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