結果
| 問題 | No.2529 Treasure Hunter |
| ユーザー |
👑  seekworser
|
| 提出日時 | 2023-11-03 22:06:19 |
| 言語 | Nim (2.0.2) |
| 結果 |
AC
|
| 実行時間 | 11 ms / 2,000 ms |
| コード長 | 23,258 bytes |
| コンパイル時間 | 3,996 ms |
| コンパイル使用メモリ | 91,552 KB |
| 実行使用メモリ | 6,944 KB |
| 最終ジャッジ日時 | 2024-09-25 20:29:16 |
| 合計ジャッジ時間 | 4,882 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
6,812 KB |
| testcase_01 | AC | 11 ms
6,940 KB |
| testcase_02 | AC | 7 ms
6,940 KB |
| testcase_03 | AC | 8 ms
6,940 KB |
| testcase_04 | AC | 8 ms
6,940 KB |
| testcase_05 | AC | 8 ms
6,944 KB |
| testcase_06 | AC | 8 ms
6,940 KB |
| testcase_07 | AC | 8 ms
6,940 KB |
| testcase_08 | AC | 8 ms
6,940 KB |
| testcase_09 | AC | 8 ms
6,940 KB |
| testcase_10 | AC | 9 ms
6,940 KB |
| testcase_11 | AC | 8 ms
6,940 KB |
| testcase_12 | AC | 9 ms
6,940 KB |
| testcase_13 | AC | 9 ms
6,944 KB |
| testcase_14 | AC | 9 ms
6,940 KB |
| testcase_15 | AC | 9 ms
6,940 KB |
| testcase_16 | AC | 9 ms
6,940 KB |
| testcase_17 | AC | 9 ms
6,944 KB |
| testcase_18 | AC | 9 ms
6,940 KB |
| testcase_19 | AC | 8 ms
6,940 KB |
| testcase_20 | AC | 9 ms
6,940 KB |
| testcase_21 | AC | 9 ms
6,940 KB |
| testcase_22 | AC | 9 ms
6,944 KB |
ソースコード
import macros;macro ImportExpand(s:untyped):untyped = parseStmt($s[2])
import macros
macro Please(x): untyped = nnkStmtList.newTree()
Please use Nim-ACL
Please use Nim-ACL
Please use Nim-ACL
import macros
# {.checks: off.}
ImportExpand "cplib/tmpl/citrus.nim" <=== "when not declared CPLIB_TMPL_CITRUS:\n const CPLIB_TMPL_CITRUS* = 1\n {.warning[UnusedImport]: off.}\n {.hint[XDeclaredButNotUsed]: off.}\n import os\n import algorithm\n import sequtils\n import tables\n import macros\n import std/math\n import sets\n import strutils\n import strformat\n import sugar\n import streams\n import deques\n import bitops\n import heapqueue\n const MODINT998244353* = 998244353\n const MODINT1000000007* = 1000000007\n const INF* = 100100111\n const INFL* = int(3300300300300300491)\n type double* = float64\n let readNext = iterator(getsChar: bool = false): string {.closure.} =\n while true:\n var si: string\n try: si = stdin.readLine\n except EOFError: yield \"\"\n for s in si.split:\n if getsChar:\n for i in 0..<s.len(): yield s[i..i]\n else:\n yield s\n proc input*(t: typedesc[string]): string = readNext()\n proc input*(t: typedesc[char]): char = readNext(true)[0]\n proc input*(t: typedesc[int]): int = readNext().parseInt\n proc input*(t: typedesc[float]): float = readNext().parseFloat\n macro input*(t: typedesc, n: varargs[int]): untyped =\n var repStr = \"\"\n for arg in n:\n repStr &= &\"({arg.repr}).newSeqWith \"\n parseExpr(&\"{repStr}input({t})\")\n macro input*(ts: varargs[auto]): untyped =\n var tupStr = \"\"\n for t in ts:\n tupStr &= &\"input({t.repr}),\"\n parseExpr(&\"({tupStr})\")\n macro input*(n: int, ts: varargs[auto]): untyped =\n for typ in ts:\n if typ.typeKind != ntyAnything:\n error(\"Expected typedesc, got \" & typ.repr, typ)\n parseExpr(&\"({n.repr}).newSeqWith input({ts.repr})\")\n proc `fmtprint`*(x: int or string or char): string = return $x\n proc `fmtprint`*(x: float or float32 or\n float64): string = return &\"{x:.16f}\"\n proc `fmtprint`*[T](x: seq[T] or Deque[T] or HashSet[T] or set[\n T]): string = return x.toSeq.join(\" \")\n proc `fmtprint`*[T, N](x: array[T, N]): string = return x.toSeq.join(\" \")\n proc `fmtprint`*[T](x: HeapQueue[T]): string =\n var q = x\n while q.len != 0:\n result &= &\"{q.pop()}\"\n if q.len != 0: result &= \" \"\n proc `fmtprint`*[T](x: CountTable[T]): string =\n result = x.pairs.toSeq.mapIt(&\"{it[0]}: {it[1]}\").join(\" \")\n proc `fmtprint`*[K, V](x: Table[K, V]): string =\n result = x.pairs.toSeq.mapIt(&\"{it[0]}: {it[1]}\").join(\" \")\n proc print*(prop: tuple[f: File, sepc: string, endc: string, flush: bool],\n args: varargs[string, `fmtprint`]) =\n for i in 0..<len(args):\n prop.f.write(&\"{args[i]}\")\n if i != len(args) - 1: prop.f.write(prop.sepc) else: prop.f.write(prop.endc)\n if prop.flush: prop.f.flushFile()\n proc print*(args: varargs[string, `fmtprint`]) = print((f: stdout,\n sepc: \" \", endc: \"\\n\", flush: false), args)\n proc inner_debug*(x: auto) = print((f: stderr, sepc: \"\", endc: \"\",\n flush: true), x)\n const LOCAL_DEBUG{.booldefine.} = false\n macro debug*(n: varargs[typed]): untyped =\n when LOCAL_DEBUG:\n result = newNimNode(nnkStmtList, n)\n for i in 0..n.len-1:\n if n[i].kind == nnkStrLit:\n result.add(newCall(\"inner_debug\", n[i]))\n result.add(newCall(\"inner_debug\", newStrLitNode(\": \")))\n result.add(newCall(\"inner_debug\", n[i]))\n else:\n result.add(newCall(\"inner_debug\", toStrLit(n[i])))\n result.add(newCall(\"inner_debug\", newStrLitNode(\": \")))\n result.add(newCall(\"inner_debug\", n[i]))\n if i != n.len-1:\n result.add(newCall(\"inner_debug\", newStrLitNode(\", \")))\n else:\n result.add(newCall(\"inner_debug\", newStrLitNode(\"\\n\")))\n else:\n return quote do:\n discard\n proc `%`*(x: SomeInteger, y: SomeInteger): int = (((x mod y) + y) mod y)\n proc `//`*(x: int, y: int): int = ((x - (x%y)) div y)\n proc `^`*(x: int, y: int): int = x xor y\n proc `&`*(x: int, y: int): int = x and y\n proc `|`*(x: int, y: int): int = x or y\n proc `>>`*(x: int, y: int): int = x shr y\n proc `<<`*(x: int, y: int): int = x shl y\n proc `%=`*(x: var SomeInteger or int64, y: SomeInteger or\n int64): void = x = x % y\n proc `//=`*(x: var int, y: int): void = x = x // y\n proc `^=`*(x: var int, y: int): void = x = x ^ y\n proc `&=`*(x: var int, y: int): void = x = x & y\n proc `|=`*(x: var int, y: int): void = x = x | y\n proc `>>=`*(x: var int, y: int): void = x = x >> y\n proc `<<=`*(x: var int, y: int): void = x = x << y\n proc `[]`*(x: int, n: int): bool = (x and (1 shl n)) != 0\n\n proc pow*(a, n: int, m = INFL): int =\n var\n rev = 1\n a = a\n n = n\n while n > 0:\n if n % 2 != 0: rev = (rev * a) mod m\n if n > 1: a = (a * a) mod m\n n >>= 1\n return rev\n proc sqrt*(x: int): int =\n assert(x >= 0)\n result = int(sqrt(float64(x)))\n while result * result > x: result -= 1\n while (result+1) * (result+1) <= x: result += 1\n proc chmax*[T](x: var T, y: T): bool = (if x < y: (x = y; return true;\n ) return false)\n proc chmin*[T](x: var T, y: T): bool = (if x > y: (x = y; return true;\n ) return false)\n proc `max=`*[T](x: var T, y: T) = x = max(x, y)\n proc `min=`*[T](x: var T, y: T) = x = min(x, y)\n proc at*(x: char, a = '0'): int = int(x) - int(a)\n converter tofloat*(n: int): float = float(n)\n iterator rangeiter*(start: int, ends: int, step: int): int =\n var i = start\n if step < 0:\n while i > ends:\n yield i\n i += step\n elif step > 0:\n while i < ends:\n yield i\n i += step\n iterator rangeiter*(ends: int): int = (for i in 0..<ends: yield i)\n iterator rangeiter*(start: int, ends: int): int = (for i in\n start..<ends: yield i)\n proc Yes*(b: bool = true): void = print(if b: \"Yes\" else: \"No\")\n proc No*(b: bool = true): void = Yes(not b)\n proc YES_upper*(b: bool = true): void = print(if b: \"YES\" else: \"NO\")\n proc NO_upper*(b: bool = true): void = Yes_upper(not b)\n const DXY* = [(0, -1), (0, 1), (-1, 0), (1, 0)]\n const DDXY* = [(1, -1), (1, 0), (1, 1), (0, -1), (0, 1), (-1, -1), (-1, 0),\n (-1, 1)]\n macro exit*(statement: untyped): untyped =\n quote do:\n `statement`\n quit()\n proc vector*[T](d1, : int, default: T = T(0)): seq[T] = newSeqWith(d1, default)\n proc vv*[T](d1, d2: int, default: T = T(0)): seq[seq[T]] = newSeqWith(d1,\n newSeqWith(d2, default))\n proc vvv*[T](d1, d2, d3: int, default: T = T(0)): seq[seq[seq[\n T]]] = newSeqWith(d1, newSeqWith(d2, newSeqWith(d3, default)))\n proc vvvv*[T](d1, d2, d3, d4: int, default: T = T(0)): seq[seq[seq[seq[\n T]]]] = newSeqWith(d1, newSeqWith(d2, newSeqWith(d3, newSeqWith(d4, default))))\n proc vvvvv*[T](d1, d2, d3, d4, d5: int, default: T = T(0)): seq[seq[seq[seq[\n seq[T]]]]] = newSeqWith(d1, newSeqWith(d2, newSeqWith(d3,\n newSeqWith(d4, newSeqWith(d5, default)))))\n proc vvvvvv*[T](d1, d2, d3, d4, d5, d6: int, default: T = T(0)): seq[seq[\n seq[seq[seq[seq[T]]]]]] = newSeqWith(d1, newSeqWith(d2, newSeqWith(\n d3, newSeqWith(d4, newSeqWith(d5, newSeqWith(d6, default))))))\n discard\n"
# see https://github.com/zer0-star/Nim-ACL/tree/master/src/atcoder/modint.nim
ImportExpand "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 x.inv()\n \n template generateDefinitions*(name, l, r, typeObj, typeBase, body: untyped): untyped {.dirty.} =\n proc name*(l, r: typeObj): auto {.inline.} =\n type T = l.type\n body\n proc name*(l: typeBase; r: typeObj): auto {.inline.} =\n type T = r.type\n body\n proc name*(l: typeObj; r: typeBase): auto {.inline.} =\n type T = l.type\n body\n \n template generatePow*(name) {.dirty.} =\n proc pow*(m: name; p: SomeInteger): name {.inline.} =\n when name is hasInv:\n if p < 0: return pow(m.inv(), -p)\n else:\n doAssert p >= 0\n if (p.type)(0) <= p:\n var\n p = p.uint\n m = m\n result = m.unit()\n while p > 0'u:\n if (p and 1'u) != 0'u: result *= m\n m *= m\n p = p shr 1'u\n proc `^`*[T:name](m: T; p: SomeInteger): T {.inline.} = m.pow(p)\n \n macro generateConverter*(name, from_type, to_type) =\n let fname = ident(\"to\" & $`name` & \"OfGenerateConverter\")\n quote do:\n type `name`* = `to_type`\n converter `fname`*(a:`from_type`):`name` {.used.} =\n `name`.init(a)\n 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[ModInt]):bool = T is StaticModInt\n proc isDynamicModInt*(T:typedesc[ModInt]):bool = T is DynamicModInt\n #proc isModInt*(T:typedesc):bool = T.isStaticModInt or T.isDynamicModInt\n proc isStatic*(T:typedesc[ModInt]):bool = T is StaticModInt\n proc getMod*[M:static[int]](t:typedesc[StaticModInt[M]]):int {.inline.} = M\n\n\n #[ 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:cast[uint](-1) div m + 1)\n \n # @return m\n proc umod*(self: Barrett):uint =\n self.m\n \n {.emit: \"\"\"\n #include<cstdio>\n inline unsigned long long calc_mul(const unsigned long long &a, const unsigned long long &b){\n return (unsigned long long)(((unsigned __int128)(a)*b) >> 64);\n }\n \"\"\".}\n proc calc_mul*(a,b:culonglong):culonglong {.importcpp: \"calc_mul(#,#)\", nodecl, inline.}\n # @param a `0 <= a < m`\n # @param b `0 <= b < m`\n # @return `a * b % m`\n proc quo*(self: Barrett, n:int | uint):int =\n let n = n.uint\n let x = calc_mul(n.culonglong, self.im.culonglong).uint\n let r = n - x * self.m\n return int(if self.m <= r: x - 1 else: x)\n proc rem*(self: Barrett, n:int | uint):int =\n let n = n.uint\n let x = calc_mul(n.culonglong, self.im.culonglong).uint\n let r = n - x * self.m\n return int(if self.m <= r: r + self.m else: r)\n proc quorem*(self: Barrett, n:int | uint):(int, int) =\n let n = n.uint\n let x = calc_mul(n.culonglong, self.im.culonglong).uint\n let r = n - x * self.m\n return if self.m <= r: (int(x - 1), int(r + self.m)) else: (int(x), int(r))\n \n proc pow*(self: Barrett, n:uint | int, p:int):int =\n var\n a = self.rem(n)\n r:uint = if self.m == 1: 0 else: 1\n p = p\n while p > 0:\n if (p and 1) != 0: r = self.mul(r, a.uint)\n a = self.mul(a.uint, a.uint).int\n p = p shr 1\n return int(r)\n \n proc mul*(self: Barrett, a:uint, b:uint):uint {.inline.} =\n # [1] m = 1\n # a = b = im = 0, so okay\n \n # [2] m >= 2\n # im = ceil(2^64 / m)\n # -> im * m = 2^64 + r (0 <= r < m)\n # let z = a*b = c*m + d (0 <= c, d < m)\n # a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im\n # c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2\n # ((ab * im) >> 64) == c or c + 1\n let z = a * b\n # #ifdef _MSC_VER\n # unsigned long long x;\n # _umul128(z, im, &x);\n # #else\n ##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 #result = z - x * self.m\n #if self.m <= result: result += self.m\n return self.rem(z).uint\n \n # @param n `0 <= n`\n # @param m `1 <= m`\n # @return `(x ** n) % m`\n proc pow_mod_constexpr*(x, n, m:int):int =\n if m == 1: return 0\n var\n r = 1\n y = floorMod(x, m)\n n = n\n while n != 0:\n if (n and 1) != 0: r = (r * y) mod m\n y = (y * y) mod m\n n = n shr 1\n return r.int\n \n # Reference:\n # M. Forisek and J. Jancina,\n # Fast Primality Testing for Integers That Fit into a Machine Word\n # @param n `0 <= n`\n proc is_prime_constexpr*(n:int):bool =\n if n <= 1: return false\n if n == 2 or n == 7 or n == 61: return true\n if n mod 2 == 0: return false\n var d = n - 1\n while d mod 2 == 0: d = d div 2\n for a in [2, 7, 61]:\n var\n t = d\n y = pow_mod_constexpr(a, t, n)\n while t != n - 1 and y != 1 and y != n - 1:\n y = y * y mod n\n t = t shl 1\n if y != n - 1 and t mod 2 == 0:\n return false\n return true\n proc is_prime*[n:static[int]]():bool = is_prime_constexpr(n)\n # \n # # @param b `1 <= b`\n # # @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g\n proc inv_gcd*(a, b:int):(int,int) =\n var a = floorMod(a, b)\n if a == 0: return (b, 0)\n \n # Contracts:\n # [1] s - m0 * a = 0 (mod b)\n # [2] t - m1 * a = 0 (mod b)\n # [3] s * |m1| + t * |m0| <= b\n var\n s = b\n t = a\n m0 = 0\n m1 = 1\n \n while t != 0:\n var u = s div t\n s -= t * u;\n m0 -= m1 * u; # |m1 * u| <= |m1| * s <= b\n \n # [3]:\n # (s - t * u) * |m1| + t * |m0 - m1 * u|\n # <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)\n # = s * |m1| + t * |m0| <= b\n \n var tmp = s\n s = t;t = tmp;\n tmp = m0;m0 = m1;m1 = tmp;\n # by [3]: |m0| <= b/g\n # by g != b: |m0| < b/g\n if m0 < 0: m0 += b div s\n return (s, m0)\n \n # Compile time primitive root\n # @param m must be prime\n # @return primitive root (and minimum in now)\n proc primitive_root_constexpr*(m:int):int =\n if m == 2: return 1\n if m == 167772161: return 3\n if m == 469762049: return 3\n if m == 754974721: return 11\n if m == 998244353: return 3\n var divs:array[20, int]\n divs[0] = 2\n var cnt = 1\n var x = (m - 1) div 2\n while x mod 2 == 0: x = x div 2\n var i = 3\n while i * i <= x:\n if x mod i == 0:\n divs[cnt] = i\n cnt.inc\n while x mod i == 0:\n x = x div i\n i += 2\n if x > 1:\n divs[cnt] = x\n cnt.inc\n var g = 2\n while true:\n var ok = true\n for i in 0..<cnt:\n if pow_mod_constexpr(g, (m - 1) div divs[i], m) == 1:\n ok = false\n break\n if ok: return g\n g.inc\n proc primitive_root*[m:static[int]]():auto =\n primitive_root_constexpr(m)\n \n # @param n `n < 2^32`\n # @param m `1 <= m < 2^32`\n # @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)\n proc floor_sum_unsigned*(n, m, a, b:uint):uint =\n result = 0\n var (n, m, a, b) = (n, m, a, b)\n while true:\n if a >= m:\n result += n * (n - 1) div 2 * (a div m)\n a = a mod m\n if b >= m:\n result += n * (b div m)\n b = b mod m\n \n let y_max = a * n + b\n if y_max < m: break\n # y_max < m * (n + 1)\n # floor(y_max / m) <= n\n n = y_max div m\n b = y_max mod m\n swap(m, a)\n 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 \n proc getMod*[T:static[int]](t:typedesc[DynamicModInt[T]]):uint32 {.inline.} =\n (t.getBarrett)[].m.uint32\n proc setMod*[T:static[int]](t:typedesc[DynamicModInt[T]], M:SomeInteger){.inline.} =\n (t.getBarrett)[] = initBarrett(M.uint)\n\n proc val*(m: ModInt): int {.inline.} = int(m.a)\n\n proc `$`*(m: StaticModInt or DynamicModInt): string {.inline.} = $(m.val())\n\n template umod*[T:ModInt](self: typedesc[T] or T):uint32 =\n when T is typedesc:\n when T is StaticModInt:\n T.M.uint32\n elif T is DynamicModInt:\n T.getMod()\n else:\n static: assert false\n else: T.umod\n\n template `mod`*[T:ModInt](self:typedesc[T] or T):int = T.umod.int\n\n proc init*[T:ModInt](t:typedesc[T], v: SomeInteger or T): auto {.inline.} =\n when v is T: return v\n else:\n when v is SomeUnsignedInt:\n if v.uint < T.umod:\n return T(a:v.uint32)\n else:\n return T(a:(v.uint mod T.umod.uint).uint32)\n else:\n var v = v.int\n if 0 <= v:\n if v < T.mod: return T(a:v.uint32)\n else: return T(a:(v mod T.mod).uint32)\n else:\n v = v mod T.mod\n if v < 0: v += T.mod\n return T(a:v.uint32)\n proc unit*[T:ModInt](t:typedesc[T] or T):T = T.init(1)\n\n template initModInt*(v: SomeInteger or ModInt; M: static[int] = 1_000_000_007): auto =\n StaticModInt[M].init(v)\n\n# TODO\n# converter toModInt[M:static[int]](n:SomeInteger):StaticModInt[M] {.inline.} = initModInt(n, M)\n\n# proc initModIntRaw*(v: SomeInteger; M: static[int] = 1_000_000_007): auto {.inline.} =\n# ModInt[M](v.uint32)\n proc raw*[T:ModInt](t:typedesc[T], v:SomeInteger):auto = T(a:v)\n\n proc inv*[T:ModInt](v:T):T {.inline.} =\n var\n a = v.a.int\n b = T.mod\n u = 1\n v = 0\n while b > 0:\n let t = a div b\n a -= t * b;swap(a, b)\n u -= t * v;swap(u, v)\n return T.init(u)\n\n\n proc `-`*[T:ModInt](m: T): T {.inline.} =\n if int(m.a) == 0: return m\n else: return T(a:m.umod() - m.a)\n\n proc `+=`*[T:ModInt](m: var T; n: SomeInteger | T):T {.inline discardable.} =\n m.a += T.init(n).a\n if m.a >= T.umod: m.a -= T.umod\n return m\n\n proc `-=`*[T:ModInt](m: var T; n: SomeInteger | T):T {.inline discardable.} =\n m.a -= T.init(n).a\n if m.a >= T.umod: m.a += T.umod\n return m\n\n proc `*=`*[T:ModInt](m: var T; n: SomeInteger | T):T {.inline discardable.} =\n when T is StaticModInt:\n m.a = (m.a.uint * T.init(n).a.uint mod T.umod).uint32\n elif T is DynamicModInt:\n m.a = T.getBarrett[].mul(m.a.uint, T.init(n).a.uint).uint32\n else:\n static: assert false\n return m\n\n proc `/=`*[T:ModInt](m: var T; n: SomeInteger | T):T {.inline discardable.} =\n m.a = (m.a.uint * T.init(n).inv().a.uint mod T.umod).uint32\n return m\n\n generateDefinitions(`+`, m, n, ModInt, SomeInteger):\n result = T.init(m)\n result += n\n\n generateDefinitions(`-`, m, n, ModInt, SomeInteger):\n result = T.init(m)\n result -= n\n\n generateDefinitions(`*`, m, n, ModInt, SomeInteger):\n result = T.init(m)\n result *= n\n\n generateDefinitions(`/`, m, n, ModInt, SomeInteger):\n result = T.init(m)\n result /= n\n\n generateDefinitions(`==`, m, n, ModInt, SomeInteger):\n result = (T.init(m).val() == T.init(n).val())\n\n proc inc*(m: var ModInt):ModInt {.inline discardable.} =\n m.a.inc\n if m.a == m.umod.uint32:\n m.a = 0\n return m\n proc `++`*(m: var ModInt):ModInt {.inline discardable.} = m.inc\n\n proc dec*(m: var ModInt):ModInt {.inline discardable.} =\n if m.a == 0.uint32:\n m.a = m.umod - 1\n else:\n m.a.dec\n return m\n proc `--`*(m: var ModInt):ModInt {.inline discardable.} = m.dec\n\n generatePow(ModInt)\n \n # TODO: intのところはSomeIntegerに拡張したいがそうするとSystem.nimのuintのconverterとバッティングする。。。\n template useStaticModint*(name, M) =\n generateConverter(name, int, StaticModInt[M])\n template useDynamicModInt*(name, M) =\n generateConverter(name, int, DynamicModInt[M])\n\n # TODO: Nimのstatic[int]を使うconverterがバグっていて個々に宣言しないとconverterが使えない\n # したがって、下記以外のmodintを使う場合はuseStaticModIntあるいはuseDynamicModIntで宣言が必要\n useStaticModInt(modint998244353, 998244353)\n useStaticModInt(modint1000000007, 1000000007)\n useDynamicModInt(modint, -1)\n\n import std/math as math_lib_modint\n proc estimateRational*(a:ModInt, ub:int = int(sqrt(float(ModInt.mod))), output_stderr:static[bool] = false):string =\n var v:seq[tuple[s, n, d: int]]\n for d in 1 .. ub:\n var n = (a * d).val\n # n or mod - n\n if n * 2 > a.mod:\n n = - (a.mod - n)\n if gcd(n, d) > 1: continue\n v.add((n.abs + d, n, d))\n v.sort\n when output_stderr:\n stderr.write \"estimation result: \", v\n return $v[0].n & \"/\" & $v[0].d\n\n # TODO:\n # Modint -> intのconverterあるとmint(2) * 3みたいなのがintになっちゃう\n # converter toInt*(m: ModInt):int {.inline.} = m.val\n\n\n discard\n"
type mint = modint998244353
proc solve() =
var n, m = input(int)
if n == 1 and m == 1:
print(2)
return
if n == 1:
var dp = [mint(1), mint(m), mint(m * (m-1) // 2 - (m-1))]
print(dp.sum.val)
return
var dp = [mint(1), mint(n), mint(n * (n-1) // 2 - n)]
if n == 2: dp[2] = 0
for i in 0..<m-1:
var dpn = [mint(0), mint(0), mint(0)]
dpn[0] += dp.sum
dpn[1] += dp[0] * n + dp[1] * (n-1) + dp[2] * (n-2)
dpn[2] += dp[0] * (n * (n-1) // 2 - n)
dpn[2] += dp[1] * ((n-1) * (n-2) // 2 - (n-2))
dpn[2] += dp[2] * (n * (n-1) // 2 - n - (n-4) * 2 - 1)
if n == 2: dpn[2] = 0
debug(dp, dpn)
swap(dp, dpn)
print(dp.sum.val)
var t = input(int)
for i in 0..<t: solve()