結果
| 問題 | No.2156 ぞい文字列 |
| ユーザー |
👑  seekworser
|
| 提出日時 | 2024-03-28 20:26:16 |
| 言語 | Nim (2.0.2) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 2,000 ms |
| コード長 | 19,030 bytes |
| コンパイル時間 | 3,544 ms |
| コンパイル使用メモリ | 71,400 KB |
| 実行使用メモリ | 5,248 KB |
| 最終ジャッジ日時 | 2024-09-30 14:50:39 |
| 合計ジャッジ時間 | 3,775 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
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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
5,248 KB |
| testcase_01 | AC | 1 ms
5,248 KB |
| testcase_02 | AC | 2 ms
5,248 KB |
| testcase_03 | AC | 1 ms
5,248 KB |
| testcase_04 | AC | 1 ms
5,248 KB |
| testcase_05 | AC | 2 ms
5,248 KB |
| testcase_06 | AC | 1 ms
5,248 KB |
| testcase_07 | AC | 1 ms
5,248 KB |
| testcase_08 | AC | 1 ms
5,248 KB |
| testcase_09 | AC | 1 ms
5,248 KB |
| testcase_10 | AC | 1 ms
5,248 KB |
| testcase_11 | AC | 1 ms
5,248 KB |
| testcase_12 | AC | 1 ms
5,248 KB |
| testcase_13 | AC | 1 ms
5,248 KB |
| testcase_14 | AC | 1 ms
5,248 KB |
| testcase_15 | AC | 1 ms
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| testcase_16 | AC | 1 ms
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| testcase_17 | AC | 1 ms
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| testcase_18 | AC | 1 ms
5,248 KB |
| testcase_19 | AC | 1 ms
5,248 KB |
ソースコード
import macros;macro ImportExpand(s:untyped):untyped = parseStmt($s[2])
# verification-helper: PROBLEM https://atcoder.jp/contests/dp/tasks/dp_r
ImportExpand "cplib/matrix/matrix.nim" <=== "when not declared CPLIB_MATRIX_MATRIX:\n const CPLIB_MATRIX_MATRIX* = 1\n import sequtils\n import strutils\n import hashes\n import std/math\n type Matrix*[T] = object\n arr: seq[seq[T]]\n proc initMatrix*[T](arr: seq[seq[T]]): Matrix[T] =\n assert arr.len == 0 or arr.mapIt(it.len).allIt(it == arr[0].len), \"all elements in arr must be the same size.\"\n Matrix[T](arr: arr)\n proc toMatrix*[T](arr: seq[seq[T]]): Matrix[T] = initMatrix(arr)\n proc initMatrix*[T](arr: seq[T], vertical: bool = false): Matrix[T] =\n if vertical: Matrix[T](arr: arr.mapIt(@[it]))\n else: Matrix[T](arr: @[arr])\n proc initMatrix*[T](h, w: int, val: T): Matrix[T] = Matrix[T](arr: newSeqWith(h, newSeqWith(w, val)))\n\n proc h*[T](m: Matrix[T]): int = m.arr.len\n proc w*[T](m: Matrix[T]): int =\n if m.h == 0: return 0\n m.arr[0].len\n proc `$`*[T](m: Matrix[T]): string =\n for i in 0..<m.arr.len:\n result &= m.arr[i].mapIt($it).join(\" \")\n if i != m.arr.len - 1: result &= \"\\n\"\n proc `==`*[T](a, b: Matrix[T]): bool = a.arr == b.arr\n proc `[]`*[T](m: Matrix[T], r: int): seq[T] = m.arr[r]\n proc `[]`*[T](m: var Matrix[T], r: int): var seq[T] = m.arr[r]\n proc `[]=`*[T](m: var Matrix[T], r: int, row: seq[T]) = m.arr[r] = row\n\n proc `[]`*[T](m: Matrix[T], r: int, c: int): T = m.arr[r][c]\n proc `[]`*[T](m: var Matrix[T], r: int, c: int): var T = m.arr[r][c]\n proc `[]=`*[T](m: var Matrix[T], r: int, c: int, val: T) = m.arr[r][c] = val\n\n proc `-`*[T](m: Matrix[T]): Matrix[T] = Matrix[T](arr: m.arr.mapIt(it.mapIt(-it)))\n proc `@=`*[T](a: var Matrix[T], b: Matrix[T]) =\n assert a.w == b.h\n var ans = initMatrix[T](a.h, b.w, 0)\n for i in 0..<a.h:\n for j in 0..<b.w:\n for k in 0..<a.w:\n ans[i, j] += a[i, k] * b[k, j]\n swap(ans, a)\n proc `@`*[T](a, b: Matrix[T]): Matrix[T] = (result = a; result @= b)\n template defineMatrixAssignmentOp(assign, op: untyped) =\n proc assign*[T](a: var Matrix[T], b: Matrix[T]) =\n assert a.h == b.h and a.w == b.w\n for i in 0..<a.h:\n for j in 0..<a.w:\n assign(a[i, j], b[i, j])\n proc assign*[T](a: var Matrix[T], x: T) =\n for i in 0..<a.h:\n for j in 0..<a.w:\n assign(a[i, j], x)\n proc op*[T](a, b: Matrix[T]): Matrix[T] = (result = a; assign(result, b))\n proc op*[T](a: Matrix[T], x: T): Matrix[T] = (result = a; assign(result, x))\n proc op*[T](x: T, a: Matrix[T]): Matrix[T] = op(a, x)\n defineMatrixAssignmentOp(`+=`, `+`)\n defineMatrixAssignmentOp(`-=`, `-`)\n defineMatrixAssignmentOp(`*=`, `*`)\n defineMatrixAssignmentOp(`/=`, `/`)\n\n template defineMatrixIntOps(assign, op: untyped) =\n proc assign*(a: var Matrix[int], b: Matrix[int]) =\n assert a.h == b.h and a.w == b.w\n for i in 0..<a.h:\n for j in 0..<a.w:\n a[i, j] = op(a[i, j], b[i, j])\n proc assign*(a: var Matrix[int], x: int) =\n for i in 0..<a.h:\n for j in 0..<a.w:\n a[i, j] = op(a[i, j], x)\n proc op*(a, b: Matrix[int]): Matrix[int] = (result = a; assign(result, b))\n proc op*(a: Matrix[int], x: int): Matrix[int] = (result = a; assign(result, x))\n proc op*(x: int, a: Matrix[int]): Matrix[int] = op(a, x)\n defineMatrixIntOps(`and=`, `and`)\n defineMatrixIntOps(`or=`, `or`)\n defineMatrixIntOps(`xor=`, `xor`)\n defineMatrixIntOps(`shl=`, `shl`)\n defineMatrixIntOps(`shr=`, `shr`)\n defineMatrixIntOps(`div=`, `div`)\n defineMatrixIntOps(`mod=`, `mod`)\n\n proc hash*[T](m: Matrix[T]): Hash = hash(m.arr)\n proc identity_matrix*[T](n: int, one, zero: T): Matrix[T] =\n result = initMatrix[T](n, n, zero)\n for i in 0..<n: result[i][i] = one\n proc identity_matrix*[T](n: int): Matrix[T] = identity_matrix[T](n, 1, 0)\n proc pow*[T](m: Matrix[T], n: int): Matrix[T] =\n result = identity_matrix[T](m.h)\n var m = m\n var n = n\n while n > 0:\n if (n and 1) == 1: result @= m\n m @= m\n n = n shr 1\n proc sum*[T](m: Matrix[T]): T = m.arr.mapit(it.sum).sum\n"
proc scanf(formatstr: cstring){.header: "<stdio.h>", varargs.}
proc ii(): int {.inline.} = scanf("%lld\n", addr result)
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\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\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"
type mint = modint998244353
var n = ii()
var a = @[@[mint(1), mint(1)], @[mint(1), mint(0)]].toMatrix
var ans = initMatrix(@[mint(1), mint(0)], true)
ans = a.pow(n) @ ans
echo ans[0, 0] - 1