結果
| 問題 | No.2013 Can we meet? |
| ユーザー |
 chaemon
|
| 提出日時 | 2022-05-06 15:08:02 |
| 言語 | Nim (2.0.2) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 57,740 bytes |
| コンパイル時間 | 5,167 ms |
| コンパイル使用メモリ | 120,836 KB |
| 実行使用メモリ | 6,948 KB |
| 最終ジャッジ日時 | 2024-07-05 17:03:04 |
| 合計ジャッジ時間 | 6,967 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
（要ログイン）
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 | 3 ms
5,248 KB |
| testcase_01 | AC | 3 ms
5,376 KB |
| testcase_02 | AC | 3 ms
5,376 KB |
| testcase_03 | AC | 6 ms
5,376 KB |
| testcase_04 | AC | 2 ms
5,376 KB |
| testcase_05 | AC | 3 ms
5,376 KB |
| testcase_06 | AC | 4 ms
5,376 KB |
| testcase_07 | AC | 5 ms
5,376 KB |
| testcase_08 | AC | 6 ms
5,376 KB |
| testcase_09 | AC | 6 ms
5,376 KB |
| testcase_10 | AC | 7 ms
5,376 KB |
| testcase_11 | AC | 8 ms
5,376 KB |
| testcase_12 | AC | 8 ms
5,376 KB |
| testcase_13 | AC | 9 ms
5,376 KB |
| testcase_14 | RE | - |
| testcase_15 | RE | - |
| testcase_16 | RE | - |
| testcase_17 | RE | - |
| testcase_18 | RE | - |
| testcase_19 | RE | - |
| testcase_20 | RE | - |
| testcase_21 | RE | - |
| testcase_22 | RE | - |
| testcase_23 | RE | - |
| testcase_24 | RE | - |
| testcase_25 | RE | - |
| testcase_26 | RE | - |
| testcase_27 | RE | - |
| testcase_28 | RE | - |
| testcase_29 | RE | - |
| testcase_30 | RE | - |
| testcase_31 | RE | - |
| testcase_32 | RE | - |
| testcase_33 | RE | - |
| testcase_34 | RE | - |
| testcase_35 | RE | - |
| testcase_36 | RE | - |
| testcase_37 | RE | - |
| testcase_38 | RE | - |
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/header.nim
ImportExpand "src/atcoder/extra/header/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\n\n #[ import atcoder/extra/other/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/other/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 \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/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 template `>?=`*(x,y:typed):void = x.max= y\n template `<?=`*(x,y:typed):void = 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`, `<<`, `>>`, max, min, `%`, `//`, `&`, `|`, `^`)\n discard\n #[ import atcoder/extra/other/inf ]#\n when not declared ATCODER_INF_HPP:\n const ATCODER_INF_HPP* = 1\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 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 \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 for i,x in n:\n if x.kind == nnkStrLit:\n a &= fmt\"{x.repr} \"\n else:\n a &= fmt\"\"\" \"{x.repr} = \", {x.repr} \"\"\"\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/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/convolution.nim
ImportExpand "src/atcoder/convolution.nim" <=== "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 #[ 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 #[ import atcoder/internal_bit ]#\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 discard\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\n\n# template <class mint,\n# int g = internal::primitive_root<mint::mod()>,\n# internal::is_static_modint_t<mint>* = nullptr>\n type fft_info*[mint:FiniteFieldElem; g, rank2:static[int]] = object\n# static constexpr int rank2 = bsf_constexpr(mint::mod() - 1);\n root, iroot: array[rank2 + 1, mint]\n\n #std::array<mint, rank2 + 1> root; # root[i]^(2^i) == 1\n #std::array<mint, rank2 + 1> iroot; # root[i] * iroot[i] == 1\n rate2, irate2: array[max(0, rank2 - 2 + 1), mint]\n #std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;\n #std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;\n rate3, irate3: array[max(0, rank2 - 3 + 1), mint]\n \n #std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;\n #std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;\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# result = newSeqWith(n + m - 1, mint(0))\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# template <class mint, internal::is_static_modint_t<mint>* = nullptr>\n# std::vector<mint> convolution(const std::vector<mint>& a,\n# const std::vector<mint>& b) {\n# int n = int(a.size()), m = int(b.size());\n# if (!n || !m) return {};\n# if (std::min(n, m) <= 60) return convolution_naive(a, b);\n# return internal::convolution_fft(a, b);\n# }\n\n\n #[ import atcoder/modint ]#\n 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\" & $`name` & \"OfGenerateConverter\")\n quote do:\n type `name`* = `to_type`\n converter `fname`*(a:`from_type`):`name` {.used.} =\n `name`.init(a)\n discard\n \n type\n StaticModInt*[M: static[int]] = object\n a:uint32\n DynamicModInt*[T: static[int]] = object\n a:uint32\n \n type ModInt* = StaticModInt or DynamicModInt\n # type ModInt* = concept x, type T\n # T is StaticModInt or T is DynamicModInt\n \n proc isStaticModInt*(T:typedesc):bool = T is StaticModInt\n proc isDynamicModInt*(T:typedesc):bool = T is DynamicModInt\n proc isModInt*(T:typedesc):bool = T.isStaticModInt or T.isDynamicModInt\n proc isStatic*(T:typedesc[ModInt]):bool = T is StaticModInt\n \n #[ import atcoder/internal_math ]#\n \n proc getBarrett*[T:static[int]](t:typedesc[DynamicModInt[T]]):ptr Barrett =\n var Barrett_of_DynamicModInt {.global.} = initBarrett(998244353.uint)\n return Barrett_of_DynamicModInt.addr\n proc getMod*[T:static[int]](t:typedesc[DynamicModInt[T]]):uint32 {.inline.} =\n (t.getBarrett)[].m.uint32\n proc setMod*[T:static[int]](t:typedesc[DynamicModInt[T]], M:SomeInteger){.inline.} =\n (t.getBarrett)[] = initBarrett(M.uint)\n \n proc `$`*(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 proc val*(m: ModInt): int {.inline.} = int(m.a)\n converter toInt*(m: ModInt):int {.inline.} = m.val\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 discard\n# template <unsigned int mod = 998244353,\n# class T,\n# std::enable_if_t<internal::is_integral<T>::value>* = nullptr>\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 discard\n"
# see https://github.com/zer0-star/Nim-ACL/tree/master/src/atcoder/modint.nim
ImportExpand "src/atcoder/modint.nim" <=== ""
# see https://github.com/zer0-star/Nim-ACL/tree/master/src/atcoder/extra/math/combination.nim
ImportExpand "src/lib/math/combination.nim" <=== "when not defined ATCODER_COMBINATION_HPP:\n const ATCODER_COMBINATION_HPP* = 1\n #[ import atcoder/element_concepts ]#\n\n type Combination*[T] = object\n fact_a, rfact_a: seq[T]\n\n type CombinationC* = concept x\n x is typedesc[FieldElem] or x is var Combination\n\n proc enhance[T:FieldElem](cmb: var Combination[T], k:int):auto =\n if k >= cmb.fact_a.len:\n if cmb.fact_a.len == 0:\n cmb.fact_a = @[T(1)]\n cmb.rfact_a = @[T(1)]\n let sz_old = cmb.fact_a.len - 1\n let sz = max(sz_old * 2, k)\n cmb.fact_a.setlen(sz + 1)\n cmb.rfact_a.setlen(sz + 1)\n for i in sz_old + 1..sz: cmb.fact_a[i] = cmb.fact_a[i-1] * T(i)\n cmb.rfact_a[sz] = T(1) / cmb.fact_a[sz]\n for i in countdown(sz - 1, sz_old + 1): cmb.rfact_a[i] = cmb.rfact_a[i + 1] * T(i + 1)\n return cmb.addr\n\n proc enhance(T:typedesc[FieldElem], k:int):auto {.discardable.} =\n var cmb{.global.} = Combination[T]()\n return cmb.enhance(k)\n\n template zero*(T:typedesc[FieldElem]):T = T(0)\n template zero*[T:FieldElem](cmb:Combination[T]):T = T(0)\n \n template fact*(T:CombinationC, k:int):auto = T.enhance(k)[].fact_a[k]\n template rfact*(T:CombinationC, k:int):auto = T.enhance(k)[].rfact_a[k]\n template inv*(T:CombinationC, k:int):auto = T.fact(k - 1) * T.rfact(k)\n\n template resetCombination*(T:typedesc[FieldElem] or var Combination) =\n var p = T.enhance(-1)\n p[].fact_a.setLen(0)\n p[].rfact_a.setLen(0)\n\n template P*(T:CombinationC, n,r:int):auto =\n if r < 0 or n < r: T.zero()\n else: T.fact(n) * T.rfact(n - r)\n template C_impl*(T:CombinationC, n, r:int):auto =\n if r < 0 or n < r: T.zero()\n else: T.fact(n) * T.rfact(r) * T.rfact(n - r)\n template C*(T:CombinationC, n,r:int):auto =\n if n >= 0:\n T.C_impl(n, r)\n else:\n let N = -n\n var a = T.C_impl(N + r - 1, N - 1)\n if r mod 2 != 0: a *= -1\n a\n template H*(T:CombinationC, n,r:int):auto =\n if n < 0 or r < 0: T.zero()\n elif r == 0: T.zero() + 1\n else: T.C(n + r - 1, r)\n template P_large*(T:CombinationC, n,r:int):auto =\n if r < 0 or n < r: T.zero()\n else:\n var a = T(1)\n for i in 0..<r:a *= n - i\n a\n template C_large_impl*(T:CombinationC, n,r:int):auto =\n if r < 0 or n < r: T.zero()\n else: T.P_large(n, r) * T.rfact(r)\n template C_large*(T:CombinationC, n,r:int):auto =\n if n >= 0:\n T.C_large_impl(n, r)\n else:\n let N = -n\n var a = T.C_large_impl(N + r - 1, N - 1)\n if r mod 2 != 0: a *= -1\n a\n template H_large*(T:CombinationC, n,r:int):auto =\n if n < 0 or r < 0: T.zero()\n elif r == 0: T.zero() + 1\n else: T.C_large(n + r - 1, r)\n discard\n"
type mint = modint998244353
const DO_TEST = true
proc get(N, x, y:int, alpha, beta:mint):seq[mint] =
# 確率alpha, betaでN回目の移動の試行で(x, y)で出会う確率(実際には2人いるので2N回の試行となる)
# resultはインデックス0..Nをとり、インデックスiにはi回目の移動で出会う確率が入る
var l, r = newSeq[mint](N + 1)
for i in 0..N:
if i - x < 0 or (i + x) mod 2 != 0:
l[i] = 0
else:
l[i] = mint.rfact((i + x) div 2) * mint.rfact((i - x) div 2) * alpha^i
if i - y < 0 or (i + y) mod 2 != 0:
r[i] = 0
else:
r[i] = mint.rfact((i + y) div 2) * mint.rfact((i - y) div 2) * beta^i
result = convolution(l, r)[0..N]
for i in 0 ..< result.len:
result[i] *= mint.fact(i)
let
N = nextInt()
x0, y0, x1, y1 = nextInt()
A, B = nextInt()
a = @[0] & newSeqWith(N, nextInt())
x = abs(x0 - x1)
y = abs(y0 - y1)
alpha = mint(A) / mint(2 * (A + B))
beta = mint(B) / mint(2 * (A + B))
# 制約を満たすかテスト
block test:
doAssert N in 1 .. 10^5
doAssert x0 in 0 .. 10^9
doAssert y0 in 0 .. 10^9
doAssert x1 in 0 .. 10^9
doAssert y1 in 0 .. 10^9
doAssert (x0, y0) != (x1, y1)
doAssert A in 1 .. 10^6
doAssert B in 1 .. 10^6
for i in 1..N:
doAssert a[i] in 1 .. 10^9
when not DO_TEST:
var
dp = get(N * 2 + 1, x, y, alpha, beta)
dp0 = get(N * 2 + 1, 0, 0, alpha, beta)
proc calc(l, r:int) =
d := r - l
if d > 1:
m := (l + r) div 2
# l ..< mを計算する
calc(l, m)
# dp[l..<m]をdp[m..<r]に伝搬する
c := dp[l ..< m].convolution(dp0[0..<d])
for i in m ..< r:
dp[i] -= c[i - l]
# m ..< rを計算する
calc(m, r)
calc(0, N * 2 + 1)
var ans = mint(0)
for i in 1..N:
ans += a[i] * dp[i * 2]
echo ans
echo ans.estimateRational
else:
if N >= 100:
echo "too Large!!"
doAssert false
const D = 100
var ans = mint(0)
proc naive(n:int):array[-D..D, array[-D..D, mint]] =
for i in -D..D:
for j in -D..D:
result[i][j] = mint(0)
result[0][0] = 1
for t in 0 ..< n:
if t mod 2 == 0:
ans += a[t div 2] * result[x][y]
result[x][y] = 0
var result2:array[-D..D, array[-D..D, mint]]
for x in -D..D:
for y in -D..D:
if x + 1 <= D:
result2[x + 1][y] += result[x][y] * alpha
if x - 1 >= -D:
result2[x - 1][y] += result[x][y] * alpha
if y + 1 <= D:
result2[x][y + 1] += result[x][y] * beta
if y - 1 >= -D:
result2[x][y - 1] += result[x][y] * beta
swap result, result2
discard naive(N * 2 + 1)
echo ans