#916625 (D) No.2489 X and Xor 2

• 問題: No.2489 X and Xor 2
• ユーザー: 👑 hos.lyric
• 提出日時: 2023-09-29 21:56:04
• 言語: D (dmd 2.106.1)
• 結果: AC
• 実行時間: 96 ms / 2,000 ms
• コード長: 8,069 bytes
• コンパイル時間: 1,366 ms
• コンパイル使用メモリ: 151,548 KB
• 実行使用メモリ: 4,384 KB
• 最終ジャッジ日時: 2023-09-29 22:09:26
• 合計ジャッジ時間: 4,864 ms
• ジャッジサーバーID （参考情報）: judge11 / judge12

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	42 ms; 4,380 KB
testcase_01	AC	73 ms; 4,380 KB
testcase_02	AC	43 ms; 4,376 KB
testcase_03	AC	43 ms; 4,376 KB
testcase_04	AC	44 ms; 4,380 KB
testcase_05	AC	72 ms; 4,380 KB
testcase_06	AC	43 ms; 4,380 KB
testcase_07	AC	82 ms; 4,380 KB
testcase_08	AC	83 ms; 4,376 KB
testcase_09	AC	83 ms; 4,380 KB
testcase_10	AC	82 ms; 4,376 KB
testcase_11	AC	83 ms; 4,380 KB
testcase_12	AC	87 ms; 4,376 KB
testcase_13	AC	88 ms; 4,380 KB
testcase_14	AC	96 ms; 4,376 KB
testcase_15	AC	84 ms; 4,376 KB
testcase_16	AC	81 ms; 4,376 KB
testcase_17	AC	45 ms; 4,380 KB
testcase_18	AC	51 ms; 4,376 KB
testcase_19	AC	48 ms; 4,376 KB
testcase_20	AC	46 ms; 4,380 KB
testcase_21	AC	43 ms; 4,380 KB
testcase_22	AC	51 ms; 4,380 KB
testcase_23	AC	51 ms; 4,380 KB
testcase_24	AC	46 ms; 4,376 KB
testcase_25	AC	48 ms; 4,376 KB
testcase_26	AC	43 ms; 4,376 KB
testcase_27	AC	44 ms; 4,384 KB
testcase_28	AC	71 ms; 4,380 KB
testcase_29	AC	57 ms; 4,380 KB
testcase_30	AC	47 ms; 4,380 KB
testcase_31	AC	42 ms; 4,376 KB
testcase_32	AC	64 ms; 4,380 KB
testcase_33	AC	63 ms; 4,376 KB
testcase_34	AC	42 ms; 4,376 KB
testcase_35	AC	56 ms; 4,376 KB
testcase_36	AC	46 ms; 4,376 KB

ソースコード

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; }

string COLOR(string s = "") { return "\x1b[" ~ s ~ "m"; }

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;

// Pretty print (smaller abs)
int[] pretty(uint M)(ModInt!M[] as) {
  return (cast(const(ModInt!M[]))(as)).pretty;
}
int[] pretty(uint M)(const(ModInt!M[]) as) {
  import std.algorithm : map;
  import std.array : array;
  return as.map!(a => (a.x < M - a.x) ? cast(int)(a.x) : -cast(int)(M - a.x)).array;
}

// Berlekamp-Massey
//   F: field
//   \sum_{j=1}^0 cs[j] as[i - j] = 0 (d <= i < |as|), cs[0] = 1
F[] findLinearRecurrence(F)(inout(F)[] as) {
  import std.algorithm : min;
  const n = cast(int)(as.length);
  int d, m;
  auto cs = new F[n + 1], bs = new F[n + 1];
  cs[0] = bs[0] = 1;
  F invBef = 1;
  foreach (i; 0 .. n) {
    ++m;
    F dif = as[i];
    foreach (j; 1 .. d + 1) dif += cs[j] * as[i - j];
    if (dif.x != 0) {
      auto csDup = cs.dup;
      const r = dif * invBef;
      foreach (j; m .. n) cs[j] -= r * bs[j - m];
      if (2 * d <= i) {
        d = i + 1 - d;
        m = 0;
        bs = csDup;
        invBef = dif.inv;
      }
    }
  }
  return cs[0 .. d + 1];
}

ModInt!M[] findLinearRecurrence(uint M)(long[] as) {
  import std.algorithm : map;
  import std.array : array;
  return findLinearRecurrence(as.map!(a => ModInt!M(a)).array);
}


// x^e mod rev(cs)
Mint[] powerRev(const(Mint[]) cs, long e) {
  assert(!cs.empty);
  assert(cs[0].x == 1);
  const d = cast(int)(cs.length) - 1;
  if (d == 0) {
    return [];
  } else if (d == 1) {
    return [cs[0]^^e];
  }
  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 (; ; xs = mul(xs, xs)) {
    if (e & 1) ys = mul(ys, xs);
    if (!(e >>= 1)) break;
  }
  return ys;
}

Mint linearRecurrenceAt(const(Mint[]) as, const(Mint[]) cs, long e) {
  assert(!cs.empty);
  assert(cs[0].x == 1);
  const d = cast(int)(cs.length) - 1;
  assert(as.length >= d);
  const fs = powerRev(cs, e);
  Mint ans;
  foreach (i; 0 .. d) {
    ans += as[i] * fs[i];
  }
  return ans;
}


enum E = 61;
enum LIM = 4 * E + 10;

void main() {
  try {
    for (; ; ) {
      const N = readLong;
      const M = readLong;
      
      auto freq1 = new Mint[][](E, 2);
      auto freq2 = new Mint[][][][](E, E, 2, 2);
      for (long m = M; m; ) {
        const e0 = bsf(m);
        m &= m - 1;
        const Mint all = (1L << e0);
        const Mint half = all / 2;
        const Mint quar = all / 4;
        foreach (e; 0 .. e0) {
          foreach (a; 0 .. 2) {
            freq1[e][a] += half;
          }
        }
        foreach (e; e0 .. E) {
          freq1[e][m >> e & 1] += all;
        }
        foreach (e; 0 .. e0) foreach (f; 0 .. e0) {
          if (e == f) {
            foreach (a; 0 .. 2) {
              freq2[e][f][a][a] += half;
            }
          } else {
            foreach (a; 0 .. 2) foreach (b; 0 .. 2) {
              freq2[e][f][a][b] += quar;
            }
          }
        }
        foreach (e; 0 .. e0) foreach (f; e0 .. E) {
          foreach (a; 0 .. 2) {
            freq2[e][f][a][m >> f & 1] += half;
            freq2[f][e][m >> f & 1][a] += half;
          }
        }
        foreach (e; e0 .. E) foreach (f; e0 .. E) {
          freq2[e][f][m >> e & 1][m >> f & 1] += all;
        }
      }
      debug {
        if (M <= 10^^5) {
          auto brt1 = new Mint[][](E, 2);
          auto brt2 = new Mint[][][][](E, E, 2, 2);
          foreach (e; 0 .. E) {
            foreach (x; 0 .. M) {
              brt1[e][x >> e & 1] += 1;
            }
          }
          foreach (e; 0 .. E) foreach (f; 0 .. E) {
            foreach (x; 0 .. M) {
              brt2[e][f][x >> e & 1][x >> f & 1] += 1;
            }
          }
          assert(brt1 == freq1);
          assert(brt2 == freq2);
        }
      }
      
      auto dp = new Mint[][][](LIM, E, 2);
      foreach (e; 0 .. E) foreach (a; 0 .. 2) {
        dp[2][e][a] += freq1[e][a ^ 1] * Mint(1L << e);
      }
      foreach (i; 2 .. LIM - 1) {
        foreach (e; 0 .. E) foreach (a; 0 .. 2) {
          foreach (ee; 0 .. E) {
            if (e != ee) {
              foreach (aa; 0 .. 2) {
                dp[i + 1][ee][aa] += dp[i][e][a] * freq2[e][ee][a][aa ^ 1] * Mint(1L << ee);
              }
            } else {
              dp[i + 1][ee][a ^ 1] += dp[i][e][a] * freq1[e][a] * Mint(1L << ee);
            }
          }
        }
      }
      auto as = new Mint[LIM];
      foreach (i; 0 .. LIM) {
        foreach (e; 0 .. E) foreach (a; 0 .. 2) {
          as[i] += dp[i][e][a] * freq1[e][a];
        }
      }
      const cs = findLinearRecurrence(as);
      debug {
        writeln("|cs| = ", cs.length);
      }
      const ans = linearRecurrenceAt(as, cs, N);
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}