結果
| 問題 | No.3651 K-th Sum of Divisors |
| コンテスト | |
| ユーザー |
 kemuniku
|
| 提出日時 | 2026-08-28 21:41:41 |
| 言語 | Nim (2.2.8) |
| 結果 |
AC
|
| 実行時間 | 131 ms / 2,000 ms |
| + 405µs | |
| コード長 | 43,620 bytes |
| 記録 | |
| コンパイル時間 | 5,740 ms |
| コンパイル使用メモリ | 103,168 KB |
| 実行使用メモリ | 22,400 KB |
| 最終ジャッジ日時 | 2026-08-28 21:41:58 |
| 合計ジャッジ時間 | 14,498 ms |
|
ジャッジサーバーID （参考情報） |
judge1_0 / judge3_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 55 |
ソースコード
import macros;macro ImportExpand(s:untyped):untyped = parseStmt($s[2])
# source: src/cplib/tmpl/sheep.nim
ImportExpand "cplib/tmpl/sheep" <=== "when not declared CPLIB_TMPL_SHEEP:\n const CPLIB_TMPL_SHEEP* = 1\n {.warning[UnusedImport]: off.}\n {.hint[XDeclaredButNotUsed]: off.}\n import algorithm\n import sequtils\n import tables\n import macros\n import math\n import sets\n import strutils\n import strformat\n import sugar\n import heapqueue\n import streams\n import deques\n import bitops\n import std/lenientops\n import options\n #入力系\n proc scanf(formatstr: cstring){.header: \"<stdio.h>\", varargs.}\n proc getchar(): char {.importc: \"getchar_unlocked\", header: \"<stdio.h>\", discardable.}\n proc ii(): int {.inline.} = scanf(\"%lld\\n\", addr result)\n proc lii(N: int): seq[int] {.inline.} = newSeqWith(N, ii())\n proc si(): string {.inline.} =\n result = \"\"\n var c: char\n while true:\n c = getchar()\n if c == ' ' or c == '\\n' or c == '\\255':\n break\n result &= c\n \n # 出力系\n # 1. 実際の処理を行う proc (openArray を受け取る)\n proc print_internal(prop: tuple[f: File, sepc: string, endc: string, flush: bool], args: openArray[string]) =\n for i in 0 ..< args.len:\n prop.f.write(args[i])\n if i != args.len - 1:\n prop.f.write(prop.sepc)\n else:\n prop.f.write(prop.endc)\n if prop.flush:\n prop.f.flushFile()\n\n # 2. ユーザーが呼び出すためのインターフェース (varargs を受け取る)\n proc print*(prop: tuple[f: File, sepc: string, endc: string, flush: bool], args: varargs[string, `$`]) =\n # varargs は内部では openArray として扱えるので、そのまま渡せる\n print_internal(prop, args)\n\n proc print*(args: varargs[string, `$`]) =\n # こちらも内部用の proc を呼ぶ\n print_internal((f: stdout, sepc: \" \", endc: \"\\n\", flush: false), args)\n macro getSymbolName(x: typed): string = x.toStrLit\n macro debug*(args: varargs[untyped]): untyped =\n when defined(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 #chmin,chmax\n template `max=`(x, y) =\n let yVal = y # yが計算式の場合に評価を1回にするため\n if x < yVal:\n x = yVal\n\n template `min=`(x, y) =\n let yVal = y\n if x > yVal:\n x = yVal\n proc chmin[T](x: var T, y: T):bool=\n if x > y:\n x = y\n return true\n return false\n proc chmax[T](x: var T, y: T):bool=\n if x < y:\n x = y\n return true\n return false\n #bit演算\n proc `%`*(x: int, y: int): 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: int, y: int): int{.inline.} =\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: var int, y: int): void = x = x%y\n proc `//=`(x: var int, y: int): void = x = x//y\n proc `**`(x: int, y: int): int = x^y\n proc `**=`(x: var int, y: int): void = x = x^y\n proc `^`(x: int, y: int): int = x xor y\n proc `|`(x: int, y: int): int = x or y\n proc `&`(x: int, y: int): int = x and y\n proc `>>`(x: int, y: int): int = x shr y\n proc `<<`(x: int, y: int): int = x shl y\n proc `~`(x: int): int = not x\n proc `^=`(x: var int, y: int): void = x = x ^ y\n proc `&=`(x: var int, y: int): void = x = x & y\n proc `|=`(x: var int, y: int): void = x = x | y\n proc `>>=`(x: var int, y: int): void = x = x >> y\n proc `<<=`(x: var int, y: int): void = x = x << y\n proc `[]`(x: int, n: int): bool = (x and (1 shl n)) != 0\n #便利な変換\n proc `!`(x: char, a = '0'): int = int(x)-int(a)\n #定数\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 INF = INF64\n #converter\n\n #range\n iterator range(start: int, ends: int, step: int): int =\n var i = start\n if step < 0:\n while i > ends:\n yield i\n i += step\n elif step > 0:\n while i < ends:\n yield i\n i += step\n iterator range(ends: int): int = (for i in 0..<ends: yield i)\n iterator range(start: int, ends: int): int = (for i in\n start..<ends: yield i)\n\n #joinが非stringでめちゃくちゃ遅いやつのパッチ\n proc join*[T: not string](a: openArray[T], sep: string = \"\"): string = a.mapit($it).join(sep)\n\n proc dump[T](arr:seq[seq[T]])=\n for i in 0..<len(arr):\n echo arr[i]\n\n proc sum(slice:HSlice[int,int]):int=\n return (slice.a+slice.b)*len(slice)//2\n \n proc `<`[T](l,r:seq[T]):bool=\n for i in 0..<min(len(l),len(r)):\n if l[i] > r[i]:\n return false\n elif l[i] < r[i]:\n return true\n return len(l) < len(r)\n \n # Yes/No\n proc yes*(b: bool = true): void = print(if b: \"Yes\" else: \"No\")\n proc no*(b: bool = true): void = yes(not b)\n\n proc takahashi(b:bool = true) : void = print(if b: \"Takahashi\" else: \"Aoki\")\n proc aoki(b:bool = true) : void = takahashi(not b)\n\n template dblock(body: untyped) =\n when defined(debug):\n block:\n body\n"
# source: src/cplib/math/divisor.nim
ImportExpand "cplib/math/divisor" <=== "when not declared CPLIB_MATH_DIVISOR:\n const CPLIB_MATH_DIVISOR* = 1\n import sequtils\n import tables\n import algorithm\n when not declared CPLIB_MATH_PRIMEFACTOR:\n const CPLIB_MATH_PRIMEFACTOR* = 1\n when not declared CPLIB_MATH_INNER_MATH:\n const CPLIB_MATH_INNER_MATH* = 1\n proc add*(a, b, m: int): int {.importcpp: \"((__int128)(#) + (__int128)(#)) % (__int128)(#)\", nodecl.}\n proc mul*(a, b, m: int): int {.importcpp: \"(__int128)(#) * (__int128)(#) % (__int128)(#)\", nodecl.}\n \n when not declared CPLIB_MATH_ISPRIME:\n const CPLIB_MATH_ISPRIME* = 1\n when not declared CPLIB_MATH_POWMOD:\n const CPLIB_MATH_POWMOD* = 1\n proc powmod*(a, n, m: int): int =\n assert m != 0\n if m == 1:\n return 0\n var\n rev = 1\n a = a\n n = n\n while n > 0:\n if n mod 2 != 0: rev = mul(rev, a, m)\n if n > 1: a = mul(a, a, m)\n n = n shr 1\n return rev\n \n proc isprime*(N: int): bool =\n let bases = [2, 325, 9375, 28178, 450775, 9780504, 1795265022]\n if N == 2:\n return true\n if N < 2 or (N and 1) == 0:\n return false\n let N1 = N-1\n var d = N1\n var s = 0\n while (d and 1) == 0:\n d = d shr 1\n s += 1\n for a in bases:\n var t: int\n if a mod N == 0:\n continue\n t = powmod(a, d, N)\n if t == 1 or t == N1:\n continue\n block test:\n for _ in 0..<(s-1):\n t = powmod(t, 2, N)\n if t == N1:\n break test\n return false\n return true\n \n when not declared CPLIB_STR_RUN_LENGTH_ENCODE_UTILS:\n const CPLIB_STR_RUN_LENGTH_ENCODE_UTILS* = 1\n import sequtils\n proc run_length_encode*[T](a: seq[T]): seq[(T, int)] =\n for i in 0..<len(a):\n if result.len == 0:\n result.add((a[i], 1))\n continue\n if result[^1][0] == a[i]: result[^1][1] += 1\n else: result.add((a[i], 1))\n \n proc run_length_encode*(s: string): seq[(char, int)] =\n var a = s.items.toSeq\n return run_length_encode(a)\n \n import random\n import std/math\n import algorithm\n import tables\n \n randomize()\n proc find_factor(n: int): int =\n if not ((n and 1) != 0): return 2\n if isprime(n): return n\n const m = 128\n while true:\n var x, ys, q, r, g = 1\n var rnd, y = rand(0..n-3) + 2\n proc f(x: int): int = add(mul(x, x, n), rnd, n)\n while g == 1:\n x = y\n for i in 0..<r: y = f(y)\n for k in countup(0, r-1, m):\n ys = y\n for _ in 0..<min(m, r-k):\n y = f(y)\n q = mul(q, abs(x-y), n)\n g = gcd(q, n)\n if g != 1: break\n r = r shl 1\n if g == n:\n g = 1\n while g == 1:\n ys = f(ys)\n g = gcd(n, abs(x - ys))\n if g < n:\n if isprime(g): return g\n elif isprime(n div g): return n div g\n return find_factor(g)\n \n proc primefactor*(n: int, sorted: bool = true): seq[int] =\n var n = n\n while n > 1 and not isprime(n):\n var p = find_factor(n)\n while n mod p == 0:\n result.add(p)\n n = n div p\n if n > 1: result.add(n)\n if sorted: return result.sorted\n \n proc primefactor_table*(n: int): Table[int, int] =\n for p in primefactor(n):\n if p in result: result[p] += 1\n else: result[p] = 1\n \n proc primefactor_tuple*(n: int): seq[(int, int)] = primefactor(n, true).run_length_encode\n \n proc divisor_naive(x: int, sorted: bool): seq[int] =\n for i in 1..x:\n if i*i > x: break\n if x mod i == 0:\n result.add(i)\n if i*i != x:\n result.add(x div i)\n if sorted: result.sort\n\n proc divisor*(x: int, sorted: bool = true): seq[int] =\n if x <= 1000_000: return divisor_naive(x, sorted)\n var factor = primefactor(x).toCountTable.pairs.toSeq\n var ans = newSeq[int](0)\n proc dfs(d, x: int) =\n if d == factor.len:\n ans.add(x)\n return\n var mul = 1\n for i in 0..factor[d][1]:\n dfs(d+1, x*mul)\n if i != factor[d][1]: mul *= factor[d][0]\n dfs(0, 1)\n if sorted: ans.sort\n return ans\n"
# source: src/cplib/graph/functional_graph.nim
ImportExpand "cplib/graph/functional_graph" <=== "when not declared CPLIB_GRAPH_FUNCTIONALGRAPH:\n const CPLIB_GRAPH_FUNCTIONALGRAPH* = 1\n import sequtils\n 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..<g.src.len:\n g.start[g.src[i]] += 1\n g.start.cumsum\n g.elist = newSeq[(int32, T)](g.start[^1])\n for i in countdown(g.src.len - 1, 0):\n var u = g.src[i]\n var v = g.dst[i]\n g.start[u] -= 1\n g.elist[g.start[u]] = (v, g.cost[i])\n proc build*(g: StaticGraphTypes) = g.build_impl()\n \n proc initWeightedDirectedStaticGraph*(N: int, edgetype: typedesc = int, capacity: int = 0): WeightedDirectedStaticGraph[edgetype] =\n result = WeightedDirectedStaticGraph[edgetype](\n src: newSeqOfCap[int32](capacity),\n dst: newSeqOfCap[int32](capacity),\n cost: newSeqOfCap[edgetype](capacity),\n elist: newSeq[(int32, edgetype)](0),\n start: newSeq[int32](0),\n len: N\n )\n proc add_edge*[T](g: var WeightedDirectedStaticGraph[T], u, v: int, cost: T) =\n g.add_edge_static_impl(u, v, cost, true)\n \n proc initWeightedUnDirectedStaticGraph*(N: int, edgetype: typedesc = int, capacity: int = 0): WeightedUnDirectedStaticGraph[edgetype] =\n result = WeightedUnDirectedStaticGraph[edgetype](\n src: newSeqOfCap[int32](capacity*2),\n dst: newSeqOfCap[int32](capacity*2),\n cost: newSeqOfCap[edgetype](capacity*2),\n elist: newSeq[(int32, edgetype)](0),\n start: newSeq[int32](0),\n len: N\n )\n proc add_edge*[T](g: var WeightedUnDirectedStaticGraph[T], u, v: int, cost: T) =\n g.add_edge_static_impl(u, v, cost, false)\n \n proc initUnWeightedDirectedStaticGraph*(N: int, capacity: int = 0): UnWeightedDirectedStaticGraph =\n result = UnWeightedDirectedStaticGraph(\n src: newSeqOfCap[int32](capacity),\n dst: newSeqOfCap[int32](capacity),\n cost: newSeqOfCap[int](capacity),\n elist: newSeq[(int32, int)](0),\n start: newSeq[int32](0),\n len: N\n )\n proc add_edge*(g: var UnWeightedDirectedStaticGraph, u, v: int) =\n g.add_edge_static_impl(u, v, 1, true)\n \n proc initUnWeightedUnDirectedStaticGraph*(N: int, capacity: int = 0): UnWeightedUnDirectedStaticGraph =\n result = UnWeightedUnDirectedStaticGraph(\n src: newSeqOfCap[int32](capacity*2),\n dst: newSeqOfCap[int32](capacity*2),\n cost: newSeqOfCap[int](capacity*2),\n elist: newSeq[(int32, int)](0),\n start: newSeq[int32](0),\n len: N\n )\n proc add_edge*(g: var UnWeightedUnDirectedStaticGraph, u, v: int) =\n g.add_edge_static_impl(u, v, 1, false)\n \n proc static_graph_initialized_check*[T](g: StaticGraph[T]) = assert g.start.len > 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]..<g.start[x+1]: yield (g.elist[i][0].int, g.elist[i][1])\n iterator `[]`*(g: UnWeightedDirectedStaticGraph or UnWeightedUnDirectedStaticGraph, x: int): int =\n g.static_graph_initialized_check()\n for i in g.start[x]..<g.start[x+1]: yield g.elist[i][0].int\n \n iterator to_and_cost*[T](g: DynamicGraph[T], x: int): (int, T) =\n for e in g.edges[x]: yield (e[0].int, e[1])\n iterator to_and_cost*[T](g: StaticGraph[T], x: int): (int, T) =\n g.static_graph_initialized_check()\n for i in g.start[x]..<g.start[x+1]: yield (g.elist[i][0].int, g.elist[i][1])\n \n import tables\n \n type UnWeightedUnDirectedTableGraph*[T] = object \n toi* : Table[T,int]\n v* : seq[T]\n graph* : UnWeightedUnDirectedGraph\n \n type UnWeightedDirectedTableGraph*[T] = object \n toi* : Table[T,int]\n v* : seq[T]\n graph* : UnWeightedDirectedGraph\n \n type WeightedUnDirectedTableGraph*[T,S] = object \n toi* : Table[T,int]\n v* : seq[T]\n graph* : WeightedUnDirectedGraph[S]\n \n type WeightedDirectedTableGraph*[T,S] = object \n toi* : Table[T,int]\n v* : seq[T]\n graph* : WeightedDirectedGraph[S]\n \n type UnWeightedTableGraph*[T] = UnWeightedUnDirectedTableGraph[T] or UnWeightedDirectedTableGraph[T]\n type WeightedTableGraph*[T,S] = WeightedUnDirectedTableGraph[T,S] or WeightedDirectedTableGraph[T,S]\n \n proc initUnWeightedUnDirectedTableGraph*[T](V:openArray[T]):UnWeightedUnDirectedTableGraph[T]=\n for i in 0..<len(V):\n result.toi[V[i]] = i\n result.graph = initUnWeightedUnDirectedGraph(len(V))\n result.v = @V\n \n proc initUnWeightedDirectedTableGraph*[T](V:openArray[T]):UnWeightedDirectedTableGraph[T]=\n for i in 0..<len(V):\n result.toi[V[i]] = i\n result.graph = initUnWeightedDirectedGraph(len(V))\n result.v = @V\n \n proc initWeightedUnDirectedTableGraph*[T](V:openArray[T],S:typedesc = int):WeightedUnDirectedTableGraph[T,S]=\n for i in 0..<len(V):\n result.toi[V[i]] = i\n result.graph = initWeightedUnDirectedGraph(len(V),S)\n result.v = @V\n \n proc initWeightedDirectedTableGraph*[T](V:openArray[T],S:typedesc = int):WeightedDirectedTableGraph[T,S]=\n for i in 0..<len(V):\n result.toi[V[i]] = i\n result.graph = initWeightedDirectedGraph(len(V),S)\n result.v = @V\n \n proc add_edge*[T](g: var UnWeightedTableGraph[T],u,v:T)=\n g.graph.add_edge(g.toi[u],g.toi[v])\n \n proc add_edge*[T,S](g: var WeightedTableGraph[T,S],u,v:T,cost:S)=\n g.graph.add_edge(g.toi[u],g.toi[v],cost)\n \n iterator `[]`*[T,S](g: WeightedDirectedTableGraph[T,S] or WeightedUnDirectedTableGraph[T,S], x: T): (T, S) = \n for (x,y) in g.graph[g.toi[x]]:\n yield (g.v[x],y)\n iterator `[]`*[T](g: UnWeightedDirectedTableGraph[T] or UnWeightedUnDirectedTableGraph[T], x: T): T = \n for x in g.graph[g.toi[x]]:\n yield g.v[x]\n \n when not declared CPLIB_TREE_HLD:\n const CPLIB_TREE_HLD* = 1\n import sequtils\n import algorithm\n import sets\n # https://atcoder.jp/contests/abc337/submissions/50216964\n # ↑上記の提出より引用\n type HeavyLightDecomposition* = ref object \n N*: int\n P*, PP*, PD*, D*, I*, rangeL*, rangeR*: seq[int]\n \n proc initHldFromParent*(parent: openArray[int], root: int): HeavyLightDecomposition =\n let n = len(parent)\n assert 0 <= root and root < n\n var hld = HeavyLightDecomposition(N:n)\n hld.P = @parent\n hld.P[root] = -1\n \n # 親から子を列挙するための連結リスト。\n var head = newSeqWith(n,-1)\n var next = newSeqWith(n,-1)\n for v in 0..<n:\n if v != root:\n assert 0 <= hld.P[v] and hld.P[v] < n\n next[v] = head[hld.P[v]]\n head[hld.P[v]] = v\n \n # 親が必ず子より先に現れる順序。\n hld.I = newSeq[int](n)\n hld.I[0] = root\n var iI = 1\n for i in 0..<n:\n var v = head[hld.I[i]]\n while v != -1:\n hld.I[iI] = v\n iI += 1\n v = next[v]\n assert iI == n\n \n var size = newSeqWith(n,1)\n var heavy = newSeqWith(n,-1)\n for i in countdown(n-1,1):\n let v = hld.I[i]\n let p = hld.P[v]\n size[p] += size[v]\n if heavy[p] == -1 or size[heavy[p]] < size[v]:\n heavy[p] = v\n \n hld.PP = newSeq[int](n)\n for v in 0..<n:\n hld.PP[v] = v\n for v in hld.I:\n if heavy[v] != -1:\n hld.PP[heavy[v]] = v\n \n hld.PD = newSeqWith(n,n)\n hld.PD[root] = 0\n hld.D = newSeq[int](n)\n for v in hld.I:\n if v != root:\n hld.PP[v] = hld.PP[hld.PP[v]]\n hld.PD[v] = min(hld.PD[hld.PP[v]],hld.PD[hld.P[v]]+1)\n hld.D[v] = hld.D[hld.P[v]]+1\n \n hld.rangeL = newSeq[int](n)\n hld.rangeR = newSeq[int](n)\n for p in hld.I:\n hld.rangeR[p] = hld.rangeL[p]+size[p]\n var ir = hld.rangeR[p]\n var v = head[p]\n while v != -1:\n if v != heavy[p]:\n ir -= size[v]\n hld.rangeL[v] = ir\n v = next[v]\n if heavy[p] != -1:\n hld.rangeL[heavy[p]] = hld.rangeL[p]+1\n \n for v in 0..<n:\n hld.I[hld.rangeL[v]] = v\n return hld\n \n proc initHld*(g: UnDirectedGraph, root: int): HeavyLightDecomposition =\n var hld = HeavyLightDecomposition()\n var n: int = g.len\n hld.N = n\n hld.P = newSeqWith(n, -1)\n hld.I = newSeqWith(n, 0)\n hld.I[0] = root\n var iI = 1\n for i in 0..<n:\n var p = hld.I[i]\n for (e, _) in g.to_and_cost(p):\n if hld.P[p] != e:\n hld.I[iI] = e\n hld.P[e] = p\n iI += 1\n var Z = newSeqWith(n, 1)\n var nx = newSeqWith(n, -1)\n hld.PP = newSeqWith(n, 0)\n for i in 0..<n:\n hld.PP[i] = i\n for i in 1..<n:\n var p = hld.I[n-i]\n Z[hld.P[p]] += Z[p]\n if nx[hld.P[p]] == -1 or Z[nx[hld.P[p]]] < Z[p]:\n nx[hld.P[p]] = p\n for p in hld.I:\n if nx[p] != -1:\n hld.PP[nx[p]] = p\n hld.PD = newSeqWith(n, n)\n hld.PD[root] = 0\n hld.D = newSeqWith(n, 0)\n for p in hld.I:\n if p != root:\n hld.PP[p] = hld.PP[hld.PP[p]]\n hld.PD[p] = min(hld.PD[hld.PP[p]], hld.PD[hld.P[p]]+1)\n hld.D[p] = hld.D[hld.P[p]]+1\n hld.rangeL = newSeqWith(n, 0)\n hld.rangeR = newSeqWith(n, 0)\n for p in hld.I:\n hld.rangeR[p] = hld.rangeL[p] + Z[p]\n var ir = hld.rangeR[p]\n for (e, _) in g.to_and_cost(p):\n if hld.P[p] != e and e != nx[p]:\n ir -= Z[e]\n hld.rangeL[e] = ir\n if nx[p] != -1:\n hld.rangeL[nx[p]] = hld.rangeL[p] + 1\n for i in 0..<n:\n hld.I[hld.rangeL[i]] = i\n return hld\n proc initHld*(g: DirectedGraph, root: int): HeavyLightDecomposition =\n var n = g.len\n var gn = initUnWeightedUnDirectedStaticGraph(n)\n var seen = initHashSet[(int, int)]()\n for i in 0..<n:\n for (j, _) in g.to_and_cost(i):\n if (i, j) notin seen:\n gn.add_edge(i, j)\n seen.incl((i, j))\n seen.incl((j, i))\n gn.build\n return initHld(gn, root)\n proc initHld*(adj: openArray[seq[int]], root: int): HeavyLightDecomposition =\n var n = adj.len\n var gn = initUnWeightedUnDirectedStaticGraph(n)\n var seen = initHashSet[(int, int)]()\n for i in 0..<n:\n for j in adj[i]:\n if (i, j) notin seen:\n gn.add_edge(i, j)\n seen.incl((i, j))\n seen.incl((j, i))\n gn.build\n return initHld(gn, root)\n proc numVertices*(hld: HeavyLightDecomposition): int = hld.N\n proc depth*(hld: HeavyLightDecomposition, p: int): int = hld.D[p]\n proc toSeq*(hld: HeavyLightDecomposition, vtx: int): int = hld.rangeL[vtx]\n proc toVtx*(hld: HeavyLightDecomposition, seqidx: int): int = hld.I[seqidx]\n proc toSeq2In*(hld: HeavyLightDecomposition, vtx: int): int = hld.rangeL[vtx] * 2 - hld.D[vtx]\n proc toSeq2Out*(hld: HeavyLightDecomposition, vtx: int): int = hld.rangeR[vtx] * 2 - hld.D[vtx] - 1\n proc parentOf*(hld: HeavyLightDecomposition, v: int): int = hld.P[v]\n proc heavyRootOf*(hld: HeavyLightDecomposition, v: int): int = hld.PP[v]\n proc heavyChildOf*(hld: HeavyLightDecomposition, v: int): int =\n if hld.toSeq(v) == hld.N-1:\n return -1\n var cand = hld.toVtx(hld.toSeq(v) + 1)\n if hld.PP[v] == hld.PP[cand]:\n return cand\n -1\n proc lca*(hld: HeavyLightDecomposition, u: int, v: int): int =\n var (u, v) = (u, v)\n if hld.PD[u] < hld.PD[v]:\n swap(u, v)\n while hld.PD[u] > hld.PD[v]:\n u = hld.P[hld.PP[u]]\n while hld.PP[u] != hld.PP[v]:\n u = hld.P[hld.PP[u]]\n v = hld.P[hld.PP[v]]\n if hld.D[u] > hld.D[v]:\n return v\n u\n proc dist*(hld: HeavyLightDecomposition, u: int, v: int): int =\n hld.depth(u) + hld.depth(v) - hld.depth(hld.lca(u, v)) * 2\n proc path*(hld: HeavyLightDecomposition, r: int, c: int, include_root: bool, reverse_path: bool): seq[(int, int)] =\n var (r, c) = (r, c)\n var k = hld.PD[c] - hld.PD[r] + 1\n if k <= 0:\n return @[]\n var res = newSeqWith(k, (0, 0))\n for i in 0..<k-1:\n res[i] = (hld.rangeL[hld.PP[c]], hld.rangeL[c] + 1)\n c = hld.P[hld.PP[c]]\n if hld.PP[r] != hld.PP[c] or hld.D[r] > hld.D[c]:\n return @[]\n var root_off = int(not include_root)\n res[^1] = (hld.rangeL[r]+root_off, hld.rangeL[c]+1)\n if res[^1][0] == res[^1][1]:\n discard res.pop()\n k -= 1\n if reverse_path:\n for i in 0..<k:\n res[i] = (hld.N - res[i][1], hld.N - res[i][0])\n else:\n res.reverse()\n res\n proc subtree*(hld: HeavyLightDecomposition, p: int): (int, int) = (hld.rangeL[p], hld.rangeR[p])\n iterator subtreeV*(hld: HeavyLightDecomposition, p: int):int=\n for i in hld.rangeL[p]..<hld.rangeR[p]:\n yield hld.toVtx(i)\n proc median*(hld: HeavyLightDecomposition, x: int, y: int, z: int): int =\n hld.lca(x, y) xor hld.lca(y, z) xor hld.lca(x, z)\n proc la*(hld: HeavyLightDecomposition, starting: int, goal: int, d: int): int =\n var (u, v, d) = (starting, goal, d)\n if d < 0:\n return -1\n var g = hld.lca(u, v)\n var dist0 = hld.D[u] - hld.D[g] * 2 + hld.D[v]\n if dist0 < d:\n return -1\n var p = u\n if hld.D[u] - hld.D[g] < d:\n p = v\n d = dist0 - d\n while hld.D[p] - hld.D[hld.PP[p]] < d:\n d -= hld.D[p] - hld.D[hld.PP[p]] + 1\n p = hld.P[hld.PP[p]]\n hld.I[hld.rangeL[p] - d]\n iterator children*(hld: HeavyLightDecomposition, v: int): int =\n var s = hld.rangeL[v] + 1\n while s < hld.rangeR[v]:\n var w = hld.toVtx(s)\n yield w\n s += hld.rangeR[w] - hld.rangeL[w]\n \n \n proc initAuxiliaryTree*(hld:HeavyLightDecomposition,v:openArray[int]):UnWeightedUnDirectedTableGraph[int]=\n var v = v.sortedByit(hld.toseq(it))\n for i in 0..<(len(v)-1):\n v.add(hld.lca(v[i],v[i+1]))\n v = v.sortedByIt(hld.toseq(it)).deduplicate(true)\n var stack :seq[int]\n result = initUnWeightedUnDirectedTableGraph[int](v)\n stack.add(v[0])\n \n for i in 1..<len(v):\n while len(stack) > 0 and hld.toSeq2Out(stack[^1]) < hld.toseq2In(v[i]):\n discard stack.pop()\n if len(stack) != 0:\n result.add_edge(stack[^1],v[i])\n stack.add(v[i])\n \n proc initAuxiliaryWeightedTree*(hld: HeavyLightDecomposition, v: openArray[int], S: typedesc = int): WeightedUnDirectedTableGraph[int, S] =\n var v = v.sortedByit(hld.toseq(it))\n for i in 0..<(len(v)-1):\n v.add(hld.lca(v[i],v[i+1]))\n v = v.sortedByIt(hld.toseq(it)).deduplicate(true)\n var stack :seq[int]\n result = initWeightedUnDirectedTableGraph(v, S)\n stack.add(v[0])\n for i in 1..<len(v):\n while len(stack) > 0 and hld.toSeq2Out(stack[^1]) < hld.toseq2In(v[i]):\n discard stack.pop()\n if len(stack) != 0:\n result.add_edge(stack[^1], v[i], S(hld.depth(v[i]) - hld.depth(stack[^1])))\n stack.add(v[i])\n \n type Functional_Graph* = ref object \n tree* : HeavyLightDecomposition\n cycle_number* : seq[int]\n cycle_idx* : seq[int]\n roots* : seq[int]\n cycle* : seq[seq[int]]\n depth_tin : seq[seq[int]]\n cycle_depth : seq[seq[seq[int]]]\n component_size : seq[int]\n\n proc initFunctionalGraph*(v:openArray[int]):Functional_Graph=\n let n = len(v)\n var removed = newSeqOfCap[int](n)\n var sizes = newseqwith(n,0)\n var cycle_number = newseqwith(n,-1)\n var cycle_idx = newseqwith(n,-1)\n var parent = newSeqWith(n+1,-1)\n var roots = newseqwith(n,0)\n var cycle : seq[seq[int]]\n for i in 0..<n:\n assert 0 <= v[i] and v[i] < n\n sizes[v[i]] += 1\n for i in 0..<n:\n if sizes[i] == 0:\n removed.add(i)\n var removed_idx = 0\n while removed_idx < len(removed):\n let i = removed[removed_idx]\n removed_idx += 1\n let j = v[i]\n parent[i] = j\n sizes[j] -= 1\n if sizes[j] == 0:\n removed.add(j)\n\n var alr = newseqwith(n,false)\n for i in 0..<n:\n if sizes[i] != 0 and not alr[i]:\n let cycle_n = len(cycle)\n var now = i\n cycle.add(@[])\n while not alr[now]:\n alr[now] = true\n cycle_number[now] = cycle_n\n cycle_idx[now] = len(cycle[cycle_n])\n roots[now] = now\n cycle[cycle_n].add(now)\n parent[now] = n\n now = v[now]\n # 削除順の逆から見れば、遷移先のrootは既に決まっている。\n var i = len(removed)\n while i > 0:\n i -= 1\n let x = removed[i]\n roots[x] = roots[v[x]]\n\n result = Functional_Graph(\n tree:initHldFromParent(parent,n),\n cycle_number:cycle_number,\n roots:roots,\n cycle:cycle,\n cycle_idx:cycle_idx\n )\n\n # depthごとにHLDのEuler Tour上の位置を昇順で持つ。\n result.depth_tin = newSeq[seq[int]](n)\n for tin in 0..<result.tree.N:\n let x = result.tree.toVtx(tin)\n if x < n:\n let d = result.tree.depth(x)-1\n result.depth_tin[d].add(tin)\n\n # cycleごとに (cycle_idx[root]-depth) mod cycle_size で分類し、\n # 各列にはdepthを昇順で持つ。\n result.cycle_depth = newSeq[seq[seq[int]]](len(cycle))\n result.component_size = newSeq[int](len(cycle))\n for cid in 0..<len(cycle):\n result.cycle_depth[cid] = newSeq[seq[int]](len(cycle[cid]))\n for d in 0..<len(result.depth_tin):\n for tin in result.depth_tin[d]:\n let v = result.tree.toVtx(tin)\n let root = roots[v]\n let cid = cycle_number[root]\n let csiz = len(cycle[cid])\n let residue = (cycle_idx[root]-(d mod csiz)+csiz) mod csiz\n result.cycle_depth[cid][residue].add(d)\n result.component_size[cid] += 1\n\n proc initFunctionalGraph*(graph:UnWeightedDirectedGraph):Functional_Graph=\n var v = newSeq[int](len(graph))\n for i in 0..<len(graph):\n for j in graph[i]:\n v[i] = j\n return initFunctionalGraph(v)\n\n proc incycle*(namori:Functional_Graph,x:int):bool=\n return namori.cycle_number[x] != -1\n\n proc movekth*(functional_graph:Functional_Graph,x,cnt:int):int=\n #xからcnt回動いたらどこに行くか\n if functional_graph.tree.depth(x)-1 >= cnt:\n return functional_graph.tree.la(x,len(functional_graph.cycle_number),cnt)\n else:\n var root = functional_graph.roots[x]\n var cnt = cnt-(functional_graph.tree.depth(x)-1)\n return functional_graph.cycle[functional_graph.cycle_number[root]][(functional_graph.cycle_idx[root]+cnt) mod len(functional_graph.cycle[functional_graph.cycle_number[root]])]\n\n proc cyclesize*(functional_graph:Functional_Graph,x:int):int=\n var root = functional_graph.roots[x]\n return functional_graph.cycle[functional_graph.cycle_number[root]].len()\n\n proc canmove_size*(functional_graph:Functional_Graph,x:int):int=\n return functional_graph.tree.depth(x)-1+functional_graph.cyclesize(x)\n\n proc reachable_to_size*(functional_graph:Functional_Graph,x:int):int=\n if functional_graph.incycle(x):\n return functional_graph.component_size[functional_graph.cycle_number[x]]\n let (l,r) = functional_graph.tree.subtree(x)\n return r-l\n\n proc depth*(functional_graph:Functional_Graph,x:int):int=\n return functional_graph.tree.depth(x)-1\n\n proc dist*(functional_graph:Functional_Graph,u,v:int):int=\n if functional_graph.cycle_number[functional_graph.roots[u]] != functional_graph.cycle_number[functional_graph.roots[v]]:\n return -1\n var lca = functional_graph.tree.lca(u,v)\n if lca == v:\n return functional_graph.tree.depth(u)-functional_graph.tree.depth(v)\n if lca == len(functional_graph.cycle_number):\n if functional_graph.incycle(v):\n var x = functional_graph.cycle_idx[functional_graph.roots[u]]\n var y = functional_graph.cycle_idx[v]\n if x < y:\n return y-x+functional_graph.depth(u)\n else:\n return y+len(functional_graph.cycle[functional_graph.cycle_number[v]])-x+functional_graph.depth(u)\n return -1\n\n proc get_cycle*(functional_graph:Functional_Graph,x:int):seq[int]=\n var root = functional_graph.roots[x]\n return functional_graph.cycle[functional_graph.cycle_number[root]]\n\n proc root*(functional_graph:Functional_Graph,x:int):int=\n return functional_graph.roots[x]\n\n proc compressed_forest*(functional_graph:Functional_Graph):(UnWeightedUnDirectedGraph,seq[int],seq[int])=\n let n = len(functional_graph.cycle_number)\n var compressed = newSeqWith(n,-1)\n var roots = newSeq[int](len(functional_graph.cycle))\n var compressed_n = 0\n\n for cid,cycle in functional_graph.cycle:\n roots[cid] = compressed_n\n for v in cycle:\n compressed[v] = compressed_n\n compressed_n += 1\n\n for v in 0..<n:\n if compressed[v] == -1:\n compressed[v] = compressed_n\n compressed_n += 1\n\n var forest = initUnWeightedUnDirectedGraph(compressed_n)\n for v in 0..<n:\n if not functional_graph.incycle(v):\n forest.add_edge(compressed[v],compressed[functional_graph.tree.P[v]])\n\n return (forest,compressed,roots)\n\n proc walk*(functional_graph:Functional_Graph,x,k:int):seq[int]=\n let n = len(functional_graph.cycle_number)\n assert 0 <= x and x < n\n assert 0 <= k and k < high(int)\n result = newSeq[int](k+1)\n var now = x\n for i in 0..k:\n result[i] = now\n if i < k:\n if functional_graph.incycle(now):\n let cid = functional_graph.cycle_number[now]\n let next_idx = (functional_graph.cycle_idx[now]+1) mod len(functional_graph.cycle[cid])\n now = functional_graph.cycle[cid][next_idx]\n else:\n now = functional_graph.tree.P[now]\n\n import algorithm\n\n proc count_kth*(functional_graph:Functional_Graph,x,k:int):int=\n assert 0 <= x and x < len(functional_graph.cycle_number)\n assert k >= 0\n if not functional_graph.incycle(x):\n let d = functional_graph.depth(x)\n if k > functional_graph.depth_tin.high-d:\n return 0\n let (l,r) = functional_graph.tree.subtree(x)\n let tins = functional_graph.depth_tin[d+k]\n return tins.lowerBound(r)-tins.lowerBound(l)\n\n let cid = functional_graph.cycle_number[x]\n let csiz = len(functional_graph.cycle[cid])\n let residue = (functional_graph.cycle_idx[x]-(k mod csiz)+csiz) mod csiz\n return functional_graph.cycle_depth[cid][residue].upperBound(k)\n"
var md = 100003
proc f(x:int):int=
var res = 0
for y in divisor(x):
res += y
return res%md
var N,K = ii()
var tmp = newseqwith(md,-1)
for i in range(md):
tmp[i] = f(i)
var G = initFunctionalGraph(tmp)
if K == 1:
echo N
quit()
else:
echo G.movekth(f(N),K-2)