結果
| 問題 |
No.3095 Many Min Problems
|
| ユーザー |
👑  seekworser
|
| 提出日時 | 2025-04-06 17:26:56 |
| 言語 | Nim (2.2.0) |
| 結果 |
AC
|
| 実行時間 | 1,025 ms / 2,000 ms |
| コード長 | 60,869 bytes |
| コンパイル時間 | 8,061 ms |
| コンパイル使用メモリ | 138,744 KB |
| 実行使用メモリ | 45,376 KB |
| 最終ジャッジ日時 | 2025-04-06 17:27:21 |
| 合計ジャッジ時間 | 22,857 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 30 |
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 = 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..<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/zer0-star/Nim-ACL/tree/master/src/atcoder/extra/math/formal_power_series.nim
ImportExpand "atcoder/extra/math/formal_power_series" <=== "when not declared ATCODER_FORMAL_POWER_SERIES:\n const ATCODER_FORMAL_POWER_SERIES* = 1\n \n import std/sequtils\n import std/strformat\n import std/options\n import std/macros\n import std/tables\n import std/algorithm\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 FormalPowerSeries*[T:FieldElem] = seq[T]\n type Poly*[T:FieldElem] = FormalPowerSeries[T]\n type FPS*[T:FieldElem] = FormalPowerSeries[T]\n\n proc `$`*(f:seq): string {.inline.} =\n var s:seq[int]\n for i in f.len:\n s.add $(f[i]) & \" x^\" & i\n return s.join(\"+\")\n\n\n template hasFFT*(T:typedesc):bool =\n mixin fft\n type hasFFTC = concept x\n @[x].fft()\n T is hasFFTC\n\n template initFormalPowerSeries*[T:FieldElem](n:int):FormalPowerSeries[T] =\n block:\n FormalPowerSeries[T](newSeq[T](n))\n template initFormalPowerSeries*[T:FieldElem;U: not T](data:openArray[U]):FormalPowerSeries[T] =\n block:\n var result = newSeq[T](data.len)\n for i, it in data:\n result[i] = T(it)\n FormalPowerSeries[T](result)\n template initFormalPowerSeries*[T:FieldElem](data:openArray[T]):FormalPowerSeries[T] =\n block:\n data\n\n template init*[T:FieldElem](self:typedesc[FormalPowerSeries[T]], data:typed):auto =\n initFormalPowerSeries[T](data)\n\n # {{{ sparseFormalPowerSeries\n\n type SparseFormalPowerSeries*[T:FieldElem] = seq[tuple[d:int, c:T]] # sorted ascending order\n\n# converter toSparseFormalPowerSeries*[XI, T](a:array[XI, (int, T)]):SparseFormalPowerSeries[T] = a.toSeq()\n\n # SparseMonomial {{{\n type Monomial*[T] = object\n c:T\n d:int\n \n proc initVar*[T](c = 1, d = 1):SparseFormalPowerSeries[T] = @[(d:d, c:T(c))]\n \n proc `^`*[T](f:SparseFormalPowerSeries[T], n:int):SparseFormalPowerSeries[T] =\n assert f.len == 1\n result.add(f[0])\n result[0].d *= n\n if f[0].c != T.init(1): result[0].c = result[0].c ^ n\n \n# converter toSFPS*[T](f:Monomial[T]):SparseFormalPowerSeries[T] = @[(f.d,f.c)]\n\n# proc `+`*[T](f, g: Monomial[T]):SparseFormalPowerSeries[T] =\n# return toSFPS(f) + toSFPS(g)\n\n # }}}\n\n converter toSFPS*[T](f:Table[int, T]):SparseFormalPowerSeries[T] =\n for d, c in f:\n result.add((d, c))\n result.sort do (x, y:(int, T)) -> int:\n cmp(x[0], y[0])\n\n# converter toSFPS*[T](a:T):SparseFormalPowerSeries[T] = @[(0, a)]\n proc deg*[T](a:SparseFormalPowerSeries[T]):int =\n if a.len == 0: return int.low\n else: return a[^1].d\n proc `+=`*[T](a:var SparseFormalPowerSeries[T], b:SparseFormalPowerSeries[T]) =\n var r:SparseFormalPowerSeries[T]\n var i, j = 0\n while i < a.len or j < b.len:\n if i < a.len and j < b.len and a[i].d == b[j].d:\n r.add((a[i].d, a[i].c + b[j].c))\n i.inc;j.inc\n else:\n if j == b.len or (i < a.len and a[i].d < b[j].d):\n r.add(a[i]);i.inc\n else:\n r.add(b[j]);j.inc\n swap(r, a)\n proc `+=`*[T](a:var SparseFormalPowerSeries[T], b:T) = a += @[(0, b)]\n proc `+=`*[T](a:var FormalPowerSeries[T], b:SparseFormalPowerSeries[T]) =\n for p in b:\n while a.len <= p.d: a.add(T.init(0))\n a[p.d] += p.c\n proc `-=`*[T](a:var SparseFormalPowerSeries[T], b:SparseFormalPowerSeries[T]) =\n var r:SparseFormalPowerSeries[T]\n var i, j = 0\n while i < a.len or j < b.len:\n if i < a.len and j < b.len and a[i].d == b[j].d:\n r.add((a[i].d, a[i].c - b[j].c))\n i.inc;j.inc\n else:\n if j == b.len or (i < a.len and a[i].d < b[j].d):\n r.add(a[i]);i.inc\n else:\n r.add((b[j].d, -b[j].c));j.inc\n swap(r, a)\n proc `-=`*[T](a:var SparseFormalPowerSeries[T], b:T) = a -= @[(0, b)]\n proc `-=`*[T](a:var FormalPowerSeries[T], b:SparseFormalPowerSeries[T]) =\n for p in b:\n while a.len <= p.d: a.add(T.init(0))\n a[p.d] -= p.c\n\n proc `*`*[T](a:FormalPowerSeries[T], b:SparseFormalPowerSeries[T], deg = -1):FormalPowerSeries[T] =\n var deg = deg\n if deg == -1:\n let bdeg = b[^1][0]\n deg = a.len + bdeg\n result = initFormalPowerSeries[T](deg)\n for i in 0..<a.len:\n for (j, c) in b:\n let k = i + j\n if k < deg: result[k] += a[i] * c\n proc `*=`*[T](a:var SparseFormalPowerSeries[T], b:SparseFormalPowerSeries[T], deg = -1) =\n var r = initTable[int,T]()\n for (i, c0) in a:\n for (j, c1) in b:\n let k = i + j\n if deg != -1 and k >= deg: continue\n if k notin r: r[k] = T.init(0)\n r[k] += c0 * c1\n var rs = SparseFormalPowerSeries[T](r)\n swap(rs, a)\n proc `*=`*[T](a:var SparseFormalPowerSeries[T], b:T) =\n for (i, c) in a.mitems:\n c = c * b\n proc `*`*[T](a:SparseFormalPowerSeries[T], b:T):SparseFormalPowerSeries[T] =\n result = a\n result *= b\n proc `*`*[T](b:T, a:var SparseFormalPowerSeries[T]):SparseFormalPowerSeries[T] =\n result = a\n for (i, c) in result.mitems:\n c = b * c\n\n macro declareSparseFormalPowerSeriesOperators(op) =\n fmt\"\"\"proc `{op}`*[T](self:SparseFormalPowerSeries[T];r:SparseFormalPowerSeries[T] or T):SparseFormalPowerSeries[T] = result = self;result {op}= r\nproc `{op}`*[T](self: not SparseFormalPowerSeries and not Monomial, r:SparseFormalPowerSeries[T]):SparseFormalPowerSeries[T] = result = @[(0, T(self))];result {op}= r\"\"\".parsestmt\n\n declareSparseFormalPowerSeriesOperators(`+`)\n declareSparseFormalPowerSeriesOperators(`-`)\n declareSparseFormalPowerSeriesOperators(`*`)\n\n proc divMod*[T](a: FormalPowerSeries[T], b:SparseFormalPowerSeries[T]):(FormalPowerSeries[T], FormalPowerSeries[T]) =\n mixin inv\n var a = a\n let\n max_deg = b[^1][0]\n inv_max_coef = b[^1][1].inv\n var q = initFormalPowerSeries[T](a.len - max_deg)\n for i in countdown(q.len - 1, 0):\n q[i] = a[i + max_deg] * inv_max_coef\n for (d, v) in b:\n a[i + d] -= q[i] * v\n return (q, a[0..<max_deg])\n proc `div`*[T:FieldElem](a: FormalPowerSeries[T], b:SparseFormalPowerSeries[T]):auto = a.divMod(b)[0]\n proc `mod`*[T:FieldElem](a: FormalPowerSeries[T], b:SparseFormalPowerSeries[T]):auto = a.divMod(b)[1]\n\n proc EQUAL*[T](a, b:T):bool =\n when T is hasInf:\n return (abs(a - b) < T(0.0000001))\n else:\n return a == b\n\n macro revise*(a, b) =\n parseStmt(fmt\"\"\"let {a.repr} = if {a.repr} == -1: {b.repr} else: {a.repr}\"\"\")\n proc shrink*[T](self: var FormalPowerSeries[T]) =\n while self.len > 0 and EQUAL(self[^1], T(0)): discard self.pop()\n proc resize*[T](self: var FormalPowerSeries[T], n:int) =\n mixin setLen\n let l = self.len\n self.setLen(n)\n if l < n:\n self.fill(l, n - 1, T(0))\n\n converter toFPS*[T](f:Monomial[T]):FormalPowerSeries[T] =\n result = newSeq[T](f.d + 1)\n result[f.d] = f.c\n converter toFPS*[T](f:SparseFormalPowerSeries[T]):FormalPowerSeries[T] =\n let d = f.deg\n if d < 0: return\n result.resize(d + 1)\n result.fill(T(0))\n for p in f: result[p.d] += p.c\n\n# proc `+`*[T](f, g: Monomial[T]):FormalPowerSeries[T] =\n# return toFPS(f) + toFPS(g)\n \n proc `*`*[T](f, g:Monomial[T]):Monomial[T] =\n result.c = f.c * g.c\n result.d = f.d + g.d\n proc `*`*[T](a:T, f:Monomial[T]):Monomial[T] =\n result = f\n result.c *= a\n proc `*`*[T](a:SomeInteger, f:Monomial[T]):Monomial[T] =\n result = f\n result.c *= T.init(a)\n\n # operators +=, -=, *=, mod=, -, /= {{{\n proc `+=`*[T](self: var FormalPowerSeries[T], r:FormalPowerSeries[T]) =\n if r.len > self.len: self.setlen(r.len)\n for i in 0..<r.len: self[i] += r[i]\n proc `+=`*[T](self: var FormalPowerSeries[T], r:T) =\n if self.len == 0: self.setlen(1)\n self[0] += r\n \n proc `-=`*[T](self: var FormalPowerSeries[T], r:FormalPowerSeries[T]) =\n if r.len > self.len: self.setlen(r.len)\n for i in 0..<r.len: self[i] -= r[i]\n# self.shrink()\n proc `-=`*[T](self: var FormalPowerSeries[T], r:T) =\n if self.len == 0: self.setlen(1)\n self[0] -= r\n# self.shrink()\n\n proc `*=`*[T](self: var FormalPowerSeries[T], v:T) = self.applyIt(it * v)\n\n proc mult_naive*[T](a, b:FormalPowerSeries[T]):FormalPowerSeries[T] =\n result = initFormalPowerSeries[T](a.len + b.len - 1)\n for i in 0..<a.len:\n for j in 0..<b.len:\n result[i + j] += a[i] * b[j]\n proc div_naive*[T](a, b:FormalPowerSeries[T], deg = -1):FormalPowerSeries[T] =\n mixin inv\n var deg = if deg == -1: a.len else: deg\n result = newSeq[T](deg)\n # a = b * result\n var b0inv = b[0].inv\n for i in 0 ..< deg:\n var u = a[i]\n for j in 1 ..< min(i + 1, b.len):\n u -= b[j] * result[i - j]\n u *= b0inv\n result[i] = u\n\n proc `*=`*[T](self: var FormalPowerSeries[T], r: FormalPowerSeries[T]) =\n if self.len == 0 or r.len == 0:\n self.setlen(0)\n else:\n when T.hasFFT:\n mixin multiply\n self = multiply(self, r)\n else:\n static:\n echo(\"Warning: multiply is slow, please write import atcoder/extra/math/ntt\")\n self = mult_naive(self, r)\n\n proc `mod=`*[T](self: var FormalPowerSeries[T], r:FormalPowerSeries[T]) =\n self -= (self div r) * r\n self.resize(r.len - 1)\n self.shrink()\n #proc `divMod`*[T](self, r: FormalPowerSeries[T]):(FPS[T], FPS[T]) =\n # var self = self\n # let q = self div r\n # self -= q * r\n # self.resize(r.len - 1)\n # self.shrink()\n # return (q, self)\n\n proc `-`*[T](self: FormalPowerSeries[T]):FormalPowerSeries[T] =\n var ret = self\n ret.applyIt(-it)\n return ret\n proc `/=`*[T](self: var FormalPowerSeries[T], v:T) = self.applyIt(it / v)\n #}}}\n\n proc rev*[T](self: FormalPowerSeries[T], deg = -1):auto =\n result = self\n if deg != -1: result.setlen(deg)\n result.reverse\n \n proc pre*[T](self: FormalPowerSeries[T], sz:int):auto =\n result = self\n result.setlen(min(self.len, sz))\n \n proc `shr`*[T](self: FormalPowerSeries[T], sz:int):auto =\n if self.len <= sz: return initFormalPowerSeries[T](0)\n result = self\n if sz >= 1: result.delete(0, sz - 1)\n proc `shl`*[T](self: FormalPowerSeries[T], sz:int):auto =\n result = initFormalPowerSeries[T](sz)\n result = result & self\n \n proc diff*[T](self: FormalPowerSeries[T]):auto =\n let n = self.len\n result = initFormalPowerSeries[T](max(0, n - 1))\n for i in 1..<n:\n result[i - 1] = self[i] * T(i)\n \n proc integral*[T](self: FormalPowerSeries[T]):auto =\n let n = self.len\n result = initFormalPowerSeries[T](n + 1)\n result[0] = T(0)\n for i in 0..<n: result[i + 1] = self[i] / T(i + 1)\n # F(0) must not be 0\n proc inv*[T](self: FormalPowerSeries[T], deg = -1):auto =\n assert(not EQUAL(self[0], T(0)))\n deg.revise(self.len)\n# type F = T.get_fft_type()\n# when T is ModInt:\n when true:\n proc invFast[T](self: FormalPowerSeries[T]):auto =\n# assert(self[0] != T(0))\n let n = self.len\n var res = initFormalPowerSeries[T](1)\n res[0] = T(1) / self[0]\n var d = 1\n while d < n:\n var f, g = initFormalPowerSeries[T](2 * d)\n for j in 0..<min(n, 2 * d): f[j] = self[j]\n for j in 0..<d: g[j] = res[j]\n let g1 = fft(g)\n f = ifft(dot(fft(f), g1, T), T)\n for j in 0..<d:\n f[j] = T(0)\n f[j + d] = -f[j + d]\n f = ifft(dot(fft(f), g1, T), T)\n f[0..<d] = res[0..<d]\n res = f\n d = d shl 1\n return res.pre(n)\n var ret = self\n ret.setlen(deg)\n return ret.invFast()\n else:\n var ret = initFormalPowerSeries[T](1)\n ret[0] = T(1) / self[0]\n var i = 1\n while i < deg:\n ret = (ret + ret - ret * ret * self.pre(i shl 1)).pre(i shl 1)\n i = i shl 1\n return ret.pre(deg)\n proc `/=`*[T](self: var FormalPowerSeries[T], r: FormalPowerSeries[T]) =\n when T.hasFFT():\n self *= r.inv()\n else:\n static:\n echo(\"Warning: div is slow, please write import atcoder/extra/math/ntt\")\n self = self.divNaive(r)\n\n proc `div=`*[T](self: var FormalPowerSeries[T], r: FormalPowerSeries[T]) =\n if self.len < r.len:\n self.resize(0)\n else:\n let n = self.len - r.len + 1\n self = (self.rev().pre(n) * r.rev().inv(n)).pre(n).rev(n)\n\n# operators +, -, *, div, mod {{{\n macro declareFormalPowerSeriesOperators(op, op_eq) =\n result = quote do:\n proc `op`*[T](self:FormalPowerSeries[T];r:FormalPowerSeries[T] or T):FormalPowerSeries[T] = result = self;`op_eq`(result, r)\n proc `op`*[T](self: not FormalPowerSeries and not Monomial, r:FormalPowerSeries[T]):FormalPowerSeries[T] = result = initFormalPowerSeries[T](@[T(self)]);`op_eq`(result, r)\n\n declareFormalPowerSeriesOperators(`+`, `+=`)\n declareFormalPowerSeriesOperators(`-`, `-=`)\n declareFormalPowerSeriesOperators(`*`, `*=`)\n declareFormalPowerSeriesOperators(`/`, `/=`)\n \n proc `div`*[T](self, r:FormalPowerSeries[T]):FormalPowerSeries[T] = result = self;result.`div=` (r)\n proc `mod`*[T](self, r:FormalPowerSeries[T]):FormalPowerSeries[T] = result = self;result.`mod=` (r)\n # }}}\n \n # F(0) must be 1\n proc log*[T](self:FormalPowerSeries[T], deg = -1):auto =\n assert EQUAL(self[0], T(1))\n deg.revise(self.len)\n return (self.diff() * self.inv(deg)).pre(deg - 1).integral()\n\n proc expFast[T:FieldElem](self: FormalPowerSeries[T], deg:int):auto =\n deg.revise(self.len)\n assert EQUAL(self[0], T(0))\n\n var inv = newSeqOfCap[T](deg + 1)\n inv.add(T(0))\n inv.add(T(1))\n\n proc inplace_integral(F:var FormalPowerSeries[T]) =\n let\n n = F.len\n when T is FiniteFieldElem:\n let\n M = T.mod\n while inv.len <= n:\n let i = inv.len\n when T is FiniteFieldElem:\n inv.add((-inv[M mod i]) * (M div i))\n else:\n inv.add(T(1)/T(i))\n F = @[T(0)] & F\n for i in 1..n: F[i] *= inv[i]\n\n proc inplace_diff(F:var FormalPowerSeries[T]):auto =\n if F.len == 0: return\n F = F[1..<F.len]\n var coeff = T(1)\n let one = T(1)\n for i in 0..<F.len:\n F[i] *= coeff\n coeff += one\n mixin fft, ifft, dot\n type FFTType = fft(initFormalPowerSeries[T](0)).type\n mixin inplace_partial_dot\n var\n b = @[T(1), if 1 < self.len: self[1] else: T(0)]\n c = @[T(1)]\n z1f:FFTType\n z2 = @[T(1), T(0)]\n z2f = z2.fft\n var m = 2\n while m < deg:\n var y = b\n y.resize(2 * m)\n var yf = y.fft\n z1f = z2f\n var zf = yf\n zf.setLen(m)\n inplace_partial_dot(zf, z1f, 0..<m, T)\n var z = zf.ifft(T)\n for i in 0..<m div 2: z[i] = T(0)\n zf = z.fft\n z = ifft(dot(zf, z1f, T), T)\n for i in 0..<m:z[i] *= -1\n c = c & z[m div 2..^1]\n z2 = c\n z2.resize(2 * m)\n z2f = z2.fft\n var x = self[0..<min(self.len, m)]\n inplace_diff(x)\n x.add(T(0))\n var xf = x.fft\n inplace_partial_dot(xf, yf, 0..<m, T)\n x = xf.ifft(T)\n x -= b.diff()\n x.resize(2 * m)\n for i in 0..<m - 1: x[m + i] = x[i]; x[i] = T(0)\n xf = x.fft\n inplace_partial_dot(xf, z2f, 0..<2*m, T)\n x = xf.ifft(T)\n discard x.pop()\n inplace_integral(x)\n for i in m..<min(self.len, 2 * m): x[i] += self[i]\n for i in 0..<m: x[i] = T(0)\n xf = x.fft\n inplace_partial_dot(xf, yf, 0..<2*m, T)\n x = xf.ifft(T)\n b = b & x[m..^1]\n m *= 2\n return b[0..<deg]\n\n# F(0) must be 0\n proc exp*[T](self: FormalPowerSeries[T], deg = -1):auto =\n assert EQUAL(self[0], T(0))\n deg.revise(self.len)\n\n when T is FiniteFieldElem:\n var self = self\n self.resize(deg)\n return self.expFast(deg)\n else:\n var\n ret = initFormalPowerSeries[T](@[T(1)])\n i = 1\n while i < deg:\n ret = (ret * (self.pre(i shl 1) + T(1) - ret.log(i shl 1))).pre(i shl 1)\n i = i shl 1\n return ret.pre(deg)\n\n proc pow*[T:FieldElem](self: FormalPowerSeries[T], k:int, deg = -1):FormalPowerSeries[T] =\n mixin pow, init\n var self = self\n deg.revise(self.len)\n self.resize(deg)\n for i in 0..<deg:\n if not EQUAL(self[i], T(0)):\n let rev = T(1) / self[i]\n result = (((self * rev) shr i).log(deg) * T.init(k)).exp() * (self[i].pow(k))\n if i * k > deg: return initFormalPowerSeries[T](deg)\n result = (result shl (i * k)).pre(deg)\n if result.len < deg: result.setlen(deg)\n return\n return self\n\n proc eval*[T](self: FormalPowerSeries[T], x:T):T =\n var\n (r, w) = (T(0), T(1))\n for v in self:\n r += w * v\n w *= x\n return r\n\n {.push experimental: \"callOperator\".}\n template `()`*[T](self: FormalPowerSeries[T], x:T):T = self.eval(x)\n {.pop.}\n\n proc powMod*[T](self: FormalPowerSeries[T], n:int, M:FormalPowerSeries[T]):auto =\n assert not EQUAL(M[^1], T(0))\n let modinv = M.rev().inv()\n proc getDiv(base:FormalPowerSeries[T]):FormalPowerSeries[T] =\n var base = base\n if base.len < M.len:\n base.setlen(0)\n return base\n let n = base.len - M.len + 1\n return (base.rev().pre(n) * modinv.pre(n)).pre(n).rev(n)\n var\n n = n\n x = self\n result = initFormalPowerSeries[T](M.len - 1)\n result[0] = T(1)\n while n > 0:\n if (n and 1) > 0:\n result *= x\n result -= getDiv(result) * M\n result = result.pre(M.len - 1)\n x *= x\n x -= getDiv(x) * M\n x = x.pre(M.len - 1)\n n = n shr 1\n proc gcdImpl*[T](a, b:FormalPowerSeries[T]):FormalPowerSeries[T] =\n if a.len < b.len: return gcdImpl(b, a)\n if b.len == 0: return a\n let r = a mod b\n #echo a.len, \" \", b.len, \" \", r.len\n return gcdImpl(b, r)\n proc gcd*[T](a, b:FormalPowerSeries[T]):FormalPowerSeries[T] =\n var (a, b) = (a, b)\n a.shrink\n b.shrink\n return gcdImpl(a, b)\n\n\n\n"
# source: https://github.com/zer0-star/Nim-ACL/tree/master/src/atcoder/extra/math/ntt.nim
ImportExpand "atcoder/extra/math/ntt" <=== "when not declared ATCODER_NTT_HPP:\n const ATCODER_NTT_HPP* = 1\n when not declared ATCODER_PARTICULAR_MOD_CONVOLUTION:\n const ATCODER_PARTICULAR_MOD_CONVOLUTION* = 1\n when not declared ATCODER_CONVOLUTION_HPP:\n when not declared ATCODER_CONVOLUTION_HPP:\n const ATCODER_CONVOLUTION_HPP* = 1\n \n import std/math\n import std/sequtils\n import std/sugar\n when not declared ATCODER_INTERNAL_MATH_HPP:\n const ATCODER_INTERNAL_MATH_HPP* = 1\n import std/math\n \n # Fast moduler by barrett reduction\n # Reference: https:#en.wikipedia.org/wiki/Barrett_reduction\n # NOTE: reconsider after Ice Lake\n type Barrett* = object\n m*, im*:uint\n \n # @param m `1 <= m`\n proc initBarrett*(m:uint):auto = Barrett(m:m, im:cast[uint](-1) div m + 1)\n \n # @return m\n proc umod*(self: Barrett):uint =\n self.m\n \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)(((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..<cnt:\n if pow_mod_constexpr(g, (m - 1) div divs[i], m) == 1:\n ok = false\n break\n if ok: return g\n g.inc\n proc primitive_root*[m:static[int]]():auto =\n primitive_root_constexpr(m)\n \n # @param n `n < 2^32`\n # @param m `1 <= m < 2^32`\n # @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)\n proc floor_sum_unsigned*(n, m, a, b:uint):uint =\n result = 0\n var (n, m, a, b) = (n, m, a, b)\n while true:\n if a >= 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 <intrin.h>\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 \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..<p:\n let l = a[i + offset]\n let r = a[i + offset + p] * rot\n a[i + offset] = l + r\n a[i + offset + p] = l - r\n if s + 1 != (1 shl len):\n rot *= info.rate2[bsf(not s.uint)]\n len.inc\n else:\n # 4-base\n let p = 1 shl (h - len - 2)\n var\n rot = mint.init(1)\n imag = info.root[2]\n for s in 0..<(1 shl len):\n let\n rot2 = rot * rot\n rot3 = rot2 * rot\n offset = s shl (h - len)\n for i in 0..<p:\n let\n mod2 = (mint.mod() * mint.mod()).uint\n a0 = (a[i + offset].val()).uint\n a1 = (a[i + offset + p].val() * rot.val()).uint\n a2 = (a[i + offset + 2 * p].val() * rot2.val()).uint\n a3 = (a[i + offset + 3 * p].val() * rot3.val()).uint\n a1na3imag = (mint.init(a1 + mod2 - a3).val() * imag.val()).uint\n na2 = mod2 - a2\n a[i + offset] = mint.init(a0 + a2 + a1 + a3)\n a[i + offset + 1 * p] = mint.init(a0 + a2 + (2.uint * mod2 - (a1 + a3)))\n a[i + offset + 2 * p] = mint.init(a0 + na2 + a1na3imag)\n a[i + offset + 3 * p] = mint.init(a0 + na2 + (mod2 - a1na3imag))\n if s + 1 != (1 shl len):\n rot *= info.rate3[bsf(not s.uint)]\n len += 2\n \n proc butterfly_inv*[mint:FiniteFieldElem](a:var seq[mint]) =\n let n = a.len\n let h = ceilpow2(n)\n mixin init\n \n const info = initFFTInfo[mint]()\n \n var len = h; # a[i, i+(n>>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..<p:\n let\n l = a[i + offset]\n r = a[i + offset + p]\n a[i + offset] = l + r\n a[i + offset + p] = mint.init((mint.mod() + l.val() - r.val()) * irot.val())\n if s + 1 != (1 shl (len - 1)):\n irot *= info.irate2[bsf(not s.uint)]\n len.dec\n else:\n # 4-base\n let p = 1 shl (h - len);\n var irot = mint.init(1)\n let iimag = info.iroot[2]\n for s in 0..<(1 shl (len - 2)):\n let\n irot2 = irot * irot\n irot3 = irot2 * irot\n offset = s shl (h - len + 2)\n for i in 0..<p:\n let\n a0 = a[i + offset + 0 * p].val().uint\n a1 = a[i + offset + 1 * p].val().uint\n a2 = a[i + offset + 2 * p].val().uint\n a3 = a[i + offset + 3 * p].val().uint\n a2na3iimag = mint.init((mint.mod.uint + a2 - a3) * iimag.val().uint).val().uint\n \n a[i + offset] = mint.init(a0 + a1 + a2 + a3)\n a[i + offset + 1 * p] = mint.init((a0 + (mint.mod().uint - a1) + a2na3iimag) * irot.val().uint)\n a[i + offset + 2 * p] = mint.init((a0 + a1 + (mint.mod().uint - a2) + (mint.mod().uint - a3)) * irot2.val().uint)\n a[i + offset + 3 * p] = mint.init((a0 + (mint.mod().uint - a1) + (mint.mod().uint - a2na3iimag)) * irot3.val().uint)\n if s + 1 != (1 shl (len - 2)):\n irot *= info.irate3[bsf(not s.uint)]\n len -= 2\n \n proc convolution_naive*[mint:FiniteFieldElem](a, b:seq[mint]):seq[mint] =\n mixin `+=`\n let (n, m) = (a.len, b.len)\n result = newSeq[mint](n + m - 1)\n if n < m:\n for j in 0..<m:\n for i in 0..<n:\n result[i + j] += a[i] * b[j]\n else:\n for i in 0..<n:\n for j in 0..<m:\n result[i + j] += a[i] * b[j]\n \n proc convolution_fft*[mint:FiniteFieldElem](a, b:seq[mint]):seq[mint] =\n mixin init, inv\n let\n (n, m) = (a.len, b.len)\n z = 1 shl ceil_pow2(n + m - 1)\n var (a, b) = (a, b)\n a.setLen(z)\n butterfly(a)\n b.setLen(z)\n butterfly(b)\n for i in 0..<z:\n a[i] *= b[i];\n butterfly_inv(a)\n a.setLen(n + m - 1)\n let iz = mint.init(z).inv()\n for i in 0..<n + m - 1: a[i] *= iz\n return a\n \n proc convolution*[mint:FiniteFieldElem](a, b:seq[mint]):seq[mint] =\n let (n, m) = (a.len, b.len)\n if n == 0 or m == 0: return\n if min(n, m) <= 60: return convolution_naive(a, b)\n return convolution_fft(a, b)\n \n when not declared ATCODER_MODINT_HPP:\n const ATCODER_MODINT_HPP* = 1\n import std/macros\n when not declared ATCODER_GENERATE_DEFINITIONS_NIM:\n const ATCODER_GENERATE_DEFINITIONS_NIM* = 1\n import std/macros\n \n type hasInv* = concept x\n x.inv()\n \n template generateDefinitions*(name, l, r, typeObj, typeBase, body: untyped): untyped {.dirty.} =\n proc name*(l, r: typeObj): auto {.inline.} =\n type T = l.type\n body\n proc name*(l: typeBase; r: typeObj): auto {.inline.} =\n type T = r.type\n body\n proc name*(l: typeObj; r: typeBase): auto {.inline.} =\n type T = l.type\n body\n \n template generatePow*(name) {.dirty.} =\n proc pow*(m: name; p: SomeInteger): name {.inline.} =\n when name is hasInv:\n if p < 0: return pow(m.inv(), -p)\n else:\n doAssert p >= 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..<n + m - 1:\n var x = 0.uint\n x += (c1[i].uint * i1) mod MOD1 * M2M3\n x += (c2[i].uint * i2) mod MOD2 * M1M3\n x += (c3[i].uint * i3) mod MOD3 * M1M2\n # B = 2^63, -B <= x, r(real value) < B\n # (x, x - M, x - 2M, or x - 3M) = r (mod 2B)\n # r = c1[i] (mod MOD1)\n # focus on MOD1\n # r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)\n # r = x,\n # x - M' + (0 or 2B),\n # x - 2M' + (0, 2B or 4B),\n # x - 3M' + (0, 2B, 4B or 6B) (without mod!)\n # (r - x) = 0, (0)\n # - M' + (0 or 2B), (1)\n # -2M' + (0 or 2B or 4B), (2)\n # -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)\n # we checked that\n # ((1) mod MOD1) mod 5 = 2\n # ((2) mod MOD1) mod 5 = 3\n # ((3) mod MOD1) mod 5 = 4\n # var diff = c1[i] - floorMod(x.int, MOD1.int)\n var diff = c1[i] - floorMod(cast[int](x), MOD1.int)\n if diff < 0: diff += MOD1.int\n const offset = [0'u, 0'u, M1M2M3, 2'u * M1M2M3, 3'u * M1M2M3]\n x -= offset[diff mod 5]\n c[i] = cast[int](x)\n return c\n \n discard\n import std/sequtils\n type ParticularModConvolution* = object\n discard\n #type ParticularModFFTType*[T:FiniteFieldElem] = seq[T]\n proc fft*[T:FiniteFieldElem](t:typedesc[ParticularModConvolution], a:seq[T]):seq[T] {.inline.} =\n result = a\n butterfly(result)\n proc inplace_fft*[T:FiniteFieldElem](t:typedesc[ParticularModConvolution], a:var seq[T]) {.inline.} =\n butterfly(a)\n proc inplace_partial_dot*[T](t:typedesc[ParticularModConvolution], a:var seq[T], b:seq[T], p:Slice[int]) =\n for i in p:\n a[i] *= b[i]\n proc dot*[T](t:typedesc[ParticularModConvolution], a, b:seq[T]):seq[T] =\n result = a\n inplace_partial_dot(t, result, b, 0..<a.len)\n \n proc ifft*[T](t:typedesc[ParticularModConvolution], a:seq[T]):seq[T] {.inline.} =\n mixin init, inv\n result = a\n result.butterfly_inv\n let iz = T.init(a.len).inv()\n result.applyIt(it * iz)\n proc inplace_ifft*[T](t:typedesc[ParticularModConvolution], a:var seq[T]) {.inline.} =\n mixin init, inv\n a.butterfly_inv\n let iz = T.init(a.len).inv()\n a.applyIt(it * iz)\n \n proc convolution*[T:FiniteFieldElem](t:typedesc[ParticularModConvolution], a, b:seq[T]):auto {.inline.} = convolution(a, b)\n proc ntt_doubling*[T](t:typedesc[ParticularModConvolution], a:var seq[T]) =\n let M = a.len\n var b = a\n const fftInfo = initFFTInfo[T]()\n t.inplace_ifft(b)\n var\n r:T = 1\n zeta:T = T(fftInfo.g).pow((T.getMod() - 1) div (M shl 1))\n for i in 0 ..< M:\n b[i] *= r\n r *= zeta\n t.inplace_fft(b)\n a = a & b\n \n when not declared ATCODER_ARBITRARY_MOD_CONVOLUTION:\n const ATCODER_ARBITRARY_MOD_CONVOLUTION* = 1\n when not declared ATCODER_CONVOLUTION_HPP:\n discard\n import std/sequtils\n \n type ArbitraryModConvolution* = object\n discard\n \n const\n m0 = 167772161.uint\n m1 = 469762049.uint\n m2 = 754974721.uint\n type\n mint0 = StaticModInt[m0.int]\n mint1 = StaticModInt[m1.int]\n mint2 = StaticModint[m2.int]\n type ArbitraryModFFTElem* = (mint0, mint1, mint2)\n proc setLen*(v:var (seq[mint0], seq[mint1], seq[mint2]), n:int) =\n v[0].setLen(n)\n v[1].setLen(n)\n v[2].setLen(n)\n \n proc `*=`(a:var ArbitraryModFFTElem, b:ArbitraryModFFTElem) =\n a[0] *= b[0];a[1] *= b[1];a[2] *= b[2]\n proc `-`(a:ArbitraryModFFTElem):auto = (-a[0], -a[1], -a[2])\n \n const\n r01 = mint1.init(m0).inv().val().uint\n r02 = mint2.init(m0).inv().val().uint\n r12 = mint2.init(m1).inv().val().uint\n r02r12 = r02 * r12 mod m2\n \n proc fft*[T:ModInt](t:typedesc[ArbitraryModConvolution], a:seq[T]):auto {.inline.} =\n type F = ParticularModConvolution\n var\n v0 = newSeq[mint0](a.len)\n v1 = newSeq[mint1](a.len)\n v2 = newSeq[mint2](a.len)\n for i in 0..<a.len:\n v0[i] = mint0.init(a[i].val())\n v1[i] = mint1.init(a[i].val())\n v2[i] = mint2.init(a[i].val())\n v0 = F.fft(v0)\n v1 = F.fft(v1)\n v2 = F.fft(v2)\n return (v0,v1,v2)\n proc inplace_partial_dot*(t:typedesc[ArbitraryModConvolution], a:var (seq[mint0], seq[mint1], seq[mint2]), b:(seq[mint0], seq[mint1], seq[mint2]), p:Slice[int]):auto =\n for i in p:\n a[0][i] *= b[0][i]\n a[1][i] *= b[1][i]\n a[2][i] *= b[2][i]\n proc dot*(t:typedesc[ArbitraryModConvolution], a, b:(seq[mint0], seq[mint1], seq[mint2])):auto =\n result = a\n t.inplace_partial_dot(result, b, 0..<a[0].len)\n \n proc calc_garner[T:ModInt](a0:seq[mint0], a1:seq[mint1], a2:seq[mint2], deg:int):seq[T] =\n let\n w1 = m0 mod T.umod\n w2 = w1 * m1 mod T.umod\n result = newSeq[T](deg)\n for i in 0..<deg:\n let\n (n0, n1, n2) = (a0[i].val().uint, a1[i].val().uint, a2[i].val().uint)\n b = (n1 + m1 - n0) * r01 mod m1\n c = ((n2 + m2 - n0) * r02r12 + (m2 - b) * r12) mod m2\n result[i] = T.init(n0 + b * w1 + c * w2)\n \n proc ifft*[T:ModInt](t:typedesc[ArbitraryModConvolution], a:(seq[mint0], seq[mint1], seq[mint2]), deg = -1):auto {.inline.} =\n type F = ParticularModConvolution\n let\n deg = if deg == -1: a[0].len else: deg\n a0 = F.ifft(a[0])\n a1 = F.ifft(a[1])\n a2 = F.ifft(a[2])\n return calc_garner[T](a0, a1, a2, deg)\n proc convolution*[T:ModInt](t:typedesc[ArbitraryModConvolution], a, b:seq[T]):seq[T] {.inline.} =\n proc f0(x:T):mint0 = mint0.init(x.val())\n proc f1(x:T):mint1 = mint1.init(x.val())\n proc f2(x:T):mint2 = mint2.init(x.val())\n let\n c0 = convolution(a.map(f0), b.map(f0))\n c1 = convolution(a.map(f1), b.map(f1))\n c2 = convolution(a.map(f2), b.map(f2))\n return calc_garner[T](c0, c1, c2, a.len + b.len - 1)\n \n import std/bitops\n\n template get_fft_type*[T:FiniteFieldElem](self: typedesc[T]):typedesc =\n when T.isStatic and countTrailingZeroBits(T.mod - 1) >= 20:\n ParticularModConvolution\n else:\n ArbitraryModConvolution\n proc fft*[T:FiniteFieldElem](a:seq[T]):auto =\n type fft_type = get_fft_type(T)\n fft(fft_type, a)\n proc ifft*(a:auto, T:typedesc[FiniteFieldElem]):auto =\n type fft_type = get_fft_type(T)\n ifft[T](fft_type, a)\n proc dot*(a, b:auto, T:typedesc[FiniteFieldElem]):auto =\n dot(get_fft_type(T), a, b)\n proc inplace_partial_dot*(a:var auto, b:auto, p:Slice[int], T:typedesc[FiniteFieldElem]) =\n inplace_partial_dot(get_fft_type(T), a, b, p)\n proc multiply*[T:FiniteFieldElem](a, b:seq[T]):seq[T] =\n convolution(get_fft_type(T), a, b)\n"
# {.checks: off.}
type mint = modint998244353
var n, m = input(int)
var q = newSeq[FormalPowerSeries[mint]]()
for i in 1..m:
q.add(initFormalPowerSeries[mint](@[mint(1), -mint(i)]))
while q.len > 1:
var qn = newSeq[FormalPowerSeries[mint]]()
for i in 0..<(q.len//2):
qn.add(q[i*2] * q[i*2+1])
if q.len % 2 == 1:
qn.add(q[^1])
swap(q, qn)
var f = -log(q[0], n+1)
debug($q[0])
debug($f)
var ans = mint(0)
for i in 1..n:
# var ans = f[i] * i
ans += f[i] * i * mint(m).pow(n-i)
# debug(ans.val)
print($ans)