT:\n const CPLIB_MODINT_MODINT_BARRETT* = 1\n import std/macros\n import std/tables\n type StaticBarrettModint*[M: static[uint32]] = object\n a: uint32\n type DynamicBarrettModint*[M: static[uint32]] = object\n a: uint32\n type BarrettModint* = StaticBarrettModint or DynamicBarrettModint\n \n proc get_im*(M: uint32): uint = cast[uint](-1) div M + 1\n var barrettParamCache {.compileTime.}: Table[uint32, NimNode]\n var barrettCachedParam: tuple[M: uint32, im: uint]\n \n macro get_param*[M: static[uint32]](self: typedesc[StaticBarrettModint[M]]): untyped =\n if M notin barrettParamCache:\n let value = (M.uint32, get_im(M))\n barrettParamCache[M] = newLit(value)\n return barrettParamCache[M]\n template get_param*(self: typedesc[DynamicBarrettModint]): tuple[M: uint32, im: uint] =\n barrettCachedParam\n template get_M*(T: typedesc[BarrettModint]): uint =\n when T is StaticBarrettModint: T.M.uint\n else: get_param(T).M.uint\n proc setMod*[T: static[uint32]](self: typedesc[DynamicBarrettModint[T]], M: SomeInteger or SomeUnsignedInt) =\n barrettCachedParam = (M: M.uint32, im: get_im(M.uint32))\n \n template umod*[T: BarrettModint](self: typedesc[T] or T): uint32 =\n when self is typedesc:\n when self is StaticBarrettModint: self.M\n else: (get_param(self)).M\n else: T.umod\n template `mod`*[T: BarrettModint](self: typedesc[T] or T): int32 = (T.umod).int32\n {.emit: \"\"\"\n #include <cstdio>\n inline unsigned long long calc_mul(const unsigned long long &a, const unsigned long long &b) {\n return (unsigned long long)(((__uint128_t)(a) * b) >> 64);\n }\n \"\"\".}\n proc calc_mul*(a, b: culonglong): culonglong {.importcpp: \"calc_mul(#, #)\", nodecl, inline.}\n proc rem*(T: typedesc[BarrettModint], a: uint): uint32 =\n when T is StaticBarrettModint:\n const im = get_im(T.M)\n const M = get_M(T)\n var x = (calc_mul(cast[culonglong](a), cast[culonglong](im))).uint\n var r = a - x * M\n if M <= r: r += M\n return cast[uint32](r)\n else:\n var p = get_param(T)\n var x = (calc_mul(cast[culonglong](a), cast[culonglong](p.im))).uint\n var r = a - x * p.M\n if p.M <= r: r += p.M\n return cast[uint32](r)\n proc init*(T: typedesc[BarrettModint], a: T or SomeInteger): auto =\n when a is T: return a\n else:\n if a in 0..<T.mod.int: return T(a: a.uint32)\n var a = a mod T.mod.int\n if a < 0: a += T.mod.int\n return T(a: a.uint32)\n \n proc `-`*[T: BarrettModint](a: T): T = T(a: T.umod - a.a)\n proc `+=`*[T: BarrettModint](a: var T, b: T or SomeInteger) =\n a.a += init(T, b).a\n if a.a >= T.umod: a.a -= T.umod\n proc `-=`*[T: BarrettModint](a: var T, b: T or SomeInteger) =\n a.a -= init(T, b).a\n if a.a >= T.umod: a.a += T.umod\n proc `*=`*[T: BarrettModint] (a: var T, b: T or SomeInteger) =\n a.a = rem(T, (a.a).uint * (init(T, b).a).uint)\n proc inv*[T: BarrettModint](x: T): T =\n assert x.val != 0\n var x: int32 = int32(x.val)\n var y: int32 = T.mod\n var u = 1i32\n var v, t = 0i32\n while y > 0:\n t = x div y\n x -= t * y\n u -= t * v\n swap(x, y)\n swap(u, v)\n return init(T, u)\n proc `/=`*[T: BarrettModint](a: var T, b: T or SomeInteger) = a *= init(T, b).inv\n proc val*(a: BarrettModint): int = a.a.int\n macro declarStaticBarrettModint*(name, M) =\n let converter_name = ident(\"to\" & $`name`)\n quote do:\n type `name`* = StaticBarrettModint[`M`]\n converter `converter_name`*(a: int): StaticBarrettModint[`M`] = init(StaticBarrettModint[`M`], a)\n macro declarDynamicBarrettModint*(name, id) =\n let converter_name = ident(\"to\" & $`name`)\n quote do:\n type `name`* = DynamicBarrettModint[`id`]\n converter `converter_name`*(a: int): DynamicBarrettModint[`id`] = init(DynamicBarrettModint[`id`], a)\n \n when not declared CPLIB_MODINT_MODINT_MONTGOMERY:\n const CPLIB_MODINT_MODINT_MONTGOMERY* = 1\n import std/macros\n import std/tables\n type StaticMontgomeryModint*[M: static[uint32]] = object\n a: uint32\n type DynamicMontgomeryModint*[M: static[uint32]] = object\n a: uint32\n type MontgomeryModint* = StaticMontgomeryModint or DynamicMontgomeryModint\n \n proc get_r*(M: uint32): uint32 =\n result = M\n for _ in 0..<4: result *= 2u32 - M * result\n proc get_n2*(M: uint32): uint32 = uint32((not uint(M - 1u32)) mod uint(M))\n proc check_params(M, r: uint32) =\n assert M < (1u32 shl 30), \"invalid mod >= 2^30\"\n assert (M and 1u32) == 1u32, \"invalid mod % 2 == 0\"\n assert r * M == 1, \"r * mod != 1\"\n var montgomeryParamCache {.compileTime.}: Table[uint32, NimNode]\n var montgomeryCachedParam: tuple[M, r, n2: uint32]\n macro get_param*[M: static[uint32]](self: typedesc[StaticMontgomeryModint[M]]): untyped =\n if M notin montgomeryParamCache:\n let value = (M.uint32, get_r(M), get_n2(M))\n montgomeryParamCache[M] = newLit(value)\n return montgomeryParamCache[M]\n template get_param*(self: typedesc[DynamicMontgomeryModint]): tuple[M, r, n2: uint32] =\n # FIXME: cast(noSideEffect)を付けないと、set_of_mint.join(\" \")とかで死ぬ。\n # もうちょっと筋の良い解決方法があればそうしたい\n {.cast(noSideEffect).}:\n montgomeryCachedParam\n template get_M*(T: typedesc[MontgomeryModint]): uint32 =\n when T is StaticMontgomeryModint: T.M\n else: get_param(T).M\n proc setMod*[T: static[uint32]](self: typedesc[DynamicMontgomeryModint[T]], M: SomeInteger or SomeUnsignedInt) =\n var r = get_r(M.uint32)\n var n2 = get_n2(M.uint32)\n montgomeryCachedParam = (M: M.uint32, r: get_r(M.uint32), n2: n2)\n check_params(M.uint32, r)\n template umod*[T: MontgomeryModint](self: typedesc[T] or T): uint32 =\n when self is typedesc:\n when self is StaticMontgomeryModint: self.M\n else: get_param(self).M\n else: T.umod\n template `mod`*[T: MontgomeryModint](self: typedesc[T] or T): int32 = (T.umod).int32\n \n proc reduce(T: typedesc[StaticMontgomeryModint], b: uint): uint32 =\n let (_, r, _) = get_param(T)\n return cast[uint32]((b + uint(cast[uint32](b) * (not (r - 1u32))) * T.M) shr 32)\n proc reduce(T: typedesc[DynamicMontgomeryModint], b: uint): uint32 =\n var p = get_param(T)\n return cast[uint32]((b + uint(cast[uint32](b) * (not (p.r - 1u32))) * p.M) shr 32)\n proc init*(T: typedesc[MontgomeryModint], a: T or SomeInteger): auto =\n when a is T: return a\n elif T is StaticMontgomeryModint:\n let (_, r, n2) = get_param(T)\n check_params(T.M, r)\n var ai = reduce(T, uint(a.int32 mod T.M.int32 + T.M.int32) * n2)\n result = StaticMontgomeryModint[T.M](a: ai)\n elif T is DynamicMontgomeryModint:\n var p = get_param(T)\n var ai = reduce(T, uint(a.int32 mod p.M.int32 + p.M.int32) * p.n2)\n result = DynamicMontgomeryModint[T.M](a: ai)\n \n proc `+=`*[T: MontgomeryModint](a: var T, b: T or SomeInteger) =\n a.a += init(T, b).a - T.get_M * 2u32\n if cast[int32](a.a) < 0i32: a.a += T.get_M * 2u32\n proc `-=`*[T: MontgomeryModint](a: var T, b: T or SomeInteger) =\n a.a -= init(T, b).a\n if cast[int32](a.a) < 0i32: a.a += T.get_M * 2u32\n proc val*[T: MontgomeryModint](a: T): int =\n result = reduce(T, a.a).int\n if result.uint32 >= T.get_M: result -= T.get_M.int\n \n proc `-`*[T: MontgomeryModint](a: T): T = init(T, 0) - a\n proc `*=`*[T: MontgomeryModint] (a: var T, b: T or SomeInteger) = a.a = reduce(T, uint(a.a) * init(T, b).a)\n proc inv*[T: MontgomeryModint](x: T): T =\n assert x.val != 0\n var x: int32 = int32(x.val)\n var y: int32 = T.mod\n var u = 1i32\n var v, t = 0i32\n while y > 0:\n t = x div y\n x -= t * y\n u -= t * v\n swap(x, y)\n swap(u, v)\n return init(T, u)\n proc `/=`*[T: MontgomeryModint](a: var T, b: T or SomeInteger) = a *= init(T, b).inv\n \n macro declarStaticMontgomeryModint*(name, M) =\n let converter_name = ident(\"to\" & $`name`)\n quote do:\n type `name`* = StaticMontgomeryModint[`M`]\n converter `converter_name`*(a: int): StaticMontgomeryModint[`M`] = init(StaticMontgomeryModint[`M`], a)\n macro declarDynamicMontgomeryModint*(name, id) =\n let converter_name = ident(\"to\" & $`name`)\n quote do:\n type `name`* = DynamicMontgomeryModint[`id`]\n converter `converter_name`*(a: int): DynamicMontgomeryModint[`id`] = init(DynamicMontgomeryModint[`id`], a)\n \n import std/math\n import std/algorithm\n declarStaticMontgomeryModint(modint998244353_montgomery, 998244353u32)\n declarStaticMontgomeryModint(modint1000000007_montgomery, 1000000007u32)\n declarDynamicMontgomeryModint(modint_montgomery, 1u32)\n declarStaticBarrettModint(modint998244353_barrett, 998244353u32)\n declarStaticBarrettModint(modint1000000007_barrett, 1000000007u32)\n declarDynamicBarrettModint(modint_barrett, 1u32)\n proc `+`*(a, b: MontgomeryModint or BarrettModint): auto = (result = a; result += b)\n proc `-`*(a, b: MontgomeryModint or BarrettModint): auto = (result = a; result -= b)\n proc `*`*(a, b: MontgomeryModint or BarrettModint): auto = (result = a; result *= b)\n proc `/`*(a, b: MontgomeryModint or BarrettModint): auto = (result = a; result /= b)\n proc `+`*(a: MontgomeryModint or BarrettModint, b: SomeInteger): auto = (result = a; result += b)\n proc `-`*(a: MontgomeryModint or BarrettModint, b: SomeInteger): auto = (result = a; result -= b)\n proc `*`*(a: MontgomeryModint or BarrettModint, b: SomeInteger): auto = (result = a; result *= b)\n proc `/`*(a: MontgomeryModint or BarrettModint, b: SomeInteger): auto = (result = a; result /= b)\n proc `+`*[ModInt: MontgomeryModint or BarrettModint](a: SomeInteger, b: Modint): auto = init(Modint, a) + b\n proc `-`*[ModInt: MontgomeryModint or BarrettModint](a: SomeInteger, b: Modint): auto = init(Modint, a) - b\n proc `*`*[ModInt: MontgomeryModint or BarrettModint](a: SomeInteger, b: Modint): auto = init(Modint, a) * b\n proc `/`*[ModInt: MontgomeryModint or BarrettModint](a: SomeInteger, b: Modint): auto = init(Modint, a) / b\n proc `/`*[ModInt: MontgomeryModint or BarrettModint](a: ModInt, b: static int): auto =\n const tmp = init(Modint, b).inv\n return a * tmp\n proc pow*(a: MontgomeryModint or BarrettModint, n: int): auto =\n result = init(typeof(a), 1)\n var a = a\n var n = n\n while n > 0:\n if (n and 1) == 1: result *= a\n a *= a\n n = (n shr 1)\n proc `$`*(a: MontgomeryModint or BarrettModint): string = $(a.val)\n proc estimate_rational*(a: MontgomeryModint or BarrettModint, ub: int = isqrt(typeof(a).mod)): string =\n var v: seq[tuple[s, n, d: int]]\n for d in 1..ub:\n var n = (a * d).val\n if n * 2 > a.mod:\n n = - (a.mod - n)\n if gcd(n, d) > 1: continue\n v.add((n.abs + d, n, d))\n v.sort\n return $v[0].n & \"/\" & $v[0].d\n \n # original: https://tayu0110.hatenablog.com/entry/2023/05/06/023244\n when not declared CPLIB_CONVOLUTION_NTT:\n const CPLIB_CONVOLUTION_NTT* = 1\n import options\n import macros\n import tables\n import bitops\n proc ntt_powmod_compiletime(a, x, p: int): int =\n var ans = 1\n var a = a\n var x = x\n while x > 0:\n if (x and 1) == 1:\n ans = (ans * a) mod p\n a = (a * a) mod p\n x = (x shr 1)\n return ans mod p\n \n proc ntt_primefactor_compiletime(p: int): seq[int] =\n var x = p\n var ans = newSeq[int]()\n for i in 2..p:\n if i * i > p: break\n if x mod i != 0: continue\n ans.add(i)\n while x mod i == 0:\n x = x div i\n if x != 1: ans.add(x)\n return ans\n \n proc ntt_primitive_root_compiletime(p: int): int =\n var pf = (p-1).ntt_primefactor_compiletime\n for a in 3..<p:\n proc check(): bool =\n for q in pf:\n if ntt_powmod_compiletime(a, (p-1) div q, p) == 1:\n return false\n return true\n if check():\n return a\n \n proc nth_root(primitive_root, nth, m: int): int = ntt_powmod_compiletime(primitive_root, (m - 1) div nth, m)\n type NttConfig = object\n sum_e, m, forth_root, forth_root_inv, primitive_root: int\n rate2, rate3, irate2, irate3: array[30, int]\n proc initNttConfig(m: int): NttConfig =\n var sum_e = 0\n var rate2, rate3, irate2, irate3: array[30, int]\n var prod = 1\n var iprod = 1\n var primitive_root = ntt_primitive_root_compiletime(m)\n while sum_e + 2 <= ((m - 1).countTrailingZeroBits - 1):\n var root = nth_root(primitive_root, 1 shl (sum_e + 2), m)\n var iroot = ntt_powmod_compiletime(root, m - 2, m)\n rate2[sum_e] = (root * iprod) mod m\n irate2[sum_e] = (iroot * prod) mod m\n prod = (prod * root) mod m\n iprod = (iprod * iroot) mod m\n sum_e += 1\n sum_e = 0\n prod = 1\n iprod = 1\n while sum_e + 3 <= ((m - 1).countTrailingZeroBits):\n var root = nth_root(primitive_root, 1 shl (sum_e + 3), m)\n var iroot = ntt_powmod_compiletime(root, m - 2, m)\n rate3[sum_e] = (root * iprod) mod m\n irate3[sum_e] = (iroot * prod) mod m\n prod = (prod * root) mod m\n iprod = (iprod * iroot) mod m\n sum_e += 1\n var forth_root = nth_root(primitive_root, 4, m)\n var forth_root_inv = ntt_powmod_compiletime(forth_root, m-2, m)\n return NttConfig(sum_e: sum_e + 2, m: m, forth_root: forth_root, forth_root_inv: forth_root_inv, primitive_root: primitive_root, rate2: rate2, rate3: rate3, irate2: irate2, irate3: irate3)\n \n var ntt_config_cache {.compileTime.}: Table[uint32, NimNode]\n var dynamic_ntt_config = NttConfig()\n macro get_ntt_config[M: static[uint32]](self: typedesc[StaticBarrettModint[M] or StaticMontgomeryModint[M]]): untyped =\n if M notin ntt_config_cache:\n let value = initNttConfig(int(M))\n ntt_config_cache[M] = newLit(value)\n result = ntt_config_cache[M]\n proc get_ntt_config(self: typedesc[DynamicBarrettModint or DynamicMontgomeryModint]): NttConfig =\n if dynamic_ntt_config.m != self.umod.int:\n dynamic_ntt_config = initNttConfig(self.umod.int)\n return dynamic_ntt_config\n \n proc ntt*[T: BarrettModint or MontgomeryModint](f: var seq[T]) =\n let n = f.len\n if n <= 1: return\n let ntt_config = get_ntt_config(T)\n assert(n.popcount == 1, \"len(f) must be power of two, please add zeros\")\n var width = n\n while width > 1:\n if width == 2:\n let offset = (width shr 1)\n var root = T(1)\n for top in countup(0, n-1, width):\n for i in top..<(top+offset):\n let (c0, c1) = (f[i], f[i+offset] * root)\n f[i] = c0 + c1\n f[i+offset] = c0 - c1\n let b = top div width\n root *= ntt_config.rate2[countTrailingZeroBits(not b)]\n width = (width shr 1)\n else:\n let offset = (width shr 2)\n var root = T(1)\n for top in countup(0, n-1, width):\n let root2 = root * root\n let root3 = root * root2\n for i in top..<(top+offset):\n let (c0, c1, c2, c3) = (f[i], f[i+offset] * root, f[i+offset*2] * root2, f[i+offset*3] * root3)\n let c0c2 = c0 + c2\n let c0c2n = c0 - c2\n let c1c3 = c1 + c3\n let c1c3nim = (c1 - c3) * ntt_config.forth_root\n f[i] = c0c2 + c1c3\n f[i+offset] = c0c2 - c1c3\n f[i+offset*2] = c0c2n + c1c3nim\n f[i+offset*3] = c0c2n - c1c3nim\n let b = top div width\n root *= ntt_config.rate3[countTrailingZeroBits(not b)]\n width = (width shr 2)\n \n proc intt*[T: BarrettModint or MontgomeryModint](f: var seq[T]) =\n let n = f.len\n if n <= 1: return\n let ntt_config = get_ntt_config(T)\n assert(n.popcount == 1, \"len(f) must be power of two, please add zeros\")\n var width = (if n.countTrailingZeroBits mod 2 == 1: 2 else: 4)\n while width <= n:\n if width == 2:\n let offset = (width shr 1)\n var root = T(1)\n for top in countup(0, n-1, width):\n for i in top..<(top+offset):\n let (c0, c1) = (f[i], f[i+offset])\n f[i] = c0 + c1\n f[i+offset] = (c0 - c1) * root\n let b = top div width\n root *= ntt_config.irate2[countTrailingZeroBits(not b)]\n else:\n let offset = (width shr 2)\n var root = T(1)\n for top in countup(0, n-1, width):\n let root2 = root * root\n let root3 = root * root2\n for i in top..<(top+offset):\n let (c0, c1, c2, c3) = (f[i], f[i+offset], f[i+offset*2], f[i+offset*3])\n let c0c1 = c0 + c1\n let c0c1n = c0 - c1\n let c2c3 = c2 + c3\n let c2c3nim = (c2 - c3) * ntt_config.forth_root_inv\n f[i] = c0c1 + c2c3\n f[i+offset] = (c0c1n + c2c3nim) * root\n f[i+offset*2] = (c0c1 - c2c3) * root2\n f[i+offset*3] = (c0c1n - c2c3nim) * root3\n let b = top div width\n root *= ntt_config.irate3[countTrailingZeroBits(not b)]\n width = (width shl 2)\n var ninv = T(n).inv\n for i in 0..<n: f[i] *= ninv\n \n when not declared CPLIB_MATH_INVGCD:\n const CPLIB_MATH_INVGCD* = 1\n # @param b `1 <= b`\n # @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g\n import std/math\n proc inv_gcd*(a, b: int): (int, int) =\n var a = floorMod(a, b)\n if a == 0: return (b, 0)\n var\n s = b\n t = a\n m0 = 0\n m1 = 1\n \n while t != 0:\n var u = s div t\n s -= t * u\n m0 -= m1 * u\n \n var tmp = s\n s = t\n t = tmp\n tmp = m0\n m0 = m1\n m1 = tmp\n if m0 < 0: m0 += b div s\n return (s, m0)\n \n \n\n declarStaticMontgomeryModint(mint754974721, 754974721u32)\n declarStaticMontgomeryModint(mint167772161, 167772161u32)\n declarStaticMontgomeryModint(mint469762049, 469762049u32)\n\n proc convolution_naive*[T: BarrettModint or MontgomeryModint or int](f, g: seq[T]): seq[T] =\n var ans = newSeqWith(f.len + g.len - 1, T(0))\n if f.len > g.len:\n for i in 0..<f.len:\n for j in 0..<g.len:\n ans[i+j] += f[i] * g[j]\n else:\n for j in 0..<g.len:\n for i in 0..<f.len:\n ans[i+j] += f[i] * g[j]\n return ans\n\n proc convolution*[T: BarrettModint or MontgomeryModint](f, g: seq[T]): seq[T] =\n var f = f\n var g = g\n let m = f.len\n let n = g.len\n let deg = m + n - 1\n if min(n, m) <= 60: return convolution_naive(f, g)\n var l = (if deg == 1: 1 else: (1 shl (fastLog2(deg - 1) + 1)))\n f.setLen(l)\n g.setLen(l)\n ntt(f)\n ntt(g)\n for i in 0..<f.len:\n f[i] *= g[i]\n intt(f)\n f.setlen(deg)\n return f\n\n\n proc convolution_ll*(f, g: seq[int]): seq[int] =\n var n = f.len\n var m = g.len\n if n == 0 or m == 0: return newSeq[int]()\n\n const\n M1 = 754974721u\n M2 = 167772161u\n M3 = 469762049u\n M12 = M1 * M2\n M23 = M2 * M3\n M31 = M3 * M1\n M123 = M1 * M2 * M3\n i1 = inv_gcd((M2 * M3).int, M1.int)[1].uint\n i2 = inv_gcd((M3 * M1).int, M2.int)[1].uint\n i3 = inv_gcd((M1 * M2).int, M3.int)[1].uint\n # FIXME: mapitでf1, g1を作ろうとするとなぜか壊れる……\n var f1 = newSeq[mint754974721](n)\n var g1 = newSeq[mint754974721](m)\n for i in 0..<n: f1[i] = mint754974721(f[i])\n for i in 0..<m: g1[i] = mint754974721(g[i])\n let c1 = convolution(f1, g1)\n var f2 = newSeq[mint167772161](n)\n var g2 = newSeq[mint167772161](m)\n for i in 0..<n: f2[i] = mint167772161(f[i])\n for i in 0..<m: g2[i] = mint167772161(g[i])\n let c2 = convolution(f2, g2)\n var f3 = newSeq[mint469762049](n)\n var g3 = newSeq[mint469762049](m)\n for i in 0..<n: f3[i] = mint469762049(f[i])\n for i in 0..<m: g3[i] = mint469762049(g[i])\n let c3 = convolution(f3, g3)\n var ans = newseqwith(n + m - 1, 0)\n for i in 0..<ans.len:\n var x = 0.uint\n x += (c1[i].val.uint * i1) mod M1 * M23\n x += (c2[i].val.uint * i2) mod M2 * M31\n x += (c3[i].val.uint * i3) mod M3 * M12\n var diff = c1[i].val - floorMod(x.int, M1.int)\n if diff < 0: diff += M1.int\n const offset = [0u, 0u, M123, 2u * M123, 3u * M123]\n x -= offset[diff mod 5]\n ans[i] = cast[int](x)\n return ans\n"
# source: https://github.com/kemuniku/cplib/tree/main/src/cplib/math/combination.nim
ImportExpand "cplib/math/combination" <=== "when not declared CPLIB_MATH_COMBINATION:\n const CPLIB_MATH_COMBINATION* = 1\n type Combination_Type[ModInt] = object\n fact*: seq[ModInt]\n inv*: seq[ModInt]\n fact_inv*: seq[ModInt]\n\n proc initCombination*[ModInt](max_N: int): Combination_Type[ModInt] =\n var fact = newSeq[ModInt](max_N+1)\n var inv = newSeq[ModInt](max_N+1)\n var fact_inv = newSeq[ModInt](max_N+1)\n fact[0] = 1\n fact[1] = 1\n inv[1] = 1\n fact_inv[0] = 1\n fact_inv[1] = 1\n for i in 2..max_N:\n fact[i] = fact[i-1] * i\n inv[i] = -inv[int(ModInt.umod()) mod i]*(int(ModInt.umod()) div i)\n fact_inv[i] = fact_inv[i-1] * inv[i]\n result = Combination_Type[ModInt](fact: fact, inv: inv, fact_inv: fact_inv)\n\n proc ncr*[ModInt](c: Combination_Type[ModInt], n, r: int): ModInt =\n if n < 0 or r < 0 or n < r:\n return 0\n return c.fact[n]*c.fact_inv[n-r]*c.fact_inv[r]\n\n proc npr*[ModInt](c: Combination_Type[ModInt], n, r: int): ModInt =\n if n < 0 or r < 0 or n < r:\n return 0\n return c.fact[n]*c.fact_inv[n-r]\n\n proc nhr*[ModInt](c: Combination_Type[ModInt], n, r: int): ModInt =\n return c.ncr(n+r-1, r)\n"
# {.checks: off.}
type mint = modint998244353_barrett
var comb = initCombination[mint](200000)
proc solve() =
var n,l = input(int)
var d = input(int, n)
var a = 0
if l % 2 == 0:
for i in 0..<n:
var x = d[i]
var y = (x + l // 2) % l
debug(x, y)
if x < y:
var p = d.lowerBound(y)
if p < d.len and d[p] == y:
a += 1
var b = n - 2 * a
var f = newSeqWith(a+1, mint(0))
var g = newSeqWith(b+1, mint(0))
var f2 = newSeqWith(a+1, mint(0))
for i in 0..a:
f[i] = mint(2).pow(i) * comb.ncr(a, i)
if i >= 1:
f2[i-1] = mint(2).pow(i-1) * comb.ncr(a-1, i-1)
for i in 0..b:
g[i] = comb.ncr(b, i)
var h = convolution(f, g)
var h2 = convolution(f2, g)
debug(h, h2)
while h.len <= n: h.add(mint(0))
while h2.len <= n: h2.add(mint(0))
if a >= 1:
for i in 2..n:
h[i] += mint(a) * h2[i-2]
debug(h)
for i in 0..n: h[i] /= comb.ncr(n, i)
debug(a, b)
var ans = mint(0)
for i in 0..<n:
ans += (mint(n) / mint(n - i)) * h[i]
print($ans)
var t = input(int)
for _ in 0..<t: solve()