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 = 100100111.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.. 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/graph/graph.nim ImportExpand "cplib/graph/graph" <=== "when not declared CPLIB_GRAPH_GRAPH:\n const CPLIB_GRAPH_GRAPH* = 1\n\n import sequtils\n import math\n type DynamicGraph*[T] = ref object of RootObj\n edges*: seq[seq[(int32, T)]]\n len*: int\n type StaticGraph*[T] = ref object of RootObj\n src*, dst*: seq[int32]\n cost*: seq[T]\n elist*: seq[(int32, T)]\n start*: seq[int32]\n len*: int\n\n type WeightedDirectedGraph*[T] = ref object of DynamicGraph[T]\n type WeightedUnDirectedGraph*[T] = ref object of DynamicGraph[T]\n type UnWeightedDirectedGraph* = ref object of DynamicGraph[int]\n type UnWeightedUnDirectedGraph* = ref object of DynamicGraph[int]\n type WeightedDirectedStaticGraph*[T] = ref object of StaticGraph[T]\n type WeightedUnDirectedStaticGraph*[T] = ref object of StaticGraph[T]\n type UnWeightedDirectedStaticGraph* = ref object of StaticGraph[int]\n type UnWeightedUnDirectedStaticGraph* = ref object of StaticGraph[int]\n\n type GraphTypes*[T] = DynamicGraph[T] or StaticGraph[T]\n type DirectedGraph* = WeightedDirectedGraph or UnWeightedDirectedGraph or WeightedDirectedStaticGraph or UnWeightedDirectedStaticGraph\n type UnDirectedGraph* = WeightedUnDirectedGraph or UnWeightedUnDirectedGraph or WeightedUnDirectedStaticGraph or UnWeightedUnDirectedStaticGraph\n type WeightedGraph*[T] = WeightedDirectedGraph[T] or WeightedUnDirectedGraph[T] or WeightedDirectedStaticGraph[T] or WeightedUnDirectedStaticGraph[T]\n type UnWeightedGraph* = UnWeightedDirectedGraph or UnWeightedUnDirectedGraph or UnWeightedDirectedStaticGraph or UnWeightedUnDirectedStaticGraph\n type DynamicGraphTypes* = WeightedDirectedGraph or UnWeightedDirectedGraph or WeightedUnDirectedGraph or UnWeightedUnDirectedGraph\n type StaticGraphTypes* = WeightedDirectedStaticGraph or UnWeightedDirectedStaticGraph or WeightedUnDirectedStaticGraph or UnWeightedUnDirectedStaticGraph\n\n proc add_edge_dynamic_impl*[T](g: DynamicGraph[T], u, v: int, cost: T, directed: bool) =\n g.edges[u].add((v.int32, cost))\n if not directed: g.edges[v].add((u.int32, cost))\n\n proc initWeightedDirectedGraph*(N: int, edgetype: typedesc = int): WeightedDirectedGraph[edgetype] =\n result = WeightedDirectedGraph[edgetype](edges: newSeq[seq[(int32, edgetype)]](N), len: N)\n proc add_edge*[T](g: var WeightedDirectedGraph[T], u, v: int, cost: T) =\n g.add_edge_dynamic_impl(u, v, cost, true)\n\n proc initWeightedUnDirectedGraph*(N: int, edgetype: typedesc = int): WeightedUnDirectedGraph[edgetype] =\n result = WeightedUnDirectedGraph[edgetype](edges: newSeq[seq[(int32, edgetype)]](N), len: N)\n proc add_edge*[T](g: var WeightedUnDirectedGraph[T], u, v: int, cost: T) =\n g.add_edge_dynamic_impl(u, v, cost, false)\n\n proc initUnWeightedDirectedGraph*(N: int): UnWeightedDirectedGraph =\n result = UnWeightedDirectedGraph(edges: newSeq[seq[(int32, int)]](N), len: N)\n proc add_edge*(g: var UnWeightedDirectedGraph, u, v: int) =\n g.add_edge_dynamic_impl(u, v, 1, true)\n\n proc initUnWeightedUnDirectedGraph*(N: int): UnWeightedUnDirectedGraph =\n result = UnWeightedUnDirectedGraph(edges: newSeq[seq[(int32, int)]](N), len: N)\n proc add_edge*(g: var UnWeightedUnDirectedGraph, u, v: int) =\n g.add_edge_dynamic_impl(u, v, 1, false)\n\n proc len*[T](G: WeightedGraph[T]): int = G.len\n proc len*(G: UnWeightedGraph): int = G.len\n\n iterator `[]`*[T](g: WeightedDirectedGraph[T] or WeightedUnDirectedGraph[T], x: int): (int, T) =\n for e in g.edges[x]: yield (e[0].int, e[1])\n iterator `[]`*(g: UnWeightedDirectedGraph or UnWeightedUnDirectedGraph, x: int): int =\n for e in g.edges[x]: yield e[0].int\n\n proc add_edge_static_impl*[T](g: StaticGraph[T], u, v: int, cost: T, directed: bool) =\n g.src.add(u.int32)\n g.dst.add(v.int32)\n g.cost.add(cost)\n if not directed:\n g.src.add(v.int32)\n g.dst.add(u.int32)\n g.cost.add(cost)\n\n proc build_impl*[T](g: StaticGraph[T]) =\n g.start = newSeqWith(g.len + 1, 0.int32)\n for i in 0.. 0, \"Static Graph must be initialized before use.\"\n\n iterator `[]`*[T](g: WeightedDirectedStaticGraph[T] or WeightedUnDirectedStaticGraph[T], x: int): (int, T) =\n g.static_graph_initialized_check()\n for i in g.start[x]..\n inline unsigned long long calc_mul(const unsigned long long &a, const unsigned long long &b){\n return (unsigned long long)(((unsigned __int128)(a)*b) >> 64);\n }\n \"\"\".}\n proc calc_mul*(a,b:culonglong):culonglong {.importcpp: \"calc_mul(#,#)\", nodecl, inline.}\n # @param a `0 <= a < m`\n # @param b `0 <= b < m`\n # @return `a * b % m`\n proc quo*(self: Barrett, n:int | uint):int =\n let n = n.uint\n let x = calc_mul(n.culonglong, self.im.culonglong).uint\n let r = n - x * self.m\n return int(if self.m <= r: x - 1 else: x)\n proc rem*(self: Barrett, n:int | uint):int =\n let n = n.uint\n let x = calc_mul(n.culonglong, self.im.culonglong).uint\n let r = n - x * self.m\n return int(if self.m <= r: r + self.m else: r)\n proc quorem*(self: Barrett, n:int | uint):(int, int) =\n let n = n.uint\n let x = calc_mul(n.culonglong, self.im.culonglong).uint\n let r = n - x * self.m\n return if self.m <= r: (int(x - 1), int(r + self.m)) else: (int(x), int(r))\n \n proc pow*(self: Barrett, n:uint | int, p:int):int =\n var\n a = self.rem(n)\n r:uint = if self.m == 1: 0 else: 1\n p = p\n while p > 0:\n if (p and 1) != 0: r = self.mul(r, a.uint)\n a = self.mul(a.uint, a.uint).int\n p = p shr 1\n return int(r)\n \n proc mul*(self: Barrett, a:uint, b:uint):uint {.inline.} =\n # [1] m = 1\n # a = b = im = 0, so okay\n \n # [2] m >= 2\n # im = ceil(2^64 / m)\n # -> im * m = 2^64 + r (0 <= r < m)\n # let z = a*b = c*m + d (0 <= c, d < m)\n # a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im\n # c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2\n # ((ab * im) >> 64) == c or c + 1\n let z = a * b\n # #ifdef _MSC_VER\n # unsigned long long x;\n # _umul128(z, im, &x);\n # #else\n # unsigned long long x =\n # (unsigned long long)(((unsigned __int128)(z)*im) >> 64);\n # #endif\n #let x = calc_mul(z.culonglong, self.im.culonglong).uint\n #result = z - x * self.m\n #if self.m <= result: result += self.m\n return self.rem(z).uint\n \n # @param n `0 <= n`\n # @param m `1 <= m`\n # @return `(x ** n) % m`\n proc pow_mod_constexpr*(x, n, m:int):int =\n if m == 1: return 0\n var\n r = 1\n y = floorMod(x, m)\n n = n\n while n != 0:\n if (n and 1) != 0: r = (r * y) mod m\n y = (y * y) mod m\n n = n shr 1\n return r.int\n \n # Reference:\n # M. Forisek and J. Jancina,\n # Fast Primality Testing for Integers That Fit into a Machine Word\n # @param n `0 <= n`\n proc is_prime_constexpr*(n:int):bool =\n if n <= 1: return false\n if n == 2 or n == 7 or n == 61: return true\n if n mod 2 == 0: return false\n var d = n - 1\n while d mod 2 == 0: d = d div 2\n for a in [2, 7, 61]:\n var\n t = d\n y = pow_mod_constexpr(a, t, n)\n while t != n - 1 and y != 1 and y != n - 1:\n y = y * y mod n\n t = t shl 1\n if y != n - 1 and t mod 2 == 0:\n return false\n return true\n proc is_prime*[n:static[int]]():bool = is_prime_constexpr(n)\n # \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 proc inv_gcd*(a, b:int):(int,int) =\n var a = floorMod(a, b)\n if a == 0: return (b, 0)\n \n # Contracts:\n # [1] s - m0 * a = 0 (mod b)\n # [2] t - m1 * a = 0 (mod b)\n # [3] s * |m1| + t * |m0| <= b\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; # |m1 * u| <= |m1| * s <= b\n \n # [3]:\n # (s - t * u) * |m1| + t * |m0 - m1 * u|\n # <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)\n # = s * |m1| + t * |m0| <= b\n \n var tmp = s\n s = t;t = tmp;\n tmp = m0;m0 = m1;m1 = tmp;\n # by [3]: |m0| <= b/g\n # by g != b: |m0| < b/g\n if m0 < 0: m0 += b div s\n return (s, m0)\n \n # Compile time primitive root\n # @param m must be prime\n # @return primitive root (and minimum in now)\n proc primitive_root_constexpr*(m:int):int =\n if m == 2: return 1\n if m == 167772161: return 3\n if m == 469762049: return 3\n if m == 754974721: return 11\n if m == 998244353: return 3\n var divs:array[20, int]\n divs[0] = 2\n var cnt = 1\n var x = (m - 1) div 2\n while x mod 2 == 0: x = x div 2\n var i = 3\n while i * i <= x:\n if x mod i == 0:\n divs[cnt] = i\n cnt.inc\n while x mod i == 0:\n x = x div i\n i += 2\n if x > 1:\n divs[cnt] = x\n cnt.inc\n var g = 2\n while true:\n var ok = true\n for i in 0..= m:\n result += n * (n - 1) div 2 * (a div m)\n a = a mod m\n if b >= m:\n result += n * (b div m)\n b = b mod m\n \n let y_max = a * n + b\n if y_max < m: break\n # y_max < m * (n + 1)\n # floor(y_max / m) <= n\n n = y_max div m\n b = y_max mod m\n swap(m, a)\n \n when not declared ATCODER_INTERNAL_BITOP_HPP:\n const ATCODER_INTERNAL_BITOP_HPP* = 1\n import std/bitops\n \n #ifdef _MSC_VER\n #include \n #endif\n \n # @param n `0 <= n`\n # @return minimum non-negative `x` s.t. `n <= 2**x`\n proc ceil_pow2*(n:SomeInteger):int =\n var x = 0\n while (1.uint shl x) < n.uint: x.inc\n return x\n # @param n `1 <= n`\n # @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`\n proc bsf*(n:SomeInteger):int =\n return countTrailingZeroBits(n)\n \n when not declared ATCODER_ELEMENT_CONCEPTS_HPP:\n const ATCODER_ELEMENT_CONCEPTS_HPP* = 1\n proc inv*[T:SomeFloat](a:T):auto = T(1) / a\n proc init*(self:typedesc[SomeFloat], a:SomeNumber):auto = self(a)\n type AdditiveGroupElem* = concept x, y, type T\n x + y\n x - y\n -x\n T(0)\n type MultiplicativeGroupElem* = concept x, y, type T\n x * y\n x / y\n # x.inv()\n T(1)\n type RingElem* = concept x, y, type T\n x + y\n x - y\n -x\n x * y\n T(0)\n T(1)\n type FieldElem* = concept x, y, type T\n x + y\n x - y\n x * y\n x / y\n -x\n # x.inv()\n T(0)\n T(1)\n type FiniteFieldElem* = concept x, type T\n T is FieldElem\n T.mod\n T.mod() is int\n x.pow(1000000)\n type hasInf* = concept x, type T\n T(Inf)\n \n\n type fft_info*[mint:FiniteFieldElem; g, rank2:static[int]] = object\n root, iroot: array[rank2 + 1, mint]\n rate2, irate2: array[max(0, rank2 - 2 + 1), mint]\n rate3, irate3: array[max(0, rank2 - 3 + 1), mint]\n\n proc initFFTInfo*[mint:FiniteFieldElem]():auto =\n const g = primitive_root[mint.mod]()\n const rank2 = bsf(mint.mod - 1)\n var root, iroot:array[rank2 + 1, mint]\n var rate2, irate2: array[max(0, rank2 - 2 + 1), mint]\n var rate3, irate3: array[max(0, rank2 - 3 + 1), mint]\n mixin init, inv\n\n root[rank2] = mint.init(g).pow((mint.mod - 1) shr rank2)\n iroot[rank2] = root[rank2].inv()\n for i in countdown(rank2 - 1, 0):\n root[i] = root[i + 1] * root[i + 1];\n iroot[i] = iroot[i + 1] * iroot[i + 1];\n \n block:\n var\n prod = mint.init(1)\n iprod = mint.init(1)\n for i in 0..rank2 - 2:\n rate2[i] = root[i + 2] * prod\n irate2[i] = iroot[i + 2] * iprod\n prod *= iroot[i + 2]\n iprod *= root[i + 2]\n block:\n var\n prod = mint.init(1)\n iprod = mint.init(1)\n for i in 0..rank2 - 3:\n rate3[i] = root[i + 3] * prod;\n irate3[i] = iroot[i + 3] * iprod;\n prod *= iroot[i + 3];\n iprod *= root[i + 3];\n return fft_info[mint, g, rank2](root:root, iroot:iroot, rate2:rate2, irate2:irate2, rate3: rate3, irate3:irate3)\n \n proc butterfly*[mint:FiniteFieldElem](a:var seq[mint]) =\n mixin init\n let n = a.len\n let h = ceil_pow2(n)\n\n const info = initFFTInfo[mint]()\n\n var len = 0 # a[i, i+(n>>len), i+2*(n>>len), ..] is transformed\n while len < h:\n if h - len == 1:\n let p = 1 shl (h - len - 1)\n var rot = mint.init(1)\n for s in 0..<(1 shl len):\n var offset = s shl (h - len)\n for i in 0..>len), i+2*(n>>len), ..] is transformed\n while len > 0:\n if len == 1:\n let p = 1 shl (h - len)\n var irot = mint.init(1)\n for s in 0..<(1 shl (len - 1)):\n let offset = s shl (h - len + 1)\n for i in 0..= 0\n if (p.type)(0) <= p:\n var\n p = p.uint\n m = m\n result = m.unit()\n while p > 0'u:\n if (p and 1'u) != 0'u: result *= m\n m *= m\n p = p shr 1'u\n proc `^`*[T:name](m: T; p: SomeInteger): T {.inline.} = m.pow(p)\n \n macro generateConverter*(name, from_type, to_type) =\n let fname = ident(\"to\" & $`name` & \"OfGenerateConverter\")\n quote do:\n type `name`* = `to_type`\n converter `fname`*(a:`from_type`):`name` {.used.} =\n `name`.init(a)\n \n \n type\n StaticModInt*[M: static[int]] = object\n a:uint32\n DynamicModInt*[T: static[int]] = object\n a:uint32\n \n type ModInt* = StaticModInt or DynamicModInt\n # type ModInt* = concept x, type T\n # T is StaticModInt or T is DynamicModInt\n \n proc isStaticModInt*(T:typedesc[ModInt]):bool = T is StaticModInt\n proc isDynamicModInt*(T:typedesc[ModInt]):bool = T is DynamicModInt\n #proc isModInt*(T:typedesc):bool = T.isStaticModInt or T.isDynamicModInt\n proc isStatic*(T:typedesc[ModInt]):bool = T is StaticModInt\n proc getMod*[M:static[int]](t:typedesc[StaticModInt[M]]):int {.inline.} = M\n \n \n \n proc getBarrett*[T:static[int]](t:typedesc[DynamicModInt[T]]):ptr Barrett =\n var Barrett_of_DynamicModInt {.global.} = initBarrett(998244353.uint)\n return Barrett_of_DynamicModInt.addr\n \n proc getMod*[T:static[int]](t:typedesc[DynamicModInt[T]]):uint32 {.inline.} =\n (t.getBarrett)[].m.uint32\n proc setMod*[T:static[int]](t:typedesc[DynamicModInt[T]], M:SomeInteger){.inline.} =\n (t.getBarrett)[] = initBarrett(M.uint)\n \n proc val*(m: ModInt): int {.inline.} = int(m.a)\n \n proc `$`*(m: StaticModInt or DynamicModInt): string {.inline.} = $(m.val())\n \n template umod*[T:ModInt](self: typedesc[T] or T):uint32 =\n when T is typedesc:\n when T is StaticModInt:\n T.M.uint32\n elif T is DynamicModInt:\n T.getMod()\n else:\n static: assert false\n else: T.umod\n \n template `mod`*[T:ModInt](self:typedesc[T] or T):int = T.umod.int\n \n proc init*[T:ModInt](t:typedesc[T], v: SomeInteger or T): auto {.inline.} =\n when v is T: return v\n else:\n when v is SomeUnsignedInt:\n if v.uint < T.umod:\n return T(a:v.uint32)\n else:\n return T(a:(v.uint mod T.umod.uint).uint32)\n else:\n var v = v.int\n if 0 <= v:\n if v < T.mod: return T(a:v.uint32)\n else: return T(a:(v mod T.mod).uint32)\n else:\n v = v mod T.mod\n if v < 0: v += T.mod\n return T(a:v.uint32)\n proc unit*[T:ModInt](t:typedesc[T] or T):T = T.init(1)\n \n template initModInt*(v: SomeInteger or ModInt; M: static[int] = 1_000_000_007): auto =\n StaticModInt[M].init(v)\n \n # TODO\n # converter toModInt[M:static[int]](n:SomeInteger):StaticModInt[M] {.inline.} = initModInt(n, M)\n \n # proc initModIntRaw*(v: SomeInteger; M: static[int] = 1_000_000_007): auto {.inline.} =\n # ModInt[M](v.uint32)\n proc raw*[T:ModInt](t:typedesc[T], v:SomeInteger):auto = T(a:v)\n \n proc inv*[T:ModInt](v:T):T {.inline.} =\n var\n a = v.a.int\n b = T.mod\n u = 1\n v = 0\n while b > 0:\n let t = a div b\n a -= t * b;swap(a, b)\n u -= t * v;swap(u, v)\n return T.init(u)\n \n \n proc `-`*[T:ModInt](m: T): T {.inline.} =\n if int(m.a) == 0: return m\n else: return T(a:m.umod() - m.a)\n \n proc `+=`*[T:ModInt](m: var T; n: SomeInteger | T):T {.inline discardable.} =\n m.a += T.init(n).a\n if m.a >= T.umod: m.a -= T.umod\n return m\n \n proc `-=`*[T:ModInt](m: var T; n: SomeInteger | T):T {.inline discardable.} =\n m.a -= T.init(n).a\n if m.a >= T.umod: m.a += T.umod\n return m\n \n proc `*=`*[T:ModInt](m: var T; n: SomeInteger | T):T {.inline discardable.} =\n when T is StaticModInt:\n m.a = (m.a.uint * T.init(n).a.uint mod T.umod).uint32\n elif T is DynamicModInt:\n m.a = T.getBarrett[].mul(m.a.uint, T.init(n).a.uint).uint32\n else:\n static: assert false\n return m\n \n proc `/=`*[T:ModInt](m: var T; n: SomeInteger | T):T {.inline discardable.} =\n m.a = (m.a.uint * T.init(n).inv().a.uint mod T.umod).uint32\n return m\n \n generateDefinitions(`+`, m, n, ModInt, SomeInteger):\n result = T.init(m)\n result += n\n \n generateDefinitions(`-`, m, n, ModInt, SomeInteger):\n result = T.init(m)\n result -= n\n \n generateDefinitions(`*`, m, n, ModInt, SomeInteger):\n result = T.init(m)\n result *= n\n \n generateDefinitions(`/`, m, n, ModInt, SomeInteger):\n result = T.init(m)\n result /= n\n \n generateDefinitions(`==`, m, n, ModInt, SomeInteger):\n result = (T.init(m).val() == T.init(n).val())\n \n proc inc*(m: var ModInt):ModInt {.inline discardable.} =\n m.a.inc\n if m.a == m.umod.uint32:\n m.a = 0\n return m\n proc `++`*(m: var ModInt):ModInt {.inline discardable.} = m.inc\n \n proc dec*(m: var ModInt):ModInt {.inline discardable.} =\n if m.a == 0.uint32:\n m.a = m.umod - 1\n else:\n m.a.dec\n return m\n proc `--`*(m: var ModInt):ModInt {.inline discardable.} = m.dec\n \n generatePow(ModInt)\n \n # TODO: intのところはSomeIntegerに拡張したいがそうするとSystem.nimのuintのconverterとバッティングする。。。\n template useStaticModint*(name, M) =\n generateConverter(name, int, StaticModInt[M])\n template useDynamicModInt*(name, M) =\n generateConverter(name, int, DynamicModInt[M])\n \n # TODO: Nimのstatic[int]を使うconverterがバグっていて個々に宣言しないとconverterが使えない\n # したがって、下記以外のmodintを使う場合はuseStaticModIntあるいはuseDynamicModIntで宣言が必要\n useStaticModInt(modint998244353, 998244353)\n useStaticModInt(modint1000000007, 1000000007)\n useDynamicModInt(modint, -1)\n \n import std/math as math_lib_modint\n proc estimateRational*(a:ModInt, ub:int = int(sqrt(float(ModInt.mod))), output_stderr:static[bool] = false):string =\n var v:seq[tuple[s, n, d: int]]\n for d in 1 .. ub:\n var n = (a * d).val\n # n or mod - n\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 when output_stderr:\n stderr.write \"estimation result: \", v\n return $v[0].n & \"/\" & $v[0].d\n \n # TODO:\n # Modint -> intのconverterあるとmint(2) * 3みたいなのがintになっちゃう\n # converter toInt*(m: ModInt):int {.inline.} = m.val\n \n \n \n proc convolution*[T:SomeInteger](a, b:seq[T], M:static[uint] = 998244353):seq[T] =\n let (n, m) = (a.len, b.len)\n if n == 0 or m == 0: return newSeq[T]()\n \n type mint = StaticModInt[M.int]\n static:\n assert mint is FiniteFieldElem\n return convolution(\n a.map((x:T) => mint.init(x)), \n b.map((x:T) => mint.init(x))\n ).map((x:mint) => T(x.val()))\n\n proc convolution_ll*(a, b:seq[int]):seq[int] =\n let (n, m) = (a.len, b.len)\n if n == 0 or m == 0: return newSeq[int]()\n const\n MOD1:uint = 754974721 # 2^24\n MOD2:uint = 167772161 # 2^25\n MOD3:uint = 469762049 # 2^26\n M2M3 = MOD2 * MOD3\n M1M3 = MOD1 * MOD3\n M1M2 = MOD1 * MOD2\n M1M2M3 = MOD1 * MOD2 * MOD3\n\n i1 = inv_gcd((MOD2 * MOD3).int, MOD1.int)[1].uint\n i2 = inv_gcd((MOD1 * MOD3).int, MOD2.int)[1].uint\n i3 = inv_gcd((MOD1 * MOD2).int, MOD3.int)[1].uint\n \n let\n c1 = convolution(a, b, MOD1)\n c2 = convolution(a, b, MOD2)\n c3 = convolution(a, b, MOD3)\n \n var c = newSeq[int](n + m - 1)\n for i in 0..= m and chmin(result[1], sz[u]): result[0] = u; result[1] = sz[u] var (c, _) = find_centroid(x, -1) var f = newSeq[seq[int]]() var getas = newSeq[int]() for v in g[c]: if removed[v]: continue proc calc_geta(u, par, x: int): int = result = x for v in g[u]: if v == par or removed[v]: continue result.min = calc_geta(v, u, x + s[v]) var geta = max(0, -calc_geta(v, c, s[v])) f.add(newSeqWith(geta+sz[v]+1, 0)) getas.add(geta) proc calc_f(u, par, x: int) = f[^1][x+geta] += 1 for v in g[u]: if v == par or removed[v]: continue calc_f(v, u, x + s[v]) calc_f(v, c, s[v]) for i in 0.. 0: getas.max else: 0) debug(sz[x], gmax) var total = newSeqWith(gmax+sz[x], 0) for i in 0..