結果
| 問題 | No.2008 Super Worker |
| ユーザー |
 chaemon
|
| 提出日時 | 2022-07-15 22:58:17 |
| 言語 | Nim (2.0.2) |
| 結果 |
AC
|
| 実行時間 | 217 ms / 2,000 ms |
| コード長 | 50,909 bytes |
| コンパイル時間 | 5,138 ms |
| コンパイル使用メモリ | 94,848 KB |
| 実行使用メモリ | 13,244 KB |
| 最終ジャッジ日時 | 2024-06-27 20:04:08 |
| 合計ジャッジ時間 | 9,059 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 1 ms
5,248 KB |
| testcase_01 | AC | 1 ms
5,376 KB |
| testcase_02 | AC | 2 ms
5,376 KB |
| testcase_03 | AC | 1 ms
5,376 KB |
| testcase_04 | AC | 1 ms
5,376 KB |
| testcase_05 | AC | 2 ms
5,376 KB |
| testcase_06 | AC | 2 ms
5,376 KB |
| testcase_07 | AC | 2 ms
5,376 KB |
| testcase_08 | AC | 1 ms
5,376 KB |
| testcase_09 | AC | 2 ms
5,376 KB |
| testcase_10 | AC | 2 ms
5,376 KB |
| testcase_11 | AC | 2 ms
5,376 KB |
| testcase_12 | AC | 2 ms
5,376 KB |
| testcase_13 | AC | 2 ms
5,376 KB |
| testcase_14 | AC | 2 ms
5,376 KB |
| testcase_15 | AC | 2 ms
5,376 KB |
| testcase_16 | AC | 2 ms
5,376 KB |
| testcase_17 | AC | 2 ms
5,376 KB |
| testcase_18 | AC | 3 ms
5,376 KB |
| testcase_19 | AC | 2 ms
5,376 KB |
| testcase_20 | AC | 3 ms
5,376 KB |
| testcase_21 | AC | 3 ms
5,376 KB |
| testcase_22 | AC | 2 ms
5,376 KB |
| testcase_23 | AC | 177 ms
12,996 KB |
| testcase_24 | AC | 179 ms
13,184 KB |
| testcase_25 | AC | 179 ms
13,088 KB |
| testcase_26 | AC | 181 ms
12,992 KB |
| testcase_27 | AC | 180 ms
13,072 KB |
| testcase_28 | AC | 216 ms
13,000 KB |
| testcase_29 | AC | 217 ms
13,244 KB |
| testcase_30 | AC | 215 ms
12,996 KB |
| testcase_31 | AC | 214 ms
13,056 KB |
| testcase_32 | AC | 217 ms
13,144 KB |
| testcase_33 | AC | 172 ms
13,068 KB |
| testcase_34 | AC | 217 ms
13,052 KB |
| testcase_35 | AC | 93 ms
13,092 KB |
コンパイルメッセージ
check is on
ソースコード
import macros
macro Please(x): untyped = nnkStmtList.newTree()
Please use Nim-ACL
Please use Nim-ACL
Please use Nim-ACL
import macros;macro ImportExpand(s:untyped):untyped = parseStmt($s[2])
# see https://github.com/zer0-star/Nim-ACL/tree/master/src/atcoder/extra/header/chaemon_header.nim
ImportExpand "src/atcoder/extra/header/chaemon_header.nim" <=== "when not declared ATCODER_CHAEMON_HEADER_HPP:\n const ATCODER_CHAEMON_HEADER_HPP* = 1\n\n {.hints:off warnings:off assertions:on optimization:speed.}\n when declared(DO_CHECK):\n when DO_CHECK:\n static: echo \"check is on\"\n {.checks:on.}\n else:\n static: echo \"check is off\"\n {.checks:off.}\n else:\n static: echo \"check is on\"\n {.checks:on.}\n\n import std/algorithm as algorithm_lib\n import std/sequtils as sequtils_lib\n import std/macros as macros_lib\n import std/math as math_lib\n import std/sets as sets_lib\n import std/tables as tables_lib\n import std/strutils as strutils_lib\n import std/strformat as strformat_lib\n import std/options as options_lib\n import std/bitops as bitops_lib\n import std/streams as streams_lib\n import std/deques as deques_lib\n\n #[ import atcoder/extra/forward_compatibility/internal_sugar ]#\n when not declared ATCODER_INTERNAL_SUGAR_HPP:\n const ATCODER_INTERNAL_SUGAR_HPP* = 1\n import std/macros\n import std/typetraits\n \n proc checkPragma(ex, prag: var NimNode) =\n # since (1, 3):\n block:\n if ex.kind == nnkPragmaExpr:\n prag = ex[1]\n if ex[0].kind == nnkPar and ex[0].len == 1:\n ex = ex[0][0]\n else:\n ex = ex[0]\n \n proc createProcType(p, b: NimNode): NimNode {.compileTime.} =\n result = newNimNode(nnkProcTy)\n var\n formalParams = newNimNode(nnkFormalParams).add(b)\n p = p\n prag = newEmptyNode()\n \n checkPragma(p, prag)\n \n case p.kind\n of nnkPar, nnkTupleConstr:\n for i in 0 ..< p.len:\n let ident = p[i]\n var identDefs = newNimNode(nnkIdentDefs)\n case ident.kind\n of nnkExprColonExpr:\n identDefs.add ident[0]\n identDefs.add ident[1]\n else:\n identDefs.add newIdentNode(\"i\" & $i)\n identDefs.add(ident)\n identDefs.add newEmptyNode()\n formalParams.add identDefs\n else:\n var identDefs = newNimNode(nnkIdentDefs)\n identDefs.add newIdentNode(\"i0\")\n identDefs.add(p)\n identDefs.add newEmptyNode()\n formalParams.add identDefs\n \n result.add formalParams\n result.add prag\n \n macro `=>`*(p, b: untyped): untyped =\n ## Syntax sugar for anonymous procedures.\n ## It also supports pragmas.\n var\n params = @[ident\"auto\"]\n name = newEmptyNode()\n kind = nnkLambda\n pragma = newEmptyNode()\n p = p\n \n checkPragma(p, pragma)\n \n if p.kind == nnkInfix and p[0].kind == nnkIdent and p[0].eqIdent\"->\":\n params[0] = p[2]\n p = p[1]\n \n checkPragma(p, pragma) # check again after -> transform\n # since (1, 3):\n block:\n # if p.kind == nnkCall:\n if p.kind in {nnkCall, nnkObjConstr}:\n # foo(x, y) => x + y\n kind = nnkProcDef\n name = p[0]\n let newP = newNimNode(nnkPar)\n for i in 1..<p.len:\n newP.add(p[i])\n p = newP\n \n case p.kind\n of nnkPar, nnkTupleConstr:\n var untypedBeforeColon = 0\n for i, c in p:\n var identDefs = newNimNode(nnkIdentDefs)\n case c.kind\n of nnkExprColonExpr:\n let t = c[1]\n # since (1, 3):\n block:\n # + 1 here because of return type in params\n for j in (i - untypedBeforeColon + 1) .. i:\n params[j][1] = t\n untypedBeforeColon = 0\n identDefs.add(c[0])\n identDefs.add(t)\n identDefs.add(newEmptyNode())\n of nnkIdent:\n identDefs.add(c)\n identDefs.add(newIdentNode(\"auto\"))\n identDefs.add(newEmptyNode())\n inc untypedBeforeColon\n of nnkInfix:\n if c[0].kind == nnkIdent and c[0].eqIdent\"->\":\n var procTy = createProcType(c[1], c[2])\n params[0] = procTy[0][0]\n for i in 1 ..< procTy[0].len:\n params.add(procTy[0][i])\n else:\n error(\"Expected proc type (->) got (\" & c[0].strVal & \").\", c)\n break\n else:\n error(\"Incorrect procedure parameter list.\", c)\n params.add(identDefs)\n of nnkIdent:\n var identDefs = newNimNode(nnkIdentDefs)\n identDefs.add(p)\n identDefs.add(ident\"auto\")\n identDefs.add(newEmptyNode())\n params.add(identDefs)\n else:\n error(\"Incorrect procedure parameter list.\", p)\n result = newProc(body = b, params = params,\n pragmas = pragma, name = name,\n procType = kind)\n \n macro `->`*(p, b: untyped): untyped =\n result = createProcType(p, b)\n \n macro dump*(x: untyped): untyped =\n let s = x.toStrLit\n let r = quote do:\n debugEcho `s`, \" = \", `x`\n return r\n \n # TODO: consider exporting this in macros.nim\n proc freshIdentNodes(ast: NimNode): NimNode =\n # Replace NimIdent and NimSym by a fresh ident node\n # see also https://github.com/nim-lang/Nim/pull/8531#issuecomment-410436458\n proc inspect(node: NimNode): NimNode =\n case node.kind:\n of nnkIdent, nnkSym:\n result = ident($node)\n of nnkEmpty, nnkLiterals:\n result = node\n else:\n result = node.kind.newTree()\n for child in node:\n result.add inspect(child)\n result = inspect(ast)\n \n macro capture*(locals: varargs[typed], body: untyped): untyped =\n var params = @[newIdentNode(\"auto\")]\n let locals = if locals.len == 1 and locals[0].kind == nnkBracket: locals[0]\n else: locals\n for arg in locals:\n if arg.strVal == \"result\":\n error(\"The variable name cannot be `result`!\", arg)\n params.add(newIdentDefs(ident(arg.strVal), freshIdentNodes getTypeInst arg))\n result = newNimNode(nnkCall)\n result.add(newProc(newEmptyNode(), params, body, nnkProcDef))\n for arg in locals: result.add(arg)\n \n #[ import atcoder/extra/forward_compatibility/internal_underscored_calls ]#\n when not declared ATCODER_INTERNAL_UNDERSCORED_CALLS_HPP:\n const ATCODER_INTERNAL_UNDERSCORED_CALLS_HPP* = 1\n import macros\n \n proc underscoredCall(n, arg0: NimNode): NimNode =\n proc underscorePos(n: NimNode): int =\n for i in 1 ..< n.len:\n if n[i].eqIdent(\"_\"): return i\n return 0\n \n if n.kind in nnkCallKinds:\n result = copyNimNode(n)\n result.add n[0]\n \n let u = underscorePos(n)\n for i in 1..u-1: result.add n[i]\n result.add arg0\n for i in u+1..n.len-1: result.add n[i]\n elif n.kind in {nnkAsgn, nnkExprEqExpr}:\n var field = n[0]\n if n[0].kind == nnkDotExpr and n[0][0].eqIdent(\"_\"):\n # handle _.field = ...\n field = n[0][1]\n result = newDotExpr(arg0, field).newAssignment n[1]\n else:\n # handle e.g. 'x.dup(sort)'\n result = newNimNode(nnkCall, n)\n result.add n\n result.add arg0\n \n proc underscoredCalls*(result, calls, arg0: NimNode) =\n expectKind calls, {nnkArgList, nnkStmtList, nnkStmtListExpr}\n \n for call in calls:\n if call.kind in {nnkStmtList, nnkStmtListExpr}:\n underscoredCalls(result, call, arg0)\n else:\n result.add underscoredCall(call, arg0)\n discard\n \n macro dup*[T](arg: T, calls: varargs[untyped]): T =\n result = newNimNode(nnkStmtListExpr, arg)\n let tmp = genSym(nskVar, \"dupResult\")\n result.add newVarStmt(tmp, arg)\n underscoredCalls(result, calls, tmp)\n result.add tmp\n \n proc transLastStmt(n, res, bracketExpr: NimNode): (NimNode, NimNode, NimNode) =\n # Looks for the last statement of the last statement, etc...\n case n.kind\n of nnkIfExpr, nnkIfStmt, nnkTryStmt, nnkCaseStmt:\n result[0] = copyNimTree(n)\n result[1] = copyNimTree(n)\n result[2] = copyNimTree(n)\n for i in ord(n.kind == nnkCaseStmt)..<n.len:\n (result[0][i], result[1][^1], result[2][^1]) = transLastStmt(n[i], res, bracketExpr)\n of nnkStmtList, nnkStmtListExpr, nnkBlockStmt, nnkBlockExpr, nnkWhileStmt,\n nnkForStmt, nnkElifBranch, nnkElse, nnkElifExpr, nnkOfBranch, nnkExceptBranch:\n result[0] = copyNimTree(n)\n result[1] = copyNimTree(n)\n result[2] = copyNimTree(n)\n if n.len >= 1:\n (result[0][^1], result[1][^1], result[2][^1]) = transLastStmt(n[^1], res, bracketExpr)\n of nnkTableConstr:\n result[1] = n[0][0]\n result[2] = n[0][1]\n if bracketExpr.len == 1:\n bracketExpr.add([newCall(bindSym\"typeof\", newEmptyNode()), newCall(\n bindSym\"typeof\", newEmptyNode())])\n template adder(res, k, v) = res[k] = v\n result[0] = getAst(adder(res, n[0][0], n[0][1]))\n of nnkCurly:\n result[2] = n[0]\n if bracketExpr.len == 1:\n bracketExpr.add(newCall(bindSym\"typeof\", newEmptyNode()))\n template adder(res, v) = res.incl(v)\n result[0] = getAst(adder(res, n[0]))\n else:\n result[2] = n\n if bracketExpr.len == 1:\n bracketExpr.add(newCall(bindSym\"typeof\", newEmptyNode()))\n template adder(res, v) = res.add(v)\n result[0] = getAst(adder(res, n))\n \n macro collect*(init, body: untyped): untyped =\n # analyse the body, find the deepest expression 'it' and replace it via\n # 'result.add it'\n let res = genSym(nskVar, \"collectResult\")\n expectKind init, {nnkCall, nnkIdent, nnkSym}\n let bracketExpr = newTree(nnkBracketExpr,\n if init.kind == nnkCall: init[0] else: init)\n let (resBody, keyType, valueType) = transLastStmt(body, res, bracketExpr)\n if bracketExpr.len == 3:\n bracketExpr[1][1] = keyType\n bracketExpr[2][1] = valueType\n else:\n bracketExpr[1][1] = valueType\n let call = newTree(nnkCall, bracketExpr)\n if init.kind == nnkCall:\n for i in 1 ..< init.len:\n call.add init[i]\n result = newTree(nnkStmtListExpr, newVarStmt(res, call), resBody, res)\n discard\n# import std/sugar\n #[ import atcoder/extra/other/reader ]#\n when not declared ATCODER_READER_HPP:\n const ATCODER_READER_HPP* = 1\n import streams\n import strutils\n import sequtils\n # proc scanf*(formatstr: cstring){.header: \"<stdio.h>\", varargs.}\n #proc getchar(): char {.header: \"<stdio.h>\", varargs.}\n # proc nextInt*(): int = scanf(\"%lld\",addr result)\n # proc nextFloat*(): float = scanf(\"%lf\",addr result)\n proc nextString*(f:auto = stdin): string =\n var get = false\n result = \"\"\n while true:\n let c = f.readChar\n #doassert c.int != 0\n if c.int > ' '.int:\n get = true\n result.add(c)\n elif get: return\n proc nextInt*(f:auto = stdin): int = parseInt(f.nextString)\n proc nextFloat*(f:auto = stdin): float = parseFloat(f.nextString)\n # proc nextString*():string = stdin.nextString()\n \n proc toStr*[T](v:T):string =\n proc `$`[T](v:seq[T]):string =\n v.mapIt($it).join(\" \")\n return $v\n \n proc print0*(x: varargs[string, toStr]; sep:string):string{.discardable.} =\n result = \"\"\n for i,v in x:\n if i != 0: addSep(result, sep = sep)\n add(result, v)\n result.add(\"\\n\")\n stdout.write result\n \n var print*:proc(x: varargs[string, toStr])\n print = proc(x: varargs[string, toStr]) =\n discard print0(@x, sep = \" \")\n discard\n #[ import atcoder/extra/other/cfor ]#\n when not declared ATCODER_CFOR_HPP:\n import std/macros\n const ATCODER_CFOR_HPP* = 1\n macro For*(preLoop, condition, postLoop, body:untyped):NimNode =\n var\n preLoop = if preLoop.repr == \"()\": ident(\"discard\") else: preLoop\n condition = if condition.repr == \"()\": ident(\"true\") else: condition\n postLoop = if postLoop.repr == \"()\": ident(\"discard\") else: postLoop\n quote do:\n `preLoop`\n var start_cfor {.gensym.} = true\n while true:\n if start_cfor:\n start_cfor = false\n else:\n `postLoop`\n if not `condition`:\n break\n `body`\n template cfor*(preLoop, condition, postLoop, body:untyped):NimNode =\n For(preLoop, condition, postLoop, body)\n discard\n #[ import atcoder/extra/other/sliceutils ]#\n when not declared ATCODER_SLICEUTILS_HPP:\n const ATCODER_SLICEUTILS_HPP* = 1\n proc index*[T](a:openArray[T]):Slice[int] =\n a.low..a.high\n type ReversedSlice[T] = distinct Slice[T]\n type StepSlice[T] = object\n s:Slice[T]\n d:T\n proc rev*[T](p:Slice[T]):ReversedSlice[T] = ReversedSlice[T](p)\n iterator items*(n:int):int = (for i in 0..<n: yield i)\n iterator items*[T](p:ReversedSlice[T]):T =\n if Slice[T](p).b >= Slice[T](p).a:\n var i = Slice[T](p).b\n while true:\n yield i\n if i == Slice[T](p).a:break\n i.dec\n proc `>>`*[T](s:Slice[T], d:T):StepSlice[T] =\n assert d != 0\n StepSlice[T](s:s, d:d)\n proc `<<`*[T](s:Slice[T], d:T):StepSlice[T] =\n assert d != 0\n StepSlice[T](s:s, d: -d)\n proc low*[T](s:StepSlice[T]):T = s.s.a\n proc high*[T](s:StepSlice[T]):T =\n let p = s.s.b - s.s.a\n if p < 0: return s.low - 1\n let d = abs(s.d)\n return s.s.a + (p div d) * d\n iterator items*[T](p:StepSlice[T]):T = \n assert p.d != 0\n if p.s.a <= p.s.b:\n if p.d > 0:\n var i = p.low\n let h = p.high\n while i <= h:\n yield i\n if i == h: break\n i += p.d\n else:\n var i = p.high\n let l = p.low\n while i >= l:\n yield i\n if i == l: break\n i += p.d\n proc `[]`*[T:SomeInteger, U](a:openArray[U], s:Slice[T]):seq[U] =\n for i in s:result.add(a[i])\n proc `[]=`*[T:SomeInteger, U](a:var openArray[U], s:StepSlice[T], b:openArray[U]) =\n var j = 0\n for i in s:\n a[i] = b[j]\n j.inc\n discard\n #[ import atcoder/extra/other/assignment_operator ]#\n when not declared ATCODER_ASSIGNMENT_OPERATOR_HPP:\n import std/macros\n import std/strformat\n const ATCODER_ASSIGNMENT_OPERATOR_HPP* = 1\n proc `max=`*[S, T](a: var S, b: T):bool {.discardable.} =\n return if a < b: a = b; true else: false\n proc `min=`*[S, T](a: var S, b: T):bool {.discardable.} =\n return if a > b: a = b; true else: false\n template `>?=`*(x,y:typed):bool = x.max= y\n template `<?=`*(x,y:typed):bool = x.min= y\n proc `//`*[T:SomeInteger](x,y:T):T = x div y\n proc `%`*[T:SomeInteger](x,y:T):T = x mod y\n macro generateAssignmentOperator*(ops:varargs[untyped]) =\n var strBody = \"\"\n for op in ops:\n let op = op.repr\n var op_raw = op\n if op_raw[0] == '`':\n op_raw = op_raw[1..^2]\n strBody &= fmt\"\"\"proc `{op_raw}=`*[S, T](a:var S, b:T):auto {{.inline discardable.}} = (mixin {op};a = `{op_raw}`(a, b);return a){'\\n'}\"\"\"\n parseStmt(strBody)\n generateAssignmentOperator(`mod`, `div`, `and`, `or`, `xor`, `shr`, `shl`, `<<`, `>>`, `%`, `//`, `&`, `|`, `^`)\n discard\n #[ import atcoder/extra/other/inf ]#\n when not declared ATCODER_INF_HPP:\n const ATCODER_INF_HPP* = 1\n import sequtils\n template inf*(T:typedesc): untyped = \n when T is SomeFloat: T(Inf)\n elif T is SomeInteger: T.high div 2\n else:\n static: assert(false)\n template infRepr*[T](x:T):string =\n when T is seq or T is array:\n \"@[\" & x.mapIt(it.infRepr).join(\", \") & \"]\"\n elif x is SomeInteger or x is SomeFloat:\n if x >= T.inf: \"inf\"\n elif x <= -T.inf: \"-inf\"\n else: $x\n else:\n $x\n proc `∞`*(T:typedesc):T = T.inf\n proc `*!`*[T:SomeInteger](a, b:T):T =\n if a == T(0) or b == T(0): return T(0)\n var sgn = T(1)\n if a < T(0): sgn = -sgn\n if b < T(0): sgn = -sgn\n let a = abs(a)\n let b = abs(b)\n if b > T.inf div a: result = T.inf\n else: result = min(T.inf, a * b)\n result *= sgn\n proc `+!`*[T:SomeInteger](a, b:T):T =\n result = a + b\n result = min(T.inf, result)\n result = max(-T.inf, result)\n proc `-!`*[T:SomeInteger](a, b:T):T =\n result = a - b\n result = min(T.inf, result)\n result = max(-T.inf, result)\n discard\n #[ import atcoder/extra/other/warlus_operator ]#\n when not declared ATCODER_CHAEMON_WARLUS_OPERATOR_HPP:\n const ATCODER_CHAEMON_WARLUS_OPERATOR_HPP* = 1\n import macros\n proc discardableId*[T](x: T): T {.discardable.} = x\n \n proc warlusImpl(x, y:NimNode):NimNode =\n return quote do:\n when declaredInScope(`x`):\n `x` = `y`\n else:\n var `x` = `y`\n \n macro `:=`*(x, y: untyped): untyped =\n result = newStmtList()\n if x.kind == nnkCurly:\n for i,xi in x: result.add warlusImpl(xi, y)\n elif x.kind == nnkPar:\n for i,xi in x: result.add warlusImpl(xi, y[i])\n else:\n result.add warlusImpl(x, y)\n result.add quote do:\n discardableId(`x`)\n discard\n #[ import atcoder/extra/other/seq_array_utils ]#\n when not declared ATCODER_SEQ_ARRAY_UTILS:\n const ATCODER_SEQ_ARRAY_UTILS* = 1\n import std/strformat\n import std/macros\n type SeqType = object\n type ArrayType = object\n let\n Seq* = SeqType()\n Array* = ArrayType()\n \n template fill*[T](a:var T, init:untyped) =\n when T is init.type:\n a = init\n else:\n for x in a.mitems: fill(x, init)\n \n template makeSeq*(x:int; init):auto =\n when init is typedesc: newSeq[init](x)\n else:\n var a = newSeq[typeof(init, typeofProc)](x)\n a.fill(init)\n a\n \n template makeArray*(x:int or Slice[int]; init):auto =\n var v:array[x, init.type]\n v\n \n macro `[]`*(x:ArrayType or SeqType, args:varargs[untyped]):auto =\n var a:string\n if $x == \"Seq\" and args.len == 1 and args[0].kind != nnkExprColonExpr:\n a = fmt\"newSeq[{args[0].repr}]()\"\n else:\n let tail = args[^1]\n assert tail.kind == nnkExprColonExpr, \"Wrong format of tail\"\n let\n args = args[0 .. ^2] & tail[0]\n init = tail[1]\n a = fmt\"{init.repr}\"\n if $x == \"Array\":\n for i in countdown(args.len - 1, 0): a = fmt\"makeArray({args[i].repr}, {a})\"\n a = fmt\"{'\\n'}block:{'\\n'} var a = {a}{'\\n'} when {init.repr} isnot typedesc:{'\\n'} a.fill({init.repr}){'\\n'} a\"\n elif $x == \"Seq\":\n for i in countdown(args.len - 1, 0): a = fmt\"makeSeq({args[i].repr}, {a})\"\n a = fmt\"{'\\n'}block:{'\\n'} {a}\"\n else:\n assert(false)\n parseStmt(a)\n discard\n #[ include atcoder/extra/other/debug ]#\n when not declared ATCODER_DEBUG_HPP:\n const ATCODER_DEBUG_HPP* = 1\n import macros\n import strformat\n import terminal\n #[ import atcoder/extra/other/inf ]#\n \n macro debugImpl*(n:varargs[untyped]): untyped =\n # var a = \"stderr.write \"\n var a = \"\"\n # a.add \"setForegroundColor fgYellow\\n\"\n # a.add \"stdout.write \"\n # a.add \"stderr.write \"\n a.add \"styledWriteLine stderr, fgYellow, \"\n for i,x in n:\n if x.kind == nnkStrLit:\n a &= fmt\"{x.repr} \"\n else:\n a &= fmt\"\"\" \"{x.repr} = \", {x.repr}.infRepr \"\"\"\n if i < n.len - 1:\n a.add(\"\"\", \", \",\"\"\")\n # a.add(\", \\\"\\\\n\\\"\")\n a.add \"\\n\"\n # a.add \"resetAttributes()\"\n parseStmt(a)\n template debug*(n: varargs[untyped]): untyped =\n const EVAL =\n when declared DEBUG: DEBUG\n else: false\n when EVAL:\n debugImpl(n)\n discard\n #[ import atcoder/extra/other/reference ]#\n when not declared ATCODER_REFERENCE_HPP:\n const ATCODER_REFERENCE_HPP* = 1\n import std/macros\n import std/strformat\n \n template byaddr*(lhs, typ, ex) =\n when typ is typeof(nil):\n let tmp = addr(ex)\n else:\n let tmp: ptr typ = addr(ex)\n template lhs: untyped = tmp[]\n \n macro `=&`*(lhs, rhs:untyped) =\n parseStmt(fmt\"\"\"byaddr({lhs.repr}, {rhs.repr}.type, {rhs.repr})\"\"\")\n discard\n #[ import atcoder/extra/other/floatutils ]#\n when not declared ATCODER_FLOAT_UTILS_HPP:\n const ATCODER_FLOAT_UTILS_HPP* = 1\n import std/math as math_lib_floatutils\n import std/strutils\n #[ import atcoder/element_concepts ]#\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 discard\n #[ import atcoder/extra/other/static_var ]#\n when not declared ATCODER_STATIC_VAR_HPP:\n const ATCODER_STATIC_VAR_HPP* = 1\n import std/macros\n import std/strformat\n macro staticVar*(T:typedesc, body: untyped) =\n var s = \"\"\n for n in body:\n let name = n[0]\n let t = n[1]\n let t2 = fmt\"{t.repr[1..<t.repr.len]}\"\n s &= fmt\"\"\"{'\\n'}proc get_global_addr_of_{name.repr}*[U:{T.repr}](self:typedesc[U] or U):ptr[{t2}] ={'\\n'} when self is typedesc:{'\\n'} var a {{.global.}}:{t2}.type{'\\n'} a.addr{'\\n'} else:{'\\n'} get_global_addr_of_{name.repr}(self.type){'\\n'}\n \"\"\"\n parseStmt(s)\n \n macro `$.`*(t, name:untyped):untyped =\n let s = fmt\"{t.repr}.get_global_addr_of_{name.repr}()[]\"\n parseStmt(s)\n discard\n proc getParameters*(Real:typedesc):ptr[tuple[n:int, pi, eps, inf:Real]] =\n var p {.global.}:tuple[n:int, pi, eps, inf:Real]\n return p.addr\n \n converter floatConverter*(a:SomeInteger):float = a.float\n converter float64Converter*(a:SomeInteger):float64 = a.float64\n converter float32Converter*(a:SomeInteger):float32 = a.float32\n converter floatConverter*(a:string):float = a.parseFloat\n converter float64Converter*(a:string):float64 = a.parseFloat.float64\n converter float32Converter*(a:string):float32 = a.parseFloat.float32\n \n staticVar FieldElem:\n pi:U.type\n eps:U.type\n inf:U.type\n \n proc getPi*(Real:typedesc):Real = Real.getParameters()[].pi\n proc getEPS*(Real:typedesc):Real = Real.getParameters()[].eps\n proc getINF*(Real:typedesc):Real = Real.getParameters()[].inf\n proc setEPS*(Real:typedesc, x:Real) = Real.getParameters()[].eps = x\n \n proc valid_range*[Real](l, r:Real):bool =\n # assert(l <= r)\n var (l, r) = (l, r)\n if l > r: swap(l, r)\n let d = r - l\n let eps = Real$.eps\n if d < eps: return true\n if l <= Real(0) and Real(0) <= r: return false\n return d < eps * min(abs(l), abs(r))\n \n template initPrec*(Real:typedesc) =\n Real$.pi = PI.Real\n Real$.inf = Inf.Real\n when Real is float or Real is float64:\n Real$.eps = 1e-9.Real\n elif Real is float32:\n Real$.eps = 1e-9.Real\n # float comp\n # TODO: relative error\n proc `=~`*(a,b:Real):bool = abs(a - b) < Real$.eps\n proc `!=~`*(a,b:Real):bool = abs(a - b) > Real$.eps\n proc `<~`*(a,b:Real):bool = a + Real$.eps < b\n proc `>~`*(a,b:Real):bool = a > b + Real$.eps\n proc `<=~`*(a,b:Real):bool = a < b + Real$.eps\n proc `>=~`*(a,b:Real):bool = a + Real$.eps > b\n \n # for OMC\n proc estimateRational*[Real](x:Real, n:int) =\n var m = Real$.inf\n var q = 1\n while q <= n:\n let p = round(x * q.Real)\n let d = abs(p / q.Real - x)\n if d < m:\n m = d\n echo \"found: \", p, \"/\", q, \" \", \"error: \", d\n q.inc\n return\n \n float.initPrec()\n # float64.initPrec()\n float32.initPrec()\n discard\n #[ import atcoder/extra/other/zip ]#\n when not declared ATCODER_ZIP_HPP:\n const ATCODER_ZIP_HPP* = 1\n import macros\n \n macro zip*(v:varargs[untyped]):untyped =\n result = newStmtList()\n var par = newPar()\n for i,a in v:\n var ts = newNimNode(nnkTypeSection)\n par.add(ident(\"T\" & $i))\n ts.add(newNimNode(nnkTypeDef).add(\n ident(\"T\" & $i),\n newEmptyNode(),\n newDotExpr(newNimNode(nnkBracketExpr).add(a, newIntLitNode(0)), ident(\"type\"))\n ))\n result.add ts\n var varSection = newNimNode(nnkVarSection)\n varSection.add newIdentDefs(ident(\"a\"), newEmptyNode(), newCall(\n newNimNode(nnkBracketExpr).add(\n ident(\"newSeq\"), \n par\n ), \n ident(\"n\")\n ))\n result.add newNimNode(nnkLetSection).add(newIdentDefs(ident(\"n\"), newEmptyNode(), \n newDotExpr(v[0] , ident(\"len\"))\n ))\n result.add(varSection)\n \n var forStmt = newNimNode(nnkForStmt).add(ident(\"i\")).add(\n newNimNode(nnkInfix).add(ident(\"..<\")).add(newIntLitNode(0), ident(\"n\"))\n )\n var fs = newStmtList()\n for j,a in v:\n fs.add newAssignment(\n newNimNode(nnkBracketExpr).add(\n newNimNode(nnkBracketExpr).add(\n ident(\"a\"), \n ident(\"i\")\n ), \n newIntLitNode(j)), \n newNimNode(nnkBracketExpr).add(\n a, \n ident(\"i\")\n )\n )\n forStmt.add fs\n result.add(forStmt)\n result.add(ident(\"a\"))\n result = newBlockStmt(newEmptyNode(), result)\n \n macro unzip*(n:int, p:tuple):untyped = \n result = newStmtList()\n result.add(newNimNode(nnkLetSection).add(newIdentDefs(ident(\"n\"), newEmptyNode(), n)))\n for i,a in p:\n var a = newPar(a)\n var t = newCall(\n newNimNode(nnkBracketExpr).add(\n ident(\"newSeq\"), \n newDotExpr(a, ident(\"type\"))\n ), \n ident(\"n\")\n )\n var varSection = newNimNode(nnkVarSection).add(\n newIdentDefs(ident(\"a\" & $i), newEmptyNode(), t), \n )\n result.add(varSection)\n var forStmt = newNimNode(nnkForStmt).add(ident(\"i\"))\n var rangeDef = newNimNode(nnkInfix).add(ident(\"..<\")).add(newIntLitNode(0), ident(\"n\"))\n forStmt.add(rangeDef)\n var fs = newStmtList()\n for i,a in p:\n fs.add newAssignment(\n newNimNode(nnkBracketExpr).add(\n ident(\"a\" & $i), \n ident(\"i\")), \n a\n )\n forStmt.add fs\n result.add(forStmt)\n var par = newPar()\n for i, a in p:\n par.add(ident(\"a\" & $i))\n result.add(par)\n result = newBlockStmt(newEmptyNode(), result)\n \n discard\n #[ import atcoder/extra/other/solve_proc ]#\n when not declared ATCODER_SOLVEPROC_HPP:\n const ATCODER_SOLVEPROC_HPP* = 1\n import std/macros\n import std/strformat\n import std/algorithm\n import std/sequtils\n import std/streams\n import std/strutils\n import math\n \n proc compare_answer_string*(s, t:string, error:float = NaN):bool =\n if error.classify == fcNaN:\n return s == t\n else:\n var\n s = s.split(\"\\n\")\n t = t.split(\"\\n\")\n if s.len != t.len: return false\n for i in 0 ..< s.len:\n var s = s[i].split()\n var t = t[i].split()\n if s.len != t.len: return false\n for j in 0 ..< s.len:\n if s[j].len == 0:\n if t[j].len != 0: return false\n elif t[j].len == 0:\n return false\n else:\n var fs = s[j].parseFloat\n var ft = t[j].parseFloat\n if abs(fs - ft) > error and abs(fs - ft) > min(abs(ft), abs(fs)) * error: return false\n return true\n doAssert false\n \n proc mainBodyHeader():NimNode =\n # let macro_def = \"(for s in {x.repr}: (result &= $s;(when output_stdout: stdout.write $s)));(result &= \\\"\\\\n\\\";when output_stdout: stdout.write \\\"\\\\n\\\")\"\n result = newStmtList()\n result.add quote(\"@@\") do:\n mixin echo\n result = \"\"\n var resultPointer = result.addr\n proc echo(x:varargs[string, `$`]) =\n for s in x:\n resultPointer[] &= $s\n when output_stdout: stdout.write $s\n resultPointer[] &= \"\\n\"\n when output_stdout: stdout.write \"\\n\"\n \n macro solveProc*(head, body:untyped):untyped =\n var prev_type:NimNode\n var params:seq[NimNode]\n for i in countdown(head.len - 1, 1):\n var identDefs = newNimNode(nnkIdentDefs)\n if head[i].kind == nnkExprColonExpr:\n identDefs.add(head[i][0])\n prev_type = head[i][1]\n elif head[i].kind == nnkIdent:\n identDefs.add(head[i])\n identDefs.add(prev_type)\n identDefs.add(newEmptyNode())\n params.add(identDefs)\n params.add(ident\"auto\")\n params.reverse()\n var callparams:seq[NimNode]\n for i in 1..<params.len:\n callparams.add(params[i][0])\n # var mainBody, naiveBody = mainBodyHeader()\n var mainBody, checkBody, naiveBody, testBody, generateBody = newStmtList()\n var hasNaive, hasCheck, hasTest, hasGenerate = false\n for b in body:\n if b.kind == nnkCall:\n if b[0] == ident\"Check\":\n hasCheck = true\n var checkStmt = if b.len == 2: b[1] else: b[2]\n var strmName = if b.len == 2: ident(\"strm\") else: b[1]\n checkBody.add(newNimNode(nnkWhenStmt).add(\n newNimNode(nnkElifBranch).add(ident\"DO_CHECK\").add(\n newBlockStmt(newEmptyNode(), \n newStmtList().add(\n quote do:\n var `strmName` = newStringStream(resultOutput)\n ).add(checkStmt)\n ))))\n elif b[0] == ident\"Naive\":\n hasNaive = true\n naiveBody.add b[1]\n elif b[0] == ident\"Test\":\n hasTest = true\n testBody.add b[1]\n elif b[0] == ident\"Generate\":\n hasGenerate = true\n generateBody.add b[1]\n else:\n mainBody.add b\n else:\n mainBody.add b\n mainBody = newStmtList().add(mainBodyHeader()).add(mainBody)\n #if hasCheck:\n # mainBody.add(checkBody)\n result = newStmtList()\n let procName = head[0]\n var discardablePragma = newNimNode(nnkPragma).add(ident(\"discardable\"))\n var mainParams = params\n mainParams[0] = ident\"string\"\n # var identDefsSub = newNimNode(nnkIdentDefs).add(ident\"output_stdout\").add(newNimNode(nnkBracketExpr).add(ident\"static\").add(ident\"bool\")).add(ident\"true\")\n var identDefs = newNimNode(nnkIdentDefs).add(ident\"output_stdout\").add(newNimNode(nnkBracketExpr).add(ident\"static\").add(ident\"bool\")).add(ident\"true\")\n proc copy(a:seq[NimNode]):seq[NimNode] = a.mapIt(it.copy)\n # var identDefs = newNimNode(nnkIdentDefs).add(ident\"output_stdout\").add(newNimNode(nnkBracketExpr).add(ident\"static\").add(ident\"bool\")).add(newEmptyNode())\n mainParams.add(identDefs)\n #var mainProcDef = newNimNode(nnkProcDef).add(ident\"solve\").add(newEmptyNode()).add(newEmptyNode()).add(newNimNode(nnkFormalParams).add(mainParams.copy())).add(discardablePragma).add(newEmptyNode()).add(newEmptyNode())\n #result.add(mainProcDef)\n if hasCheck:\n result.add(quote do:\n type CheckResult {.inject.} = ref object of Exception\n output, err:string\n template check(b:untyped) =\n if not b:\n raise CheckResult(err: b.astToStr, output: resultOutput)\n )\n if hasNaive:\n var naiveProcDef = newNimNode(nnkProcDef).add(ident\"solve_naive\").add(newEmptyNode()).add(newEmptyNode()).add(newNimNode(nnkFormalParams).add(mainParams.copy())).add(discardablePragma).add(newEmptyNode()).add(newEmptyNode())\n result.add(naiveProcDef)\n \n var naiveParams = mainParams.copy()\n #result.add newProc(name = ident(procName), params = mainParams.copy(), body = mainBody, pragmas = discardablePragma)\n \n var mainProcImpl =\n newStmtList().add(parseStmt(\"mixin echo\")).add quote do:\n proc solve():string =\n `mainBody`\n var resultOutput {.inject.} = solve()\n var mainTemplateBody = newStmtList().add quote do:\n `mainProcImpl`\n if hasCheck:\n mainTemplateBody.add checkBody\n mainTemplateBody.add quote do:\n resultOutput\n var mainTemplate = quote do:\n proc `procName`():string {.discardable.} =\n `mainTemplateBody`\n mainTemplate[3].add mainParams[1..^1].copy()\n result.add mainTemplate\n \n if hasNaive:\n let naiveProcName = $procName & \"naive\"\n naiveBody = mainBodyHeader().add(newBlockStmt(newEmptyNode(), naiveBody))\n result.add newProc(name = ident(naiveProcName), params = naiveParams, body = naiveBody, pragmas = discardablePragma)\n var test_body = newStmtList()\n var var_names = newSeq[string]()\n for procName in [$procName, $procName & \"_naive\"]:\n let var_name = \"v\" & procName\n var_names.add(var_name)\n var l = newNimNode(nnkCall).add(ident(procName))\n for c in callparams: l.add(c)\n l.add(ident\"false\")\n test_body.add(\n newNimNode(nnkLetSection).add(\n newNimNode(nnkIdentDefs).add(ident(var_name)).add(newEmptyNode()).add(l)\n ))\n var test_params = params\n var vars = \"\"\n for i in 1..<params.len:\n let p = params[i][0]\n vars &= &\" {p.repr} = {{{p.repr}}}\\\\n\"\n test_params[0] = ident\"bool\"\n \n var identDefs = newNimNode(nnkIdentDefs).add(ident\"error\").add(ident\"float\").add(ident(\"NaN\"))\n test_params.add identDefs\n test_body.add parseStmt(&\"if not compare_answer_string(vsolve, vsolve_naive, error): echo &\\\"test failed for\\\\n{vars}\\\", \\\"[solve]\\\\n\\\", vsolve, \\\"[solve_naive]\\\\n\\\", vsolve_naive;doAssert false\")\n result.add newProc(name = ident\"test\", params = test_params, body = test_body, pragmas = discardablePragma)\n elif hasCheck:\n var test_body_sub = newStmtList()\n var var_names = newSeq[string]()\n for procName in [$procName]:\n let var_name = \"v\" & procName\n var_names.add(var_name)\n var l = newNimNode(nnkCall).add(ident(procName))\n for c in callparams: l.add(c)\n l.add(ident\"false\")\n test_body_sub.add(\n newNimNode(nnkLetSection).add(\n newNimNode(nnkIdentDefs).add(ident(var_name)).add(newEmptyNode()).add(l)\n ))\n var test_params = params\n var vars = \"\"\n for i in 1..<params.len:\n let p = params[i][0]\n vars &= &\" {p.repr} = {{{p.repr}}}\\\\n\"\n test_params[0] = ident\"bool\"\n var test_body = newStmtList()\n var d = &\"try:\\n {test_body_sub.repr.strip}\\nexcept CheckResult as e:\\n echo &\\\"check failed for\\\\n{vars}\\\", \\\"[failed statement]\\\\n\\\", e.err.strip, \\\"\\\\n[output]\\\\n\\\", e.output;doAssert false\"\n test_body.add parseStmt(d)\n result.add newProc(name = ident\"test\", params = test_params, body = test_body, pragmas = discardablePragma)\n \n if hasGenerate:\n discard\n if hasTest:\n discard\n discard\n\n when declared USE_DEFAULT_TABLE:\n when USE_DEFAULT_TABLE:\n proc `[]`[A, B](self: var Table[A, B], key: A): var B =\n discard self.hasKeyOrPut(key, B.default)\n tables_lib.`[]`(self, key)\n\n # converter toBool[T:ref object](x:T):bool = x != nil\n # converter toBool[T](x:T):bool = x != T(0)\n # misc\n proc `<`[T](a, b:seq[T]):bool =\n for i in 0 ..< min(a.len, b.len):\n if a[i] < b[i]: return true\n elif a[i] > b[i]: return false\n if a.len < b.len: return true\n else: return false\n\n proc ceilDiv*[T:SomeInteger](a, b:T):T =\n assert b != 0\n if b < 0: return ceilDiv(-a, -b)\n result = a.floorDiv(b)\n if a mod b != 0: result.inc\n\n template `/^`*[T:SomeInteger](a, b:T):T = ceilDiv(a, b)\n discard\n"
# see https://github.com/zer0-star/Nim-ACL/tree/master/src/atcoder/modint.nim
ImportExpand "src/atcoder/modint.nim" <=== "when not declared ATCODER_MODINT_HPP:\n const ATCODER_MODINT_HPP* = 1\n import std/macros\n #[ import atcoder/generate_definitions ]#\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 var t: x\n t.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 assert 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 discard\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):bool = T is StaticModInt\n proc isDynamicModInt*(T:typedesc):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\n #[ import atcoder/internal_math ]#\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:(0'u - 1'u) div m + 1)\n \n # @return m\n proc umod*(self: Barrett):uint =\n self.m\n \n {.emit: \"\"\"\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.}\n # @param a `0 <= a < m`\n # @param b `0 <= b < m`\n # @return `a * b % m`\n proc mul*(self: Barrett, a:uint, b:uint):uint =\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 ##TODO\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 var v = z - x * self.m\n if self.m <= v: v += self.m\n return v\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 discard\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 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) {.inline.} =\n m.a += T.init(n).a\n if m.a >= T.umod: m.a -= T.umod\n\n proc `-=`*[T:ModInt](m: var T; n: SomeInteger | T) {.inline.} =\n m.a -= T.init(n).a\n if m.a >= T.umod: m.a += T.umod\n\n proc `*=`*[T:ModInt](m: var T; n: SomeInteger | T) {.inline.} =\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\n proc `/=`*[T:ModInt](m: var T; n: SomeInteger | T) {.inline.} =\n m.a = (m.a.uint * T.init(n).inv().a.uint mod T.umod).uint32\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) {.inline.} =\n m.a.inc\n if m.a == m.umod.uint32:\n m.a = 0\n\n proc dec*(m: var ModInt) {.inline.} =\n if m.a == 0.uint32:\n m.a = m.umod - 1\n else:\n m.a.dec\n\n generatePow(ModInt)\n\n template useStaticModint*(name, M) =\n generateConverter(name, int, StaticModInt[M])\n template useDynamicModInt*(name, M) =\n generateConverter(name, int, DynamicModInt[M])\n\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)))):string =\n for d in 1..ub:\n var n = (a * d).val\n if n <= ub:\n return $n & \" / \" & $d\n stderr.write \"estimate failed\"\n return \"??? / ???\"\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 discard\n"
type mint = modint1000000007
type P = tuple[n, d:int]
var
N = nextInt()
A = Seq[N: nextInt()]
B = Seq[N: nextInt()]
v = Seq[N:(P, int)]
proc `<`(l, r:P):bool =
l.n * r.d < r.n * l.d
for i in N:
v[i] = ((B[i] - 1, A[i]), i)
v.sort(SortOrder.Descending)
var
x = mint(1)
ans = mint(0)
for (r, i) in v:
ans += x * A[i]
x *= B[i]
echo ans