結果

問題 No.2952 Invision of Multiples
コンテスト
ユーザー hos.lyric
提出日時 2024-10-25 21:46:29
言語 D
(dmd 2.109.1)
結果
AC  
実行時間 3,200 ms / 4,000 ms
コード長 6,283 bytes
コンパイル時間 5,105 ms
コンパイル使用メモリ 152,520 KB
実行使用メモリ 6,940 KB
最終ジャッジ日時 2024-10-25 21:48:04
合計ジャッジ時間 91,691 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 41
権限があれば一括ダウンロードができます

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; }

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;


void bAdd(T)(T[] bit, int pos, T val)
in {
  assert(0 <= pos && pos < bit.length, "bAdd: 0 <= pos < |bit| must hold");
}
do {
  for (int x = pos; x < bit.length; x |= x + 1) {
    bit[x] += val;
  }
}

// sum of [0, pos)
T bSum(T)(T[] bit, int pos)
in {
  assert(0 <= pos && pos <= bit.length, "bSum: 0 <= pos <= |bit| must hold");
}
do {
  T ret = 0;
  for (int x = pos - 1; x >= 0; x = (x & (x + 1)) - 1) {
    ret += bit[x];
  }
  return ret;
}


// floor(a / m)
// m > 0
long floor(long a, long m) {
  return a / m - ((a % m < 0) ? 1 : 0);
}
// ceil(a / m)
// m > 0
long ceil(long a, long m) {
  return a / m + ((a % m > 0) ? 1 : 0);
}

// sum{ floor((a x + b) / m) | l <= x <= r }
// m > 0
long sumFloors(long m, long a, long b, long l, long r)
in {
  assert(m > 0, "sumFloors: m > 0 must hold");
}
do {
  long sum;
  for (; l <= r; ) {
    const q = floor(a, m);
    const aa = a - q * m;
    const ll = floor(aa * l + b, m) + 1;
    const rr = floor(aa * r + b, m);
    sum += q * ((r + 1) * r / 2 - l * (l - 1) / 2) + r * rr - (l - 1) * (ll - 1) + (rr - ll + 1);
    a = m; m = aa; l = -rr; r = -ll;
  }
  return sum;
}


void main() {
  try {
    for (; ; ) {
      const N = readInt;
      const M = readInt;
      auto D = new int[N];
      foreach (i; 0 .. N) {
        D[i] = readInt;
      }
      
      Mint all = 1;
      auto ws = new Mint[N];
      foreach (i; 0 .. N) {
        const q = M / D[i];
        all *= q;
        ws[i] = Mint(q).inv;
      }
      
      const sqrtM = cast(int)(sqrt(cast(real)(M)));
      
      Mint ans;
      // small, *
      {
        auto fs = new Mint[sqrtM + 1];
        foreach_reverse (i; 0 .. N) {
          if (D[i] <= sqrtM) {
            ans += ws[i] * fs[D[i]];
          }
          foreach (d; 1 .. sqrtM + 1) {
            // \sum[1<=x<=M/d] floor((d x - 1) / D[i])
            fs[d] += ws[i] * sumFloors(D[i], d, -1, 1, M / d);
          }
        }
      }
      // large, small
      {
        auto fs = new Mint[sqrtM + 1];
        foreach (i; 0 .. N) {
          if (D[i] <= sqrtM) {
            ans += ws[i] * fs[D[i]];
          }
          if (D[i] > sqrtM) {
            foreach (d; 1 .. sqrtM + 1) {
              // \sum[1<=x<=M/d] (floor(M / D[i]) - floor((d x) / D[i]))
              fs[d] += ws[i] * (Mint(M / d) * Mint(M / D[i]) - sumFloors(D[i], d, 0, 1, M / d));
            }
          }
        }
      }
      // large, large
      {
        auto bit = new Mint[M + 1];
        foreach_reverse (i; 0 .. N) {
          if (D[i] > sqrtM) {
            for (int a = D[i]; a <= M; a += D[i]) {
              ans += ws[i] * bit.bSum(a);
            }
          }
          if (D[i] > sqrtM) {
            for (int a = D[i]; a <= M; a += D[i]) {
              bit.bAdd(a, ws[i]);
            }
          }
        }
      }
      
      ans *= all;
      writeln(ans);
      
      debug {
        Mint brt;
        foreach (i; 0 .. N) for (int a = D[i]; a <= M; a += D[i]) {
          foreach (j; i + 1 .. N) {
            brt += ws[i] * ws[j] * ((a - 1) / D[j]);
          }
        }
        brt *= all;
        writeln("brt = ", brt);
      }
    }
  } catch (EOFException e) {
  }
}
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