結果

問題 No.2151 3 on Torus-Lohkous
ユーザー 👑 hos.lyrichos.lyric
提出日時 2022-10-31 17:59:27
言語 D
(dmd 2.106.1)
結果
AC  
実行時間 17 ms / 2,000 ms
コード長 5,034 bytes
コンパイル時間 2,104 ms
コンパイル使用メモリ 154,928 KB
実行使用メモリ 4,380 KB
最終ジャッジ日時 2023-09-04 18:46:53
合計ジャッジ時間 1,954 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge11
このコードへのチャレンジ
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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
4,380 KB
testcase_01 AC 2 ms
4,376 KB
testcase_02 AC 2 ms
4,380 KB
testcase_03 AC 16 ms
4,380 KB
testcase_04 AC 17 ms
4,380 KB
testcase_05 AC 2 ms
4,380 KB
testcase_06 AC 9 ms
4,376 KB
testcase_07 AC 9 ms
4,380 KB
testcase_08 AC 17 ms
4,380 KB
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コンパイルメッセージ
/dmd2/linux/bin64/../../src/phobos/std/numeric.d(2999): Warning: cannot inline function `std.numeric.gcdImpl!ulong.gcdImpl`

ソースコード

diff # 

import std.conv, std.functional, std.range, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons;
import core.bitop;

class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }
real readReal() { return readToken.to!real; }

bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }

int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }

struct ModInt(uint M_) {
  import std.conv : to;
  alias M = M_;
  uint x;
  this(ModInt a) { x = a.x; }
  this(uint x_) { x = x_ % M; }
  this(ulong x_) { x = cast(uint)(x_ % M); }
  this(int x_) { x = ((x_ %= cast(int)(M)) < 0) ? (x_ + cast(int)(M)) : x_; }
  this(long x_) { x = cast(uint)(((x_ %= cast(long)(M)) < 0) ? (x_ + cast(long)(M)) : x_); }
  ref ModInt opAssign(T)(inout(T) a) if (is(T == uint) || is(T == ulong) || is(T == int) || is(T == long)) { return this = ModInt(a); }
  ref ModInt opOpAssign(string op, T)(T a) {
    static if (is(T == ModInt)) {
      static if (op == "+") { x = ((x += a.x) >= M) ? (x - M) : x; }
      else static if (op == "-") { x = ((x -= a.x) >= M) ? (x + M) : x; }
      else static if (op == "*") { x = cast(uint)((cast(ulong)(x) * a.x) % M); }
      else static if (op == "/") { this *= a.inv(); }
      else static assert(false);
      return this;
    } else static if (op == "^^") {
      if (a < 0) return this = inv()^^(-a);
      ModInt b = this, c = 1U;
      for (long e = a; e; e >>= 1) { if (e & 1) c *= b; b *= b; }
      return this = c;
    } else {
      return mixin("this " ~ op ~ "= ModInt(a)");
    }
  }
  ModInt inv() const {
    uint a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const q = a / b; const c = a - q * b; a = b; b = c; const w = y - cast(int)(q) * z; y = z; z = w; }
    assert(a == 1); return ModInt(y);
  }
  ModInt opUnary(string op)() const {
    static if (op == "+") { return this; }
    else static if (op == "-") { ModInt a; a.x = x ? (M - x) : 0U; return a; }
    else static assert(false);
  }
  ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); }
  ModInt opBinaryRight(string op, T)(T a) const { return mixin("ModInt(a) " ~ op ~ "= this"); }
  bool opCast(T: bool)() const { return (x != 0U); }
  string toString() const { return x.to!string; }
}

enum MO = 998244353;
alias Mint = ModInt!MO;


Mint linearRecurrenceAt(Mint[] as, Mint[] cs, long N) {
  const d = cast(int)(cs.length) - 1;
  Mint[] mul(Mint[] fs, Mint[] gs) {
    auto hs = new Mint[d + d - 1];
    foreach (i; 0 .. d) foreach (j; 0 .. d) {
      hs[i + j] += fs[i] * gs[j];
    }
    foreach_reverse (i; d .. d + d - 1) {
      foreach (j; 1 .. d + 1) {
        hs[i - j] -= cs[j] * hs[i];
      }
    }
    hs.length = d;
    return hs;
  }
  auto xs = new Mint[d];
  auto ys = new Mint[d];
  xs[1] = 1;
  ys[0] = 1;
  for (long e = N; e; e >>= 1) {
    if (e & 1) ys = mul(ys, xs);
    xs = mul(xs, xs);
  }
  Mint ans;
  foreach (i; 0 .. d) {
    ans += as[i] * ys[i];
  }
  return ans;
}

/*
  f := x^5 / (1 - x^3)
  even = (1/2) (-log(1+f) - log(1-f))
  odd  = (1/2) ( log(1+f) - log(1-f))
  
  x(d/dx) log(1+f) = * / (1 - 2 x^3 + x^5 + x^6 - x^8)
  x(d/dx) log(1-f) = * / (1 - 2 x^3 - x^5 + x^6 + x^8)
  
  ans = 4 (([x^n] even)^2 + ([x^n] odd)^2)
      = 2 (([x^n] (x(d/dx) log(1+f)))^2 + ([x^n] (x(d/dx) log(1-f)))^2)
*/
Mint hard(long n) {
  Mint ans;
  ans += linearRecurrenceAt([0,0,0,0, 5,0,0, 8].to!(Mint[]), [1,0,0,-2,0, 1,1,0,-1].to!(Mint[]), n - 1)^^2;
  ans += linearRecurrenceAt([0,0,0,0,-5,0,0,-8].to!(Mint[]), [1,0,0,-2,0,-1,1,0, 1].to!(Mint[]), n - 1)^^2;
  ans *= 2;
  return ans;
}

void main() {
  try {
    for (; ; ) {
      const numCases = readInt;
      foreach (caseId; 0 .. numCases) {
        const H = readLong;
        const W = readLong;
        
        const N = gcd(H, W);
        
        Mint ans;
        ans += Mint(H) * Mint(W);
        if (N >= 5) {
          if (H % 3 == 0 || W % 3 == 0) {
            ans += 12 * Mint(N);
          }
        }
        if (N >= 4) {
          ans += 2 * Mint(N);
        }
        if (H % 4 == 0 && W % 4 == 0) {
          ans += 16;
        }
        if (N % 2 == 0) {
          ans += hard(N / 2);
        }
        writeln(ans);
      }
    }
  } catch (EOFException e) {
  }
}
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