結果

問題 No.980 Fibonacci Convolution Hard
ユーザー 👑 hos.lyrichos.lyric
提出日時 2020-01-31 21:36:27
言語 D
(dmd 2.106.1)
結果
AC  
実行時間 278 ms / 2,000 ms
コード長 3,894 bytes
コンパイル時間 1,548 ms
コンパイル使用メモリ 154,476 KB
実行使用メモリ 13,972 KB
最終ジャッジ日時 2024-06-22 04:49:30
合計ジャッジ時間 10,155 ms
ジャッジサーバーID
（参考情報） 		judge5 / 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 275 ms
13,232 KB
testcase_01 AC 274 ms
13,588 KB
testcase_02 AC 276 ms
12,832 KB
testcase_03 AC 278 ms
13,496 KB
testcase_04 AC 275 ms
13,828 KB
testcase_05 AC 278 ms
13,088 KB
testcase_06 AC 277 ms
13,972 KB
testcase_07 AC 275 ms
13,676 KB
testcase_08 AC 276 ms
13,316 KB
testcase_09 AC 277 ms
12,884 KB
testcase_10 AC 278 ms
13,824 KB
testcase_11 AC 275 ms
13,064 KB
testcase_12 AC 277 ms
13,284 KB
testcase_13 AC 275 ms
13,624 KB
testcase_14 AC 277 ms
12,952 KB
testcase_15 AC 275 ms
13,868 KB
testcase_16 AC 244 ms
13,612 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(int M_) {
  alias M = M_;
  int x;
  this(ModInt a) { x = a.x; }
  this(long a) { x = cast(int)(a % M); if (x < 0) x += M; }
  ref ModInt opAssign(long a) { return (this = ModInt(a)); }
  ref ModInt opOpAssign(string op)(ModInt a) {
    static if (op == "+") { x += a.x; if (x >= M) x -= M; }
    else static if (op == "-") { x -= a.x; if (x < 0) x += M; }
    else static if (op == "*") { x = cast(int)((cast(long)(x) * a.x) % M); }
    else static if (op == "/") { this *= a.inv(); }
    else static assert(false);
    return this;
  }
  ref ModInt opOpAssign(string op)(long a) {
    static if (op == "^^") {
      ModInt t2 = this, te = ModInt(1);
      for (long e = a; e; e >>= 1) {
        if (e & 1) te *= t2;
        t2 *= t2;
      }
      x = cast(int)(te.x);
      return this;
    } else return mixin("this " ~ op ~ "= ModInt(a)");
  }
  ModInt inv() const {
    int a = x, b = M, y = 1, z = 0, t;
    for (; ; ) {
      t = a / b; a -= t * b;
      if (a == 0) {
        assert(b == 1 || b == -1);
        return ModInt(b * z);
      }
      y -= t * z;
      t = b / a; b -= t * a;
      if (b == 0) {
        assert(a == 1 || a == -1);
        return ModInt(a * y);
      }
      z -= t * y;
    }
  }
  ModInt opUnary(string op)() const if (op == "-") { return ModInt(-x); }
  ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); }
  ModInt opBinaryRight(string op)(long a) const { return mixin("ModInt(a) " ~ op ~ "= this"); }
  string toString() const { return x.to!string; }
}

enum MO = 1000000007;
alias Mint = ModInt!MO;

enum LIM = 2 * 10^^6 + 10;
enum LIM_SMALL = 20;

void main() {
  try {
    for (; ; ) {
      const P = Mint(readLong());
      const Q = readInt();
      auto N = new int[Q];
      foreach (q; 0 .. Q) {
        N[q] = readInt();
      }
      
      auto as = new Mint[LIM_SMALL];
      as[1] = 0;
      as[2] = 1;
      foreach (n; 3 .. LIM_SMALL) {
        as[n] = P * as[n - 1] + as[n - 2];
      }
      
      auto bs = new Mint[LIM];
      foreach (n; 2 .. LIM_SMALL) {
        foreach (s; 1 .. n) {
          bs[n] += as[s] * as[n - s];
        }
      }
      debug {
        writeln("bs = ", bs[0 .. LIM_SMALL]);
      }
      
      // (1 - P X - X^2)^2
      auto cs = new Mint[4 + 1];
      cs[0] = 1;
      cs[1] = -2 * P;
      cs[2] = -2 + P^^2;
      cs[3] = 2 * P;
      cs[4] = 1;
      foreach (n; LIM_SMALL / 2 .. LIM) {
        bs[n] = 0;
        foreach (j; 1 .. 4 + 1) {
          bs[n] -= cs[j] * bs[n - j];
        }
      }
      debug {
        writeln("bs = ", bs[0 .. LIM_SMALL]);
      }
      
      foreach (q; 0 .. Q) {
        writeln(bs[N[q]]);
      }
    }
  } catch (EOFException e) {
  }
}
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