結果

問題 No.1559 Next Rational
ユーザー 👑 hos.lyrichos.lyric
提出日時 2021-06-25 23:06:46
言語 D
(dmd 2.106.1)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 5,002 bytes
コンパイル時間 1,605 ms
コンパイル使用メモリ 154,648 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-06-22 11:37:50
合計ジャッジ時間 2,224 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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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 1 ms
6,816 KB
testcase_01 AC 1 ms
6,940 KB
testcase_02 AC 1 ms
6,944 KB
testcase_03 AC 1 ms
6,940 KB
testcase_04 AC 2 ms
6,944 KB
testcase_05 AC 1 ms
6,940 KB
testcase_06 AC 1 ms
6,940 KB
testcase_07 AC 2 ms
6,940 KB
testcase_08 AC 2 ms
6,944 KB
testcase_09 AC 1 ms
6,940 KB
testcase_10 AC 1 ms
6,940 KB
testcase_11 AC 1 ms
6,940 KB
testcase_12 AC 1 ms
6,940 KB
testcase_13 AC 1 ms
6,944 KB
testcase_14 AC 1 ms
6,940 KB
testcase_15 AC 1 ms
6,944 KB
testcase_16 AC 1 ms
6,944 KB
testcase_17 AC 1 ms
6,944 KB
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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 = 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)(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 = 1000000007;
alias Mint = ModInt!MO;

// Berlekamp-Massey
//   F: field
//   \sum_{j=1}^0 cs[j] as[i - j] = 0 (d <= i < |as|), cs[0] = 1
//   M must be prime
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];
}

Mint solve(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;
}


enum L = 100;

void main() {
  try {
    for (; ; ) {
      const N = readLong();
      long A = readLong();
      long B = readLong();
      long K = readLong();
      
      auto as = new Mint[L];
      as[0] = 0;
      as[1] = A;
      as[2] = B;
      foreach (i; 3 .. L) {
        as[i] = (as[i - 1]^^2 + K) / as[i - 2];
      }
      auto cs = as.findLinearRecurrence;
      debug {
        writeln("as = ", as);
        writeln("cs = ", cs);
      }
      const ans = solve(as, cs, N);
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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