import macros;macro ImportExpand(s:untyped):untyped = parseStmt($s[2]) # {.checks: off.} ImportExpand "cplib/tmpl/citrus.nim" <=== "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 #[ include cplib/utils/infl ]#\n when not declared CPLIB_UTILS_INFL:\n const CPLIB_UTILS_INFL* = 1\n const INFi32* = 100100111.int32\n const INFL* = int(3300300300300300491)\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.. 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 = INFL): 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 #[ include cplib/math/isqrt ]#\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 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" ImportExpand "cplib/modint/modint.nim" <=== "when not declared CPLIB_MODINT_MODINT:\n const CPLIB_MODINT_MODINT* = 1\n #[ include cplib/modint/barrett_impl ]#\n when not declared CPLIB_MODINT_MODINT_BARRETT:\n const CPLIB_MODINT_MODINT_BARRETT* = 1\n import std/macros\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 func get_param*[M: static[uint32]](self: typedesc[DynamicBarrettModint[M]]): ptr[tuple[M, im: uint]] =\n {.cast(noSideEffect).}:\n var p {.global.}: tuple[M, im: uint] = (998244353u, get_im(998244353u32))\n return p.addr\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 (get_param(self))[] = (M: M.uint, 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: cast[uint32](((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 \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.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 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 #[ include cplib/modint/montgomery_impl ]#\n when not declared CPLIB_MODINT_MODINT_MONTGOMERY:\n const CPLIB_MODINT_MODINT_MONTGOMERY* = 1\n import std/macros\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 func get_param*[M: static[uint32]](self: typedesc[DynamicMontgomeryModint[M]]): ptr[tuple[M, r, n2: uint32]] =\n {.cast(noSideEffect).}:\n var p {.global.}: tuple[M, r, n2: uint32] = (998244353u32, get_r(998244353u32), get_n2(998244353u32))\n return p.addr\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 var p = (M.uint32, r, n2)\n (get_param(self))[] = p\n check_params(M.uint32, r)\n \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 func reduce(T: typedesc[MontgomeryModint], b: uint): uint32 =\n when T is StaticMontgomeryModint:\n const r = get_r(T.M)\n return cast[uint32]((b + uint(cast[uint32](b) * (not (r - 1u32))) * T.M) shr 32)\n else:\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 const r = get_r(T.M)\n const n2 = get_n2(T.M)\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 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\" & $`name`)\n quote do:\n type `name`* = DynamicMontgomeryModint[`id`]\n converter `converter_name`*(a: int): DynamicMontgomeryModint[`id`] = init(DynamicMontgomeryModint[`id`], a)\n import std/math\n import std/algorithm\n #[ import cplib/math/isqrt ]#\n declarStaticMontgomeryModint(modint998244353_montgomery, 998244353u32)\n declarStaticMontgomeryModint(modint1000000007_montgomery, 1000000007u32)\n declarDynamicMontgomeryModint(modint_montgomery, 1u32)\n declarStaticBarrettModint(modint998244353_barrett, 998244353u32)\n declarStaticBarrettModint(modint1000000007_barrett, 1000000007u32)\n declarDynamicBarrettModint(modint_barrett, 1u32)\n func `+`*(a, b: MontgomeryModint or BarrettModint): auto = (result = a; result += b)\n func `-`*(a, b: MontgomeryModint or BarrettModint): auto = (result = a; result -= b)\n func `*`*(a, b: MontgomeryModint or BarrettModint): auto = (result = a; result *= b)\n func `/`*(a, b: MontgomeryModint or BarrettModint): auto = (result = a; result /= b)\n func `+`*(a: MontgomeryModint or BarrettModint, b: SomeInteger): auto = (result = a; result += b)\n func `-`*(a: MontgomeryModint or BarrettModint, b: SomeInteger): auto = (result = a; result -= b)\n func `*`*(a: MontgomeryModint or BarrettModint, b: SomeInteger): auto = (result = a; result *= b)\n func `/`*(a: MontgomeryModint or BarrettModint, b: SomeInteger): auto = (result = a; result /= b)\n func `+`*(a: SomeInteger, b: MontgomeryModint or BarrettModint): auto = b + a\n func `-`*(a: SomeInteger, b: MontgomeryModint or BarrettModint): auto = b - a\n func `*`*(a: SomeInteger, b: MontgomeryModint or BarrettModint): auto = b * a\n func `/`*(a: SomeInteger, b: MontgomeryModint or BarrettModint): auto = b / a\n func pow*(a: MontgomeryModint or BarrettModint, n: int): auto =\n result = init(typeof(a), 1)\n var a = a\n var n = n\n while n > 0:\n if (n and 1) == 1: result *= a\n a *= a\n n = (n shr 1)\n func `$`*(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" type mint = modint998244353_barrett var n = input(int) var a = input(int, n) var b = input(string, n) var ans = mint(0) for i in 0..