結果

問題 No.1931 Fraction 2
コンテスト
ユーザー hos.lyric
提出日時 2022-05-06 21:30:26
言語 D
(dmd 2.109.1)
結果
RE  
実行時間 -
コード長 5,136 bytes
コンパイル時間 1,634 ms
コンパイル使用メモリ 157,992 KB
実行使用メモリ 17,536 KB
最終ジャッジ日時 2024-06-22 15:06:20
合計ジャッジ時間 8,835 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
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ファイルパターン 結果
sample AC * 3
other RE * 11 TLE * 1 -- * 24
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; }
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;


// a^-1 (mod m)
long modInv(long a, long m)
in {
  assert(m > 0, "modInv: m > 0 must hold");
}
do {
  long b = m, x = 1, y = 0, t;
  for (; ; ) {
    t = a / b; a -= t * b;
    if (a == 0) {
      assert(b == 1 || b == -1, "modInv: gcd(a, m) != 1");
      if (b == -1) y = -y;
      return (y < 0) ? (y + m) : y;
    }
    x -= t * y;
    t = b / a; b -= t * a;
    if (b == 0) {
      assert(a == 1 || a == -1, "modInv: gcd(a, m) != 1");
      if (a == -1) x = -x;
      return (x < 0) ? (x + m) : x;
    }
    y -= t * x;
  }
}


enum LIM = 10^^5 + 10;
int[] lpf;

void main() {
  lpf = iota(LIM).array;
  foreach (p; 2 .. LIM) if (lpf[p] == p) {
    for (int n = 2 * p; n < LIM; n += p) chmin(lpf[n], p);
  }
  
  try {
    for (; ; ) {
      const N = readInt;
      auto A = new int[N];
      auto B = new int[N];
      foreach (i; 0 .. N) {
        A[i] = readInt;
        B[i] = readInt;
      }
      
      auto es = new int[LIM];
      auto iss = new int[][LIM];
      foreach (i; 0 .. N) {
        for (int b = B[i]; b > 1; ) {
          const p = lpf[b];
          int e;
          do {
            ++e;
            b /= p;
          } while (b % p == 0);
          chmax(es[p], e);
          iss[p] ~= i;
        }
      }
      
      Mint denom = 1;
      foreach (p; 2 .. LIM) if (es[p] > 0) {
        const pe = p^^es[p];
        long sum;
        foreach (i; iss[p]) {
          long q = pe;
          int b = B[i];
          do {
            q /= p;
            b /= p;
          } while (b % p == 0);
          q *= A[i];
          q %= pe;
          q *= modInv(b, pe);
          sum += q;
          sum %= pe;
        }
        debug {
          writeln(p, ": ", pe, " ", sum);
        }
        int e = es[p];
        for (; e > 0 && sum % p == 0; --e, sum /= p) {}
        denom *= p^^e;
      }
      
      Mint val;
      foreach (i; 0 .. N) {
        val += Mint(A[i]) / Mint(B[i]);
      }
      const numer = val * denom;
      
      writeln(numer, " ", denom);
    }
  } catch (EOFException e) {
  }
}
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